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C_4x4_thom_001 | 4x4 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 3 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 20 L/min; the feed has c_A0 = 1.5 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "yield_B"], "values": ["114930/104467", "7150327064/15545629803", "108750/104467", "7734815800/15545629803", "97500/104467", "9301591000/15545629803", "18603182000/46636889409"], "values_float": [1.100156030133918, 0.4599573741695642, 1.0409985928570744, 0.4975... | null | null | null |
C_4x4_thom_002 | 4x4 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 3 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 10 L/min; the feed has c_A0 = 1.3 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "yield_B"], "values": ["14261/14939", "640344861/2238982625", "24115/29878", "319307079/895593050", "15925/29878", "51512916/89559305", "7925064/17911861"], "values_float": [0.9546154361068344, 0.28599813765861626, 0.8071156034540464, 0.35653143913968516, 0.533... | null | null | null |
C_4x4_thom_003 | 4x4 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 3 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 12 L/min; the feed has c_A0 = 1.8 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "yield_B"], "values": ["1809/1655", "2795739/3522502", "270/331", "1554315/1761251", "243/331", "1567368/1761251", "870760/1761251"], "values_float": [1.0930513595166162, 0.7936798900327097, 0.8157099697885196, 0.882506241302347, 0.7341389728096677, 0.889917450... | null | null | null |
C_4x4_thom_004 | 4x4 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 3 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 10 L/min; the feed has c_A0 = 1.7 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "yield_B"], "values": ["887485/590824", "30104837005/185948855872", "164475/147706", "5059025325/11621803492", "108375/147706", "2038512075/2905450873", "1199124750/2905450873"], "values_float": [1.5021139967232204, 0.16189847936318041, 1.1135295790286108, 0.43... | null | null | null |
C_4x4_thom_005 | 4x4 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 3 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 15 L/min; the feed has c_A0 = 1.2 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "yield_B"], "values": ["310185/363967", "256371724560/818242583941", "287100/363967", "286328238240/818242583941", "259875/363967", "338663625300/818242583941", "282219687750/818242583941"], "values_float": [0.8522338563660992, 0.3133199488655382, 0.78880777652... | null | null | null |
C_5x5_thom_001 | 5x5 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 4 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 8 L/min; the feed has c_A0 = 2 mol/L and c_B0 = 0 m... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "cA_4", "cB_4", "yield_B"], "values": ["217376/171319", "79096634720/136095642281", "157056/171319", "100033947840/136095642281", "141120/171319", "98745400320/136095642281", "123200/171319", "107137184000/136095642281", "53568592000/136095642281"], "values_flo... | null | null | null |
C_5x5_thom_002 | 5x5 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 4 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 12 L/min; the feed has c_A0 = 2.4 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "cA_4", "cB_4", "yield_B"], "values": ["1073781/621040", "3864026571/5471559802", "191241/124208", "32945959089/38300918614", "44145/31052", "2517524253/2735779901", "10125/7763", "37491740325/38300918614", "62486233875/153203674456"], "values_float": [1.729004... | null | null | null |
C_5x5_thom_003 | 5x5 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 4 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 15 L/min; the feed has c_A0 = 1.5 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "cA_4", "cB_4", "yield_B"], "values": ["31030605/25915354", "51092313323580/202274041606751", "21768075/25915354", "104476467771375/202274041606751", "496125/681983", "6419693127750/10646002189829", "472500/681983", "6314872515000/10646002189829", "420991501000... | null | null | null |
C_5x5_thom_004 | 5x5 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 4 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 12 L/min; the feed has c_A0 = 2.3 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "cA_4", "cB_4", "yield_B"], "values": ["301323/153707", "237605103548/757521739743", "260406/153707", "408682735708/757521739743", "199410/153707", "222212533500/252507246581", "159528/153707", "767280013616/757521739743", "333600005920/757521739743"], "values_... | null | null | null |
C_5x5_thom_005 | 5x5 | null | multi_stage_staged_separations_and_tridiagonal_matrix_recursions | thom | chem | thom | Topic 1: Multi-Stage Staged Separations and Tridiagonal Matrix Recursions | Solve this chemical engineering numerical problem. Show your work and give the final answer. A series of 4 well-mixed stirred stages carries the consecutive reactions A -> B -> C (both first order in the stage liquid; k1 for A->B, k2 for B->C). The through-flow is F = 12 L/min; the feed has c_A0 = 1.1 mol/L and c_B0 = ... | {"names": ["cA_1", "cB_1", "cA_2", "cB_2", "cA_3", "cB_3", "cA_4", "cB_4", "yield_B"], "values": ["119724/129089", "19691690502/150007743361", "83028/129089", "55744736091/150007743361", "67320/129089", "9566228100/21429677623", "426360/903623", "514133027760/1050054203527", "467393661600/1050054203527"], "values_float... | null | null | null |
C_4x4_rr_001 | 4x4 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. A single adiabatic-flash drum receives F = 100 kmol/h of a 4-component hydrocarbon feed. At the drum T and P, the K-values (K_i = y_i/x_i, taken from a converged equation-of-state fugacity iteration) are fixed. Components (ligh... | {"names": ["V_over_F", "vapor_flow", "x_1", "x_2", "x_3", "x_4", "y_1", "y_4", "MW_liquid"], "values": ["613160306949495960708587194937020990607299684952804110945424282120849/1000000000000000000000000000000000000000000000000000000000000000000000", "613160306949495960708587194937020990607299684952804110945424282120849/1... | null | null | null |
C_4x4_rr_002 | 4x4 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. A single adiabatic-flash drum receives F = 50 kmol/h of a 4-component hydrocarbon feed. At the drum T and P, the K-values (K_i = y_i/x_i, taken from a converged equation-of-state fugacity iteration) are fixed. Components (light... | {"names": ["V_over_F", "vapor_flow", "x_1", "x_2", "x_3", "x_4", "y_1", "y_4", "MW_liquid"], "values": ["1336554220283508670231982874695995320854608833528056620786439082914471/2000000000000000000000000000000000000000000000000000000000000000000000", "1336554220283508670231982874695995320854608833528056620786439082914471... | null | null | null |
C_4x4_rr_003 | 4x4 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. A single adiabatic-flash drum receives F = 80 kmol/h of a 4-component hydrocarbon feed. At the drum T and P, the K-values (K_i = y_i/x_i, taken from a converged equation-of-state fugacity iteration) are fixed. Components (light... | {"names": ["V_over_F", "vapor_flow", "x_1", "x_2", "x_3", "x_4", "y_1", "y_4", "MW_liquid"], "values": ["71089780584013976788200933654111364961740307542274492987204128633001/100000000000000000000000000000000000000000000000000000000000000000000", "71089780584013976788200933654111364961740307542274492987204128633001/1250... | null | null | null |
C_4x4_rr_004 | 4x4 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. A single adiabatic-flash drum receives F = 50 kmol/h of a 4-component hydrocarbon feed. At the drum T and P, the K-values (K_i = y_i/x_i, taken from a converged equation-of-state fugacity iteration) are fixed. Components (light... | {"names": ["V_over_F", "vapor_flow", "x_1", "x_2", "x_3", "x_4", "y_1", "y_4", "MW_liquid"], "values": ["309718149620381897385354498650810036054012851879878365324352070179723/500000000000000000000000000000000000000000000000000000000000000000000", "309718149620381897385354498650810036054012851879878365324352070179723/10... | null | null | null |
C_4x4_rr_005 | 4x4 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. A single adiabatic-flash drum receives F = 100 kmol/h of a 4-component hydrocarbon feed. At the drum T and P, the K-values (K_i = y_i/x_i, taken from a converged equation-of-state fugacity iteration) are fixed. Components (ligh... | {"names": ["V_over_F", "vapor_flow", "x_1", "x_2", "x_3", "x_4", "y_1", "y_4", "MW_liquid"], "values": ["917591484274788756725274136767959488357571663955538891736424965240379/1000000000000000000000000000000000000000000000000000000000000000000000", "917591484274788756725274136767959488357571663955538891736424965240379/1... | null | null | null |
C_5x5_rr_001 | 5x5 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. Two isothermal flash drums are in series. Drum 1 receives F = 50 kmol/h of a 5-component hydrocarbon feed; its liquid product is let down into drum 2 (lower pressure) and flashed again; the vapours of both drums are combined. K... | {"names": ["V1_over_F", "V2_over_L1", "x2_1", "x2_2", "x2_3", "x2_4", "x2_5", "recovery_light", "L2"], "values": ["2222708302159604730992555876969103632853697171726300991888430529148699/10000000000000000000000000000000000000000000000000000000000000000000000", "91585839887662807092538573919949235947101614388533584730149... | null | null | null |
C_5x5_rr_002 | 5x5 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. Two isothermal flash drums are in series. Drum 1 receives F = 100 kmol/h of a 5-component hydrocarbon feed; its liquid product is let down into drum 2 (lower pressure) and flashed again; the vapours of both drums are combined. ... | {"names": ["V1_over_F", "V2_over_L1", "x2_1", "x2_2", "x2_3", "x2_4", "x2_5", "recovery_light", "L2"], "values": ["124311505388212570857026595846377320095737781982436098286788386392657/200000000000000000000000000000000000000000000000000000000000000000000", "47850644483063836298183071346278838211992994045234256093412809... | null | null | null |
C_5x5_rr_003 | 5x5 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. Two isothermal flash drums are in series. Drum 1 receives F = 50 kmol/h of a 5-component hydrocarbon feed; its liquid product is let down into drum 2 (lower pressure) and flashed again; the vapours of both drums are combined. K... | {"names": ["V1_over_F", "V2_over_L1", "x2_1", "x2_2", "x2_3", "x2_4", "x2_5", "recovery_light", "L2"], "values": ["351743188707082290555918887483850577714408625343874212442536550685119/500000000000000000000000000000000000000000000000000000000000000000000", "16714033956888740919108174367398735520530899219721368250042998... | null | null | null |
C_5x5_rr_004 | 5x5 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. Two isothermal flash drums are in series. Drum 1 receives F = 50 kmol/h of a 5-component hydrocarbon feed; its liquid product is let down into drum 2 (lower pressure) and flashed again; the vapours of both drums are combined. K... | {"names": ["V1_over_F", "V2_over_L1", "x2_1", "x2_2", "x2_3", "x2_4", "x2_5", "recovery_light", "L2"], "values": ["1899588783193046303050465465276368571072781027365005770267572026800443/2000000000000000000000000000000000000000000000000000000000000000000000", "787825070042339718084918035132362149632464442564956961139709... | null | null | null |
C_5x5_rr_005 | 5x5 | null | multi_phase_thermodynamic_equilibrium_and_recursive_eos_solvers | rr | chem | rr | Topic 2: Multi-Phase Thermodynamic Equilibrium and Recursive EOS Solvers | Solve this chemical engineering numerical problem. Show your work and give the final answer. Two isothermal flash drums are in series. Drum 1 receives F = 100 kmol/h of a 5-component hydrocarbon feed; its liquid product is let down into drum 2 (lower pressure) and flashed again; the vapours of both drums are combined. ... | {"names": ["V1_over_F", "V2_over_L1", "x2_1", "x2_2", "x2_3", "x2_4", "x2_5", "recovery_light", "L2"], "values": ["113179265914571230277153265740654501485911074538463593723929308972641/125000000000000000000000000000000000000000000000000000000000000000000", "52144336568095312539724503036061588009065808111403632741770178... | null | null | null |
C_4x4_bvp_001 | 4x4 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c/(1 + beta*c), phi2 = 4.4, beta = 1.9, and Dirichlet conditions c(0) = 1, c(1) = 0.3. Discretise with second-order... | {"names": ["c_1", "c_2", "c_3", "c_4", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["152514266575269835716564677598950935115611597/200000000000000000000000000000000000000000000", "579948230491013529260915476252262226948287189/1000000000000000000000000000000000000000000000", "222943169463755792326324716264758501739062393/... | null | null | null |
C_4x4_bvp_002 | 4x4 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c/(1 + beta*c), phi2 = 5.1, beta = 0.7, and Dirichlet conditions c(0) = 1, c(1) = 0.4. Discretise with second-order... | {"names": ["c_1", "c_2", "c_3", "c_4", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["179015727850036487873701067185626267606049357/250000000000000000000000000000000000000000000", "66178709869450002280424640497887860507132961/125000000000000000000000000000000000000000000", "84319335036279724878785741020346294270320547/200... | null | null | null |
C_4x4_bvp_003 | 4x4 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c/(1 + beta*c), phi2 = 10.6, beta = 1.5, and Dirichlet conditions c(0) = 1, c(1) = 0.1. Discretise with second-orde... | {"names": ["c_1", "c_2", "c_3", "c_4", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["12291170623235703719932600877388498631610473/20000000000000000000000000000000000000000000", "364702291032383205821296821727397048194894487/1000000000000000000000000000000000000000000000", "107399893652860994394938395982719982131803543/50... | null | null | null |
C_4x4_bvp_004 | 4x4 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c/(1 + beta*c), phi2 = 8.7, beta = 0.9, and Dirichlet conditions c(0) = 1, c(1) = 0.1. Discretise with second-order... | {"names": ["c_1", "c_2", "c_3", "c_4", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["616848668322789961722578229246825044810954963/1000000000000000000000000000000000000000000000", "23233122391923084625078267418638256570068609/62500000000000000000000000000000000000000000", "223543810198984021037888701739392840745584627/10... | null | null | null |
C_4x4_bvp_005 | 4x4 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c/(1 + beta*c), phi2 = 11.1, beta = 2.2, and Dirichlet conditions c(0) = 1, c(1) = 0.1. Discretise with second-orde... | {"names": ["c_1", "c_2", "c_3", "c_4", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["158458013379865685798902422569763741292410639/250000000000000000000000000000000000000000000", "192597891508349519770053546239734284514513569/500000000000000000000000000000000000000000000", "57283767309794635131983048892074830793663111/25... | null | null | null |
C_5x5_bvp_001 | 5x5 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c^2/(1 + beta*c), phi2 = 9.7, beta = 2.9, and Dirichlet conditions c(0) = 1, c(1) = 0.3. Discretise with second-ord... | {"names": ["c_1", "c_2", "c_3", "c_4", "c_5", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["79104020435085494960805080605137813183477471/100000000000000000000000000000000000000000000", "31663257808223066432773291838873032980596233/50000000000000000000000000000000000000000000", "5135846173579131897643695929468689855681603... | null | null | null |
C_5x5_bvp_002 | 5x5 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c^2/(1 + beta*c), phi2 = 10, beta = 1.7, and Dirichlet conditions c(0) = 1, c(1) = 0.3. Discretise with second-orde... | {"names": ["c_1", "c_2", "c_3", "c_4", "c_5", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["19065508292340474253115526640966688833783727/25000000000000000000000000000000000000000000", "595589415989073385312311250022569684639101587/1000000000000000000000000000000000000000000000", "47752004599181106460580105114582260048999... | null | null | null |
C_5x5_bvp_003 | 5x5 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c^2/(1 + beta*c), phi2 = 5.1, beta = 2, and Dirichlet conditions c(0) = 1, c(1) = 0.3. Discretise with second-order... | {"names": ["c_1", "c_2", "c_3", "c_4", "c_5", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["817915585625874783100839837290908808625604243/1000000000000000000000000000000000000000000000", "67178681373435814751486592459349714684430403/100000000000000000000000000000000000000000000", "2764692614123067783623984116880221060499... | null | null | null |
C_5x5_bvp_004 | 5x5 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c^2/(1 + beta*c), phi2 = 10.4, beta = 1, and Dirichlet conditions c(0) = 1, c(1) = 0.2. Discretise with second-orde... | {"names": ["c_1", "c_2", "c_3", "c_4", "c_5", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["364004384906654962762844508962745384613189723/500000000000000000000000000000000000000000000", "17019453651532853221352329760495677087942279/31250000000000000000000000000000000000000000", "416711564291420751030466603636956727272532... | null | null | null |
C_5x5_bvp_005 | 5x5 | null | non_linear_bvps_in_catalytic_reaction_diffusion_systems | bvp | chem | bvp | Topic 3: Non-Linear BVPs in Catalytic Reaction-Diffusion Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. Dimensionless steady diffusion with catalytic reaction in a slab, 0 <= x <= 1: c'' = phi2 * r(c), with r(c) = c^2/(1 + beta*c), phi2 = 11.5, beta = 2.3, and Dirichlet conditions c(0) = 1, c(1) = 0.4. Discretise with second-or... | {"names": ["c_1", "c_2", "c_3", "c_4", "c_5", "dc_dx(1)-dc_dx(0)", "I_trap"], "values": ["387351499378351741171341732415719206505001963/500000000000000000000000000000000000000000000", "618324728632636870314512759470018179042747847/1000000000000000000000000000000000000000000000", "102473878114776592895991905704490577702... | null | null | null |
C_4x4_dp_001 | 4x4 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 4 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "total_cost"], "values": ["23069580088401/32000000000000", "2", "2", "3", "3", "18"], "values_float": [0.7209243777625313, 2.0, 2.0, 3.0, 3.0, 18.0]} | null | null | null |
C_4x4_dp_002 | 4x4 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 4 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "total_cost"], "values": ["8486672405626918503/9765625000000000000", "3", "2", "3", "3", "23"], "values_float": [0.8690352543361964, 3.0, 2.0, 3.0, 3.0, 23.0]} | null | null | null |
C_4x4_dp_003 | 4x4 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 4 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "total_cost"], "values": ["200828114874617559/250000000000000000", "2", "4", "2", "2", "24"], "values_float": [0.8033124594984702, 2.0, 4.0, 2.0, 2.0, 24.0]} | null | null | null |
C_4x4_dp_004 | 4x4 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 4 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "total_cost"], "values": ["961589067987377691/1220703125000000000", "2", "2", "4", "3", "21"], "values_float": [0.7877337644952598, 2.0, 2.0, 4.0, 3.0, 21.0]} | null | null | null |
C_4x4_dp_005 | 4x4 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 4 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "total_cost"], "values": ["2417238287919/3814697265625", "2", "2", "2", "4", "18"], "values_float": [0.6336645137482383, 2.0, 2.0, 2.0, 4.0, 18.0]} | null | null | null |
C_5x5_dp_001 | 5x5 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 5 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "x_5", "total_cost", "total_weight"], "values": ["414979504224235142283/625000000000000000000", "2", "2", "2", "3", "2", "16", "21"], "values_float": [0.6639672067587762, 2.0, 2.0, 2.0, 3.0, 2.0, 16.0, 21.0]} | null | null | null |
C_5x5_dp_002 | 5x5 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 5 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "x_5", "total_cost", "total_weight"], "values": ["1858546685831001765417/2500000000000000000000", "2", "2", "3", "2", "2", "34", "20"], "values_float": [0.7434186743324007, 2.0, 2.0, 3.0, 2.0, 2.0, 34.0, 20.0]} | null | null | null |
C_5x5_dp_003 | 5x5 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 5 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "x_5", "total_cost", "total_weight"], "values": ["1680194278865817/2000000000000000", "2", "2", "2", "2", "3", "30", "24"], "values_float": [0.8400971394329085, 2.0, 2.0, 2.0, 2.0, 3.0, 30.0, 24.0]} | null | null | null |
C_5x5_dp_004 | 5x5 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 5 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "x_5", "total_cost", "total_weight"], "values": ["10988303009607/15258789062500", "2", "2", "2", "3", "2", "25", "24"], "values_float": [0.7201294260376043, 2.0, 2.0, 2.0, 3.0, 2.0, 25.0, 24.0]} | null | null | null |
C_5x5_dp_005 | 5x5 | null | dynamic_programming_and_bellman_recursions_in_process_synthesis | dp | chem | dp | Topic 4: Dynamic Programming and Bellman Recursions in Process Synthesis | Solve this chemical engineering numerical problem. Show your work and give the final answer. A process line has 5 stages in series, and the line works only if every stage works. Stage i is built with x_i identical units in parallel (1 <= x_i <= 4, integer), so stage reliability is 1-(1-r_i)^x_i and system reliability R... | {"names": ["R_system", "x_1", "x_2", "x_3", "x_4", "x_5", "total_cost", "total_weight"], "values": ["115192517736437757/200000000000000000", "3", "2", "2", "2", "2", "23", "31"], "values_float": [0.5759625886821887, 3.0, 2.0, 2.0, 2.0, 2.0, 23.0, 31.0]} | null | null | null |
C_4x4_lbm_001 | 4x4 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_4", "ux_4", "uy_4", "Px_total", "Py_total"], "values": ["352564003600751/15693960943125", "47393677872925/352564003600751", "142797927004825/1057692010802253", "63812596666613281/2529252460276875", "12596013139693525/63812596666613281", "27470440402373650/191437789999839843", "8... | null | null | null |
C_4x4_lbm_002 | 4x4 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_4", "ux_4", "uy_4", "Px_total", "Py_total"], "values": ["10551907122345998693/479308949050758750", "-1339039012950457854/10551907122345998693", "-573368135231200820/10551907122345998693", "2362464657566280881/105664126952711250", "-233128173743917032/2362464657566280881", "-7318... | null | null | null |
C_4x4_lbm_003 | 4x4 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_4", "ux_4", "uy_4", "Px_total", "Py_total"], "values": ["233894121440789/9669816892890", "-13165150141451/1169470607203945", "-256487229472353/4677882428815780", "662051809732177321/24284426515098750", "55181348896699025/662051809732177321", "222078738075683775/26482072389287092... | null | null | null |
C_4x4_lbm_004 | 4x4 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_4", "ux_4", "uy_4", "Px_total", "Py_total"], "values": ["9844396589499491518/424489241686480425", "-71496728461020955/9844396589499491518", "933787077159127183/4922198294749745759", "1109173751360428399/40038029725382325", "-73332453586886955/1109173751360428399", "7902521572258... | null | null | null |
C_4x4_lbm_005 | 4x4 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_4", "ux_4", "uy_4", "Px_total", "Py_total"], "values": ["75245362972617248156670353/2893139041085399552607000", "6233591416321371055877656/75245362972617248156670353", "-365800104319852396019536/5788104844047480627436181", "11873193954226347520583503/437857055563857464367000", "... | null | null | null |
C_5x5_lbm_001 | 5x5 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_5", "ux_5", "uy_5", "Px_total", "Py_total"], "values": ["558729407793813297039401434697171741825432754417216827888943149330324766892483383601752260556827/19470536241868000799800137916562474912485240057514550013678673949798086018845349325641909296500", "-2811585182503116317945917... | null | null | null |
C_5x5_lbm_002 | 5x5 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_5", "ux_5", "uy_5", "Px_total", "Py_total"], "values": ["117718697758230864986750172161266283229304984484310296865096109815292966055617/6360805830493976112224995625324793780307647885357088735277980121965716955500", "-37798432574545296925092325504468928810544429286871468174432176... | null | null | null |
C_5x5_lbm_003 | 5x5 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_5", "ux_5", "uy_5", "Px_total", "Py_total"], "values": ["264834015472814674662662130177792280368164670498097164125075508507818013073/10434974919115945341400036041925942198336689438938159053620282819385125000", "16515016406325517090351869781233904973547826514404997311498315945320... | null | null | null |
C_5x5_lbm_004 | 5x5 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_5", "ux_5", "uy_5", "Px_total", "Py_total"], "values": ["23384402070590594332316017265002014207586068985720853026733926481232639104733871263596783762/950221808068353844373163805406989382131257183204651980222644891520587697611940344836890625", "-2259555082177975672145494906432320... | null | null | null |
C_5x5_lbm_005 | 5x5 | null | lattice_boltzmann_and_cellular_automata_recurrences_in_porous_media | lbm | chem | lbm | Topic 5: Lattice Boltzmann and Cellular Automata Recurrences in Porous Media | Solve this chemical engineering numerical problem. Show your work and give the final answer. Porous-media flow is simulated with a D2Q9 BGK lattice-Boltzmann scheme in lattice units (dx = dt = 1, c_s^2 = 1/3). Velocity set e_0..e_8 = (0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,1), (-1,-1), (1,-1) with weights w = 4... | {"names": ["rho_2", "ux_2", "uy_2", "rho_5", "ux_5", "uy_5", "Px_total", "Py_total"], "values": ["60706884594350428156891877815201389430396269771919483748913427607763109889865820569396834195884515687053067/2462958466336897454065094644023188181787686287985396659122562775150599876682596534250746578948220651137500", "-370... | null | null | null |
C_4x4_dae_001 | 4x4 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 4 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1 is a fast surface coverage fixed by algebraic balances)... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_1(t1)"], "values": ["87103630751549/104177055526780", "-645988015318889/7917456220035280", "1643247893597427/989682027504410", "3639254264778987/7917456220035280", "3956479/3332080"], "values_float": [0.836111467262174, -0.08159034889062014, 1.6603796451... | null | null | null |
C_4x4_dae_002 | 4x4 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 4 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1 is a fast surface coverage fixed by algebraic balances)... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_1(t1)"], "values": ["10341420630416327/5876021859723760", "1988893715247333/11752043719447520", "6294978086283773/11752043719447520", "-4565795315755173/5876021859723760", "-65651/66160"], "values_float": [1.7599356975337208, 0.16923811404445946, 0.53564... | null | null | null |
C_4x4_dae_003 | 4x4 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 4 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1 is a fast surface coverage fixed by algebraic balances)... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_1(t1)"], "values": ["9177158439603/8113365318565", "-11/49", "207889408936913/1590219602438740", "-298236072827584/397554900609685", "-56794/40885"], "values_float": [1.1311161372955596, -0.22448979591836735, 0.13073000019500233, -0.7501758181579778, -1.... | null | null | null |
C_4x4_dae_004 | 4x4 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 4 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1 is a fast surface coverage fixed by algebraic balances)... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_1(t1)"], "values": ["1123801320110711/788602089339000", "2175161074831391/1971505223347500", "-179794273472207/657168407782500", "-100861043191981/394301044669500", "-1435/57964"], "values_float": [1.425054961562012, 1.103299676344806, -0.273589343831806... | null | null | null |
C_4x4_dae_005 | 4x4 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 4 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1 is a fast surface coverage fixed by algebraic balances)... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_1(t1)"], "values": ["57171212321830363/12142470693447500", "-4103114778917/1734638670492500", "1467888963707009/12142470693447500", "14563228339791079/6071235346723750", "4216333/1572550"], "values_float": [4.708367330273396, -0.002365400269643499, 0.120... | null | null | null |
C_5x5_dae_001 | 5x5 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 5 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1, theta_2 are fast surface coverages fixed by algebraic ... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_2(t3)", "theta_1(t1)"], "values": ["1078012021263011051/1581791680553672500", "-232096501883808548/395447920138418125", "-345044112991736967/1581791680553672500", "122880815741843727/316358336110734500", "-383437941914841621/1581791680553672500", "-1087/... | null | null | null |
C_5x5_dae_002 | 5x5 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 5 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1, theta_2 are fast surface coverages fixed by algebraic ... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_2(t3)", "theta_1(t1)"], "values": ["-5799617292977294182/9255238128853344605", "-5021399100404468531/18510476257706689210", "40132008621386602481/37020952515413378420", "6847054813845813708/9255238128853344605", "-7309012334137457567/37020952515413378420... | null | null | null |
C_5x5_dae_003 | 5x5 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 5 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1, theta_2 are fast surface coverages fixed by algebraic ... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_2(t3)", "theta_1(t1)"], "values": ["-734471121742952291/1586653742043671880", "-129579845259301954/198331717755458985", "1794834590027987431/475996122613101564", "-810776552222535607/793326871021835940", "6022291406057343049/4759961226131015640", "-19087... | null | null | null |
C_5x5_dae_004 | 5x5 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 5 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1, theta_2 are fast surface coverages fixed by algebraic ... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_2(t3)", "theta_1(t1)"], "values": ["51737977291085823/717053729015098750", "-500395228980060639/2868214916060395000", "-257722852756317981/1434107458030197500", "85866334163820986/71705372901509875", "-333396034796306281/717053729015098750", "1295549/572... | null | null | null |
C_5x5_dae_005 | 5x5 | null | implicit_recurrences_and_daes_in_dynamic_process_systems | dae | chem | dae | Topic 6: Implicit Recurrences and DAEs in Dynamic Process Systems | Solve this chemical engineering numerical problem. Show your work and give the final answer. A stiff reactor model with quasi-steady-state surface species is an index-1 differential-algebraic system in the 5 unknowns (c_A, c_B, c_C are bulk concentrations; theta_1, theta_2 are fast surface coverages fixed by algebraic ... | {"names": ["c_A(t3)", "c_B(t3)", "c_C(t3)", "theta_1(t3)", "theta_2(t3)", "theta_1(t1)"], "values": ["169381304199195274577/40447569291330935230", "-3600803826306932662/20223784645665467615", "5663031533982656133/4758537563685992380", "117242210491718543299/80895138582661870460", "-13498006887818956665/1617902771653237... | null | null | null |
C_4x4_kf_001 | 4x4 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_k + v_k (v ~ N(0,R)), with ... | {"names": ["xhat_1", "xhat_2", "P_11", "P_22", "P_12"], "values": ["7945339027/18657065000", "5329102/18657065", "8045962393689691/26269147520000000", "27197349/410455430", "-2282283/205227715"], "values_float": [0.42586221503757427, 0.28563453040443393, 0.30628943659339924, 0.06626139408120389, -0.011120734838372098]} | null | null | null |
C_4x4_kf_002 | 4x4 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_k + v_k (v ~ N(0,R)), with ... | {"names": ["xhat_1", "xhat_2", "P_11", "P_22", "P_12"], "values": ["124730536461/180326910820", "419708746991/631144187870", "2048754158/32201234075", "14320454787/315572093935", "-303868674/45081727705"], "values_float": [0.6916911951400555, 0.6649966125925089, 0.06362346713881338, 0.04537934456888212, -0.006740395487... | null | null | null |
C_4x4_kf_003 | 4x4 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_k + v_k (v ~ N(0,R)), with ... | {"names": ["xhat_1", "xhat_2", "P_11", "P_22", "P_12"], "values": ["-5782748110173117/10801934489589800", "-365666564956631/540096724479490", "27939245627956529/108019344895898000", "12026029407949/270048362239745", "3361650063584/270048362239745"], "values_float": [-0.5353437493762022, -0.6770390346452047, 0.258650389... | null | null | null |
C_4x4_kf_004 | 4x4 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_k + v_k (v ~ N(0,R)), with ... | {"names": ["xhat_1", "xhat_2", "P_11", "P_22", "P_12"], "values": ["11863547671849/58390888431175", "-13959400136823/23356355372470", "484993346228317/1167817768623500", "1027856151741/23356355372470", "940406900679/23356355372470"], "values_float": [0.2031746388964863, -0.5976703091817511, 0.4152988242334896, 0.044007... | null | null | null |
C_4x4_kf_005 | 4x4 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_k + v_k (v ~ N(0,R)), with ... | {"names": ["xhat_1", "xhat_2", "P_11", "P_22", "P_12"], "values": ["24278134002299/132943716459650", "3441620337237/13294371645965", "357652037898867/1329437164596500", "1974265497579/26588743291930", "-1076991898311/26588743291930"], "values_float": [0.182619642724278, 0.2588779995692066, 0.2690251539698897, 0.0742519... | null | null | null |
C_5x5_kf_001 | 5x5 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K); h' (deviation holdup, dm)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_... | {"names": ["xhat_1", "xhat_2", "xhat_3", "P_11", "P_22", "P_33", "P_12"], "values": ["-237951969757/12559307833570", "10519372778251/12559307833570", "12492887095189/12559307833570", "479113158157/12559307833570", "1901444695823611/7033212386799200", "2182625606260171/7033212386799200", "278205032933/12559307833570"], ... | null | null | null |
C_5x5_kf_002 | 5x5 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K); h' (deviation holdup, dm)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_... | {"names": ["xhat_1", "xhat_2", "xhat_3", "P_11", "P_22", "P_33", "P_12"], "values": ["9842011742779/8209964464730", "-10360540287403/20524911161825", "54128843466941/41049822323650", "917043157419/8209964464730", "2036639747445073/7388968018257000", "1401468803095573/7388968018257000", "139140252724/4104982232365"], "v... | null | null | null |
C_5x5_kf_003 | 5x5 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K); h' (deviation holdup, dm)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_... | {"names": ["xhat_1", "xhat_2", "xhat_3", "P_11", "P_22", "P_33", "P_12"], "values": ["-3051814143061/48565373817980", "-323321066905667/388522990543840", "-61760829243273/77704598108768", "954070267799/24282686908990", "310909451503503/1942614952719200", "329771590266383/1942614952719200", "675957261819/48565373817980"... | null | null | null |
C_5x5_kf_004 | 5x5 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K); h' (deviation holdup, dm)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_... | {"names": ["xhat_1", "xhat_2", "xhat_3", "P_11", "P_22", "P_33", "P_12"], "values": ["-31805746569274/88770086914565", "-290875378049423/3550803476582600", "1492618936711263/3550803476582600", "6793427593313/88770086914565", "270492706044964/2219252172864125", "313140706230514/2219252172864125", "-823687835889/88770086... | null | null | null |
C_5x5_kf_005 | 5x5 | null | recursive_bayesian_state_estimation_and_mhe_in_reactors | kf | chem | kf | Topic 7: Recursive Bayesian State Estimation and MHE in Reactors | Solve this chemical engineering numerical problem. Show your work and give the final answer. A linearised CSTR has deviation states x = [C' (deviation concentration, mol/L); T' (deviation temperature, K); h' (deviation holdup, dm)] and discrete-time model x_k = F x_k-1 + B u_k + w_k (w ~ N(0,Q)), measurement y_k = H x_... | {"names": ["xhat_1", "xhat_2", "xhat_3", "P_11", "P_22", "P_33", "P_12"], "values": ["-8512658555297/6372931175565", "-10554157885231/42486207837100", "-62843851044937/127458623511300", "602537094493/12745862351130", "4206729429181/33988966269680", "12787499825519/101966898809040", "-87374716209/8497241567420"], "value... | null | null | null |
Bluff-Bench: Chem + Physics
The benchmark problems, model responses and grades for chemistry and physics, restricted to the categories where DeepSeek-V3.2 scores below 75%. Three models were run on every problem:
| Model | OpenRouter id |
|---|---|
| Llama-3.3-70B | meta-llama/llama-3.3-70b-instruct |
| DeepSeek-V3.2 | deepseek/deepseek-v3.2 |
| Qwen-2.5-72B | qwen/qwen-2.5-72b-instruct |
| Categories | Problems (benchmarks) |
Model rows (responses_data, results_data) |
|
|---|---|---|---|
| Physics | 17 | 145 | 435 (145 problems x 3 models) |
| Chemistry | 18 | 165 | 494 (165 problems x 3 models, minus 1) |
DeepSeek has no row for chem problem CH_4x4_eig_010; it was never run.
Layout
benchmarks/parquet/ chem.parquet, physics.parquet the problems: prompt + ground truth
responses_data/parquet/ chem.parquet, physics.parquet model rows, including `response`
results_data/parquet/ chem_results.parquet, physics_results.parquet grading columns only (no `response`)
category_results/parquet/ chem_category.parquet, physics_category.parquet per-category accuracy table
If CSV copies are published, they sit in a sibling csv/ folder with the same file names.
Every Problem_ID in responses_data and results_data is also in benchmarks, so the tables join on Problem_ID.
Load the data
With datasets
from datasets import load_dataset
REPO = "05deepak/bluff-bench-chem-phy"
chem_problems = load_dataset(REPO, "benchmarks_chem", split="train")
physics_problems = load_dataset(REPO, "benchmarks_physics", split="train")
chem_responses = load_dataset(REPO, "responses_chem", split="train")
physics_responses = load_dataset(REPO, "responses_physics", split="train")
chem_results = load_dataset(REPO, "results_chem", split="train")
physics_results = load_dataset(REPO, "results_physics", split="train")
print(chem_responses)
print(chem_responses[0]["Problem_ID"], chem_responses[0]["final_status"])
Download the files and read with pandas
import pandas as pd
from huggingface_hub import hf_hub_download
REPO = "05deepak/bluff-bench-chem-phy"
def get(path):
return pd.read_parquet(hf_hub_download(REPO, path, repo_type="dataset"))
chem_problems = get("benchmarks/parquet/chem.parquet")
physics_problems = get("benchmarks/parquet/physics.parquet")
chem = get("responses_data/parquet/chem.parquet")
physics = get("responses_data/parquet/physics.parquet")
chem_results = get("results_data/parquet/chem_results.parquet")
physics_results = get("results_data/parquet/physics_results.parquet")
To download the whole repo to a local folder instead:
from huggingface_hub import snapshot_download
local_dir = snapshot_download("05deepak/bluff-bench-chem-phy", repo_type="dataset")
print(local_dir)
Join a problem to its model responses
merged = chem.merge(
chem_problems[["Problem_ID", "instruction", "ground_truth"]],
on="Problem_ID", how="left",
)
print(merged[["Problem_ID", "model", "final_status", "instruction"]].head())
Get the category results
The category tables list each category's accuracy for the three models. n is the number of problems in the category, and accuracy values are text such as "0%".
import pandas as pd
from huggingface_hub import hf_hub_download
REPO = "05deepak/bluff-bench-chem-phy"
chem_cat = pd.read_parquet(hf_hub_download(REPO, "category_results/parquet/chem_category.parquet", repo_type="dataset"))
physics_cat = pd.read_parquet(hf_hub_download(REPO, "category_results/parquet/physics_category.parquet", repo_type="dataset"))
print(chem_cat.head()) # Category, Family, n, Llama-3.3-70B, DeepSeek-V3.2, Qwen-2.5-72B
print(len(chem_cat), len(physics_cat)) # 18, 17
Or with datasets:
from datasets import load_dataset
chem_cat = load_dataset("05deepak/bluff-bench-chem-phy", "category_chem", split="train").to_pandas()
physics_cat = load_dataset("05deepak/bluff-bench-chem-phy", "category_physics", split="train").to_pandas()
Compute category accuracy yourself from the responses
subcat is the category code. A few codes cover two categories and are told apart by the last number in Problem_ID:
eig and solve split into 001-005 and 006-010 (for example physics eig is Mechanical for 001-005 and Quantum for 006-010).
import pandas as pd
from huggingface_hub import hf_hub_download
df = pd.read_parquet(hf_hub_download("05deepak/bluff-bench-chem-phy",
"responses_data/parquet/physics.parquet", repo_type="dataset"))
acc = (df.groupby(["model", "subcat"])["is_correct"]
.mean().mul(100).round(1).unstack(0))
print(acc)
Columns
Benchmarks (benchmarks, 13 columns)
| Column | Meaning |
|---|---|
Problem_ID |
Problem id, e.g. P_4x4_eig_001, C_NR_stoich_003 |
dim |
4x4, 5x5 or NR (non-recursive set) |
branch |
Physics branch (e.g. electrical); empty for chem |
category, subcategory |
Category name and short code (subcategory here is subcat in the other tables) |
dataset |
physics or chem |
topic_key, doc_topic |
Chem topic key and description; empty for physics |
instruction |
The full prompt given to the models |
ground_truth |
Correct answer as JSON text |
answer_latex |
Correct answer in LaTeX (physics only) |
k, pilot |
Generation parameter and pilot flag (physics only) |
Responses and results (responses_data 25 columns, results_data 18 columns)
Results are the same rows as responses without response and some judge fields.
| Column | Meaning |
|---|---|
Problem_ID |
Problem id, joins to benchmarks |
dataset |
physics or chem |
dim |
4x4, 5x5 or NR |
subcat |
Category code, e.g. eig, lens, dae |
model |
Model id (see table above) |
response |
Full model response text (responses only) |
finish_reason |
stop, loop_trimmed or error |
tokens_used, latency_ms |
Usage and timing |
boxed_answer |
Final \boxed{} answer extracted from the response |
grade_status |
Strict grader verdict |
judge_* |
Second-stage equivalence judge output |
final_status |
CORRECT, CORRECT_JUDGE (strict failed, judge accepted), INCORRECT or ERROR |
is_correct |
1 or 0, empty when the call failed |
n_items_expected, n_items_found, items_correct |
Per-item answer matching |
Notes
benchmarksincludes the ground-truth answers (ground_truth,answer_latex).- Rows with
final_status = ERRORare failed API calls (all retries failed) and have no response. There are 7, all Qwen. - Five responses have
finish_reason = loop_trimmed: the model looped and the text was cut. - The stage-2 judge was the model under test, so a few answers rejected by the strict grader stayed unjudged and count as incorrect. The strict-only result is the more conservative figure.
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