Dataset Viewer
Auto-converted to Parquet Duplicate
Problem_ID
large_stringlengths
12
19
dim
large_stringclasses
3 values
branch
null
category
large_stringclasses
18 values
subcategory
large_stringclasses
17 values
dataset
large_stringclasses
1 value
topic_key
large_stringclasses
13 values
doc_topic
large_stringclasses
10 values
instruction
large_stringlengths
1.11k
2.41k
ground_truth
large_stringlengths
171
2.65k
answer_latex
large_stringlengths
53
561
⌀
k
int64
24
120
⌀
pilot
bool
0 classes
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
End of preview. Expand in Data Studio

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

  • benchmarks includes the ground-truth answers (ground_truth, answer_latex).
  • Rows with final_status = ERROR are 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.
Downloads last month
114