a projection method for l p norm location allocation problems we present a solution method for location allocation problems involving thel p norm where 1 p the method relaxes the 0 1 constraints on the allocations and solves for both the locations and allocations simultaneously necessary and sufficient conditions for local minima of the relaxed problem are stated and used to develop an iterative algorithm this algorithm finds a stationary point on a series of subspaces defined by the current set of activities the descent direction is a projection onto the current subspace of a direction incorporating second order information for the locations and first order information for the allocations under mild conditions the algorithm finds local minima with 0 1 allocations and exhibits quadratic convergence an implementation that exploits the special structure of these problems to dramatically reduce the computational cost of the required numerical linear algebra is described numerical results for thirty six test problems are included

fluctuation theorems and atypical trajectories in this work we have studied simple models that can be solved analytically to illustrate various fluctuation theorems these fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work wc thermodynamic work w total entropy stot and dissipated heat q when the system is driven arbitrarily out of equilibrium all these quantities can be defined for individual trajectories we have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level as the time of observation increases the fraction of such atypical trajectories decreases as expected at the macroscale the distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak most probable value in the atypical regime without violating the expected average behaviour however dissipated heat and classical work exhibit a peak in the regime of typical behaviour only

dynamic dispersion curves for non homogeneous anisotropic beams with cross sections of arbitrary geometry abstract to accurately predict the dynamic behaviour of spanwise uniform non homogeneous anisotrophic beams with arbitrary cross sectional geometry is an important part of engineering analysis classical one dimensional beam theory fails in this endeavour and development of more sophisticated one dimensional theories is an important task a basis for development of improved one dimensional theory is the dispersion curve analysis a means to find the dispersion curves is discussed in this paper the code is developed to calculate the dispersion curves as well as corresponding mode shapes the code is based on finite element discretization over the cross sectional domain use of this code provides benchmark results for the testing of any existing one dimensional theory as well as facilitating the construction of new one dimensional theories dispersion information can also be useful in non destructive evaluation as an example of a case where non classical effects are particularly important results obtained from this code for an i beam are presented qualitative comparisons with the well known case of isotropic rectangular beam is provided features that are common for all beams are emphasized along with pointing out qualitative differences that exist for beams other than rectangular or circular

a projected newton method for l p norm location problems this paper is concerned with the numerical solution of continuous minisum multifacility location problems involving thel p norm where 1 p x this class of problems is potentially difficult to solve because the objective function is not everywhere diflerentiable after developing conditions that characterize the minimum of the problems under consideration a second order algorithm is presented this algorithm is based on the solution of a finite sequence of linearly constrained subproblems descent directions for these subproblems are obtained by projecting the newton direction onto the corresponding constraint manifold univariate minimization is achieved via a specialized linesearch which recognizes the possibility of first derivative discontinuity and second derivative unboundedness at points along the search direction the algorithm motivated by earlier works of calamai and conn and related to methods recently described by overton and dax is shown to possess both global and quadratic convergence properties degeneracy can complicate the numerical solution of the subproblems this degeneracy is identified and a method for handling it is outlined an implementation of the algorithm that exploits the intrinsic structure of the location problem formulation is then described along with a discussion of numerical results

micromechanical modeling of transient waves from matrix cracking and fiber fracture in laminated beams abstract a micromechanical model for excitation of waves resulting from fiber fracture and matrix cracking in laminated beams is presented the source is described as a time dependent displacement discontinuity and the wave propagation in the beam is modeled by a higher order beam theory the equations of motion defined by the beam model are then formally solved by employing integral transforms asymptotically valid solutions are subsequently found using residue calculus and the stationary phase method as an example a 90 0 2 90 beam with a width to thickness ratio of 10 is considered the dispersion curves resulting from the beam theory and three dimensional finite element computations are compared and a maximum frequency for applicability of the beam theory is determined the time response from fiber fracture and transverse matrix cracking is presented the applications of the results to the analysis of acoustic emission experiments are also discussed

an outer approximate subdifferential method for piecewise affine optimization piecewise affine functions arise from lagrangian duals of integer programming problems and optimizing them provides good bounds for use in a branch and bound method methods such as the subgradient method and bundle methods assume only one subgradient is available at each point but in many situations there is more information available we present a new method for optimizing such functions which is related to steepest descent but uses an outer approximation to the subdifferential to avoid some of the numerical problems with the steepest descent approach we provide convergence results for a class of outer approximations and then develop a practical algorithm using such an approximation for the compact dual to the linear programming relaxation of the uncapacitated facility location problem we make a numerical comparison of our outer approximation method with the projection method of conn and cornuejols and the bundle method of schramm and zowe

propagating waves and edge vibrations in anisotropic composite cylinders the entire dispersive spectra of a cylinder with cylindrical anisotropy are determined from three different algebraic eigenvalue problems deducible from the same finite element formulation the displacement vector v in this version of the finite element method has the form f r exp i ez n t with the radial dependence f r taken as quadratic interpolation polynomials therefore this discretization procedure allows a cylinder with radially inhomogeneous material properties to be modeled the three different algebraic eigenvalue problems that emerge depend on whether the axial wave number e or the natural frequency is regarded as the eigenvalue parameter and on the real purely imaginary or complex nature of e for e specified as real an eigenvalue problem results for the natural frequencies i for waves propagating along the z direction of a cylinder of infinite extent when e is specified to be purely imaginary then an algebraic eigenvalue problem governing the edge vibrations end modes of a semi infinite cylinder is obtained the third eigenvalue problem can be obtained by considering to be prescribed and regarding e as the eigenvalue parameter the algebraic eigenvalue problem that results is quadratic in the eigenvalue parameter and admits solutions for e which may be real purely imaginary or complex complex e s correspond to edge vibrations in a cylinder which are exponentially damped trigonometric wave forms moreover for the case 0 the eigenvalue analysis yields e as the characteristic inverse decay lengths for systems of elastostatic self equilibrated edge effects in the context of st venant s principle all the eigenvalue problems are solved by efficient techniques based on subspace iteration examples of two four layer angle ply cylinders are presented to illustrate this comprehensive finite element analysis

some facets of the simple plant location polytope we relate the simple plant location problem to the vertex packing problem and derive several classes of facets of their associated integer polytopes

entropy production theorems and some consequences the total entropy production fluctuations are studied in some exactly solvable models for these systems the detailed fluctuation theorem holds even in the transient state provided initially that the system is prepared in thermal equilibrium the nature of entropy production during the relaxation of a system to equilibrium is analyzed the averaged entropy production over a finite time interval gives a better bound for the average work performed on the system than that obtained from the well known jarzynski equality moreover the average entropy production as a quantifier for information theoretic nature of irreversibility for finite time nonequilibrium processes is discussed

nonlinear fluctuation dissipation relations and stochastic models in nonequilibrium thermodynamics ii kinetic potential and variational principles for nonlinear irreversible processes abstract on the basis of a complete system of fluctuation dissipation relations considered in the first part of this series a variational principle for nonlinear irreversible processes is derived according to this principle the virtual entropy production functional analogous to the action in mechanics has an absolute minimum meaning on the real trajectory of a system the universal structure of the kinetic potential and the lagrangian of a system each contain complete information about fluctuations of macrovariables the connection of the lagrangian with the markovian kinetic operator of macrovariables is stated fundamental properties of dissipative potentials reflecting microscopic reversibility are considered the derived variational principle can be applied to closed systems the steady state of which is equilibrium as well as to open ones when external dynamic forces cause entropy flux through the system and put it into a steady non equilibrium state canonical transformations of macrovariables are considered

on the exact solution of large scale simple plant location problems abstract the simple plant location problem deals with the selection of facility sites from a set of possible locations with the intention of serving a given set of customers from the chosen locations the objective is to minimize the sum of the fixed charges for establishing the facilities and the transportation costs corresponding to the supply of the demands we show how to modify a primal dual version of erlenkotter s exact algorithm to get an improved procedure computational experience with large scale problems indicates that compared with erlenkotter s code an implementation of the modified algorithm is faster by more than one order of magnitude for real life problems with 1500 potential facility sites the increase of computational speed may even exceed the factor of 100

stokes efficiency and its stochastic properties abstract we study the stokes efficiency and its fluctuating properties in the case of a spatial asymmetric ratchet potential with a temporal asymmetric driving force from adiabatic to nonadiabatic regime our numerical investigations show that the average stokes efficiency and the average current decrease with increase in the frequency of driving for low frequency of driving i e in the case of an adiabatic regime we reproduced the analytical results supporting our numerical simulations by evaluating the probability distribution p s for stokes efficiency s we focus on the stochastic properties of stokes efficiency we find that in most of the parameter space fluctuations in s are comparable to or larger than the mean values in such a situation one has to study the nature of the full probability distribution of s we observe that with increase in frequency of driving the distribution becomes multipeaked at the same time the average stokes efficiency monotonically decreases with increase in frequency of the drive for high frequency of driving the distribution develops a peak at zero with further increase in frequency of the drive this peak gets sharper and finally at sufficiently high frequency we get a strong peak at zero indicating that there is no effective transport in this regime

reexamination of experimental tests of the fluctuation theorem the fluctuation theorem and the jarzynski equality are examined in the light of recent experimental tests for a particle dragged through a solvent it is shown that q the heat exchanged with the reservoir does not obey the jarzynski equality due to slowly decaying tails in its distribution for molecular stretching experiments substantial corrections to the jarzynski equality can result from not measuring the force at the end of the molecule that is moved we also present a proof of the fluctuation theorem for langevin dynamics that is considerably simpler than the standard proof

numerical modeling of acoustic emission in laminated tensile test specimens abstract acoustic emission from transverse matrix cracks and fiber fracture in typical laminated tensile test specimens is modeled the acoustic sources are described as time dependent displacement discontinuities which subsequently are translated to volume forces the transient waves are computed using a finite element model of the specimen s cross section the finite element modeling leads to a system of differential equations in the axial coordinate and time the differential equations are solved using fourier transforms and eigenmode superposition followed by inversion of the transforms through residue calculus and fft computed time histories for matrix cracking and fiber fracture are presented the highest frequency content in these signals corresponds typically to 300 khz a method to measure the average matrix crack propagation velocity is suggested

frequency division method for ae source characterization this paper describes a new algorithm based on a frequency division method by which a solution to the inverse source problem of acoustic emission can be obtained the algorithm is applicable to cases in which the acoustic emission signal can be expressed as a bilinear equation involving weighted green s functions or its spatial derivatives convolved with a common source time function through division of the detected signals in the frequency domain the common source time function is eliminated and the ratios of the weighting constants can be recovered by solving a set of linear equations using these recovered ratios the source time function can be found from the signal at any receiver point application of this algorithm is made to process the signals simulating the formation of a microcrack in an elastic plate modeled with a second order moment tensor dynamic information about the source is recovered by processing the signals at two receiver points if four receivers are used the second order tensor can be recovered at each frequency of the recorded signals additional information about the source can be extracted by diagonalizing and rotating the recovered moment tensor the effect of noise on the inversion scheme is also considered

a hybrid multistart heuristic for the uncapacitated facility location problem we present a multistart heuristic for the uncapacitated facility location problem based on a very successful method we originally developed for the p median problem we show extensive empirical evidence to the effectiveness of our algorithm in practice for most benchmarks instances in the literature we obtain solutions that are either optimal or a fraction of a percentage point away from it even for pathological instances created with the sole purpose of being hard to tackle our algorithm can get very close to optimality if given enough time it consistently outperforms other heuristics in the literature

extended heat fluctuation theorems for a system with deterministic and stochastic forces heat fluctuations over a time tau in a nonequilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components a brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity using a langevin equation we find the exact fourier transform of the distribution of these fluctuations for all tau by a saddle point method we obtain analytical results for the inverse fourier transform which for not too small tau agree very well with numerical results from a sampling method as well as from the fast fourier transform algorithm due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid the conventional heat fluctuation theorem is for infinite and for finite tau replaced by an extended fluctuation theorem that differs noticeably and measurably from it in particular for large fluctuations the ratio of the probability for absorption of heat by the particle from the fluid to the probability to supply heat by the particle to the fluid is much larger here than in the conventional fluctuation theorem

stationary and transient work fluctuation theorems for a dragged brownian particle recently wang et al carried out a laboratory experiment where a brownian particle was dragged through a fluid by a harmonic force with constant velocity of its center this experiment confirmed a theoretically predicted work related integrated transient fluctuation theorem itft which gives an expression for the ratio for the probability to find positive or negative values for the fluctuations of the total work done on the system in a given time in a transient state the corresponding integrated stationary state fluctuation theorem issft was not observed using an overdamped langevin equation and an arbitrary motion for the center of the harmonic force all quantities of interest for these theorems and the corresponding nonintegrated ones tft and ssft respectively are theoretically explicitly obtained in this paper while the tft and the itft are satisfied for all times the ssft and the issft only hold asymptotically in time suggestions for further experiments with arbitrary velocity of the harmonic force and in which also the issft could be observed are given in addition a nontrivial long time relation between the itft and the issft was discovered which could be observed experimentally especially in the case of a resonant circular motion of the center of the harmonic force

the usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure a method with which standard finite element programs can be used to compute dispersion relations in periodic composites is proposed the method is applied to two composite microstructures a two phase laminate and a fiber composite the dispersion relations computed for the laminate are compared with a known analytical solution and the agreement is very good the dispersion relations computed for the fibrous composite are compared with an existing approximate model and experimental results from the literature the agreement between the approximate model the experiments and the computations is very good in the wave guide case and satisfactory for the wave reflect case

probabilistic analysis of a relaxation for the k median problem this paper provides a probabilistic analysis of the so called strong linear programming relaxation of the k median problem when the number of points say n goes to infinity the analysis is performed under four classical models in location theory the euclidean network tree and uniform cost models for example we show that for the euclidean model and k k o n log n the value of the relaxation is almost surely within 0 3 percent of the optimum k median value for the uniform cost model and the same conditions on k we show that the value of the relaxation is almost surely 50 percent of the optimum k median value we also show that under various assumptions branch and bound algorithms that use the strong linear programming relaxation as a bound must almost surely expand a nonpolynomial number of nodes to solve the k median problem to optimality finally we report extensive computational experiments as predicted by the probabilistic analysis the relaxation was not as tight for the problem

hamiltonian derivation of a detailed fluctuation theorem we analyze the microscopic evolution of a system undergoing a far from equilibrium thermodynamic process explicitly accounting for the degrees of freedom of participating heat reservoirs we derive a hybrid result similar in form to both the fluctuation theorem and a statement of detailed balance we relate this result to the steady state fluctuation theorem and to a free energy relation valid far from equilibrium

on the uncapacitated plant location problem ii facets and lifting theorems several lifting procedures for facets of the uncapacitated plant location problem are discussed also necessary and sufficient conditions for nontrivial facets with 0 1 integer coefficients are derived in addition all of the facets for the case of three or more plants and three destinations are identified

a projection method for the uncapacitated facility location problem several algorithms already exist for solving the uncapacitated facility location problem the most efficient are based upon the solution of the strong linear programming relaxation the dual of this relaxation has a condensed form which consists of minimizing a certain piecewise linear convex function this paper presents a new method for solving the uncapacitated facility location problem based upon the exact solution of the condensed dual via orthogonal projections the amount of work per iteration is of the same order as that of a simplex iteration for a linear program inm variables and constraints wherem is the number of clients for comparison the underlying linear programming dual hasmn m n variables andmn n constraints wheren is the number of potential locations for the facilities the method is flexible as it can handle side constraints in particular when there is a duality gap the linear programming formulation can be strengthened by adding cuts numerical results for some classical test problems are included

a conjugate rosen s gradient projection method with global line search for piecewise linear concave optimization abstract the kelley cutting plane method is one of the methods commonly used to optimize the dual function in the lagrangian relaxation scheme usually the kelley cutting plane method uses the simplex method as the optimization engine it is well known that the simplex method leaves the current vertex follows an ascending edge and stops at the nearest vertex what would happen if one would continue the line search up to the best point instead as a possible answer we propose the face simplex method which freely explores the polyhedral surface by following the rosen s gradient projection combined with a global line search on the whole surface furthermore to avoid the zig zagging of the gradient projection we propose a conjugate gradient version of the face simplex method for our preliminary numerical tests we have implemented this method in matlab this implementation clearly outperforms basic matlab implementations of the simplex method in the case of state of the art simplex implementations in c or similar our matlab implementation is only competitive for the case of many cutting planes

the plant location problem with demand dependent setup costs and centralized allocation suppose that customers are situated at the nodes of a transportation network and a service company plans to locate a number of facilities that will serve the customers the objective is to minimize the sum of the total setup cost and the total transportation cost the setup cost of a facility is demand dependent that is it depends on the number of customers that are served by the facility centralized allocation of customers to facilities is assumed that is the service company makes a decision about allocation of customers to facilities in the case of a general network the model can be formulated as a mixed integer programming problem for the case of a tree network we develop a polynomial time dynamic programming algorithm

discontinuous piecewise linear optimization a theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems dealing with functions for which theridges are known a penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions although the theory is expounded in detail in the special case of discontinuous piecewiselinear functions it is straightforwardly extendable using standard nonlinear programming techniques tononlinear discontinuous piecewise differentiable functions the descent algorithm which is elaborated uses active set and projected gradient approaches it is a generalization of the ideas used by conn to deal with nonsmoothness in thel1 exact penalty function and it is based on the notion ofdecomposition of a function into a smooth and a nonsmooth part the constrained case is reduced to the unconstrained minimization of a piecewise linear l1 exact penalty function we also discuss how the algorithm is modified when it encounters degenerate points preliminary numerical results are presented the algorithm is applied to discontinuous optimization problems from models in industrial engineering 1998 the mathematical programming society inc published by elsevier science b v