analysis of two active set type methods to solve unilateral contact problems in this work two active set type methods are considered in order to solve a mathematical problem which describes the frictionless contact between a deformable body and a perfectly rigid obstacle the so called signorini problem these methods are the primal dual active set method and the projection iterative method our aim here is to analyze these two active set type methods and to carry out a comparison with the well known augmented lagrangian method by considering two representative contact problems in the case of large and small deformation after presenting the mechanical formulation in the hyperelasticity framework we establish weak formulations of the problem and the existence result of the weak solution is recalled then we give the finite element approximation of the problem and a description of the numerical methods is presented the main result of this work is to provide a convergence result for the projection iterative method finally we present numerical simulations which illustrate the behavior of the solution and allow the comparison of the numerical methods

exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

energy controlling time integration methods for nonlinear elastodynamics and low velocity impact it is now well established that discrete energy conservation dissipation plays a key role for the unconditional stability of time integration schemes in nonlinear elastodynamics in this paper from a rigorous conservation analysis of the hilber hughes taylor time integration scheme h hilber t hughes r taylor improved numerical dissipation for time integration algorithms in structural dynamics earthquake engrg struct dynam 5 1977 283 292 we propose an original way of introducing a controllable energy dissipation while conserving momenta in conservative strategies like j simo n tarnow the discrete energy momentum method conserving algorithms for nonlinear elastodynamics z angew math phys 43 1992 757 792 moreover we extend the technique proposed in o gonzalez exact energy and momentum conserving algorithms for general models in nonlinear elasticity comput methods appl mech engrg 190 13 14 2000 1763 1783 to provide energy controlling time integration schemes for frictionless contact problems enforcing the standard kuhn tucker conditions at time discretization points we also extend this technique to viscoelastic models numerical tests involving the impact of incompressible elastic or viscoelastic bodies in large deformation are proposed to confirm the theoretical analysis

on the formulation of high frequency dissipative time stepping algorithms for nonlinear dynamics part ii second order methods we present in this paper the formulation of a new high frequency dissipative time stepping algorithm for nonlinear elastodynamics that is second order accurate in time the new scheme exhibits unconditional energy dissipation and momentum conservation and thus the given name of energy dissipative momentum conserving second order scheme edmc 2 leading also to the conservation of the relative equilibria of the underlying physical system the unconditional character of these properties applies not only with respect to the time step size but equally important with respect to the considered elastic potential moreover the dissipation properties are fully controlled through an algorithmic parameter reducing to existing fully conserving schemes if desired the design of the new algorithm is described in detail including a complete analysis of its dissipation conservation properties in the fully nonlinear range of finite elasticity to motivate the different constructions that lead to the dissipative properties of the final scheme the same arguments are used first in the construction of new linear time stepping algorithms for the system of linear elastodynamics including first and second order schemes the new schemes exhibit a rigorous decay of the physical energy with the second order schemes formulated in a general two stage formula accommodating the aforementioned control parameter in the dissipation of the energy a complete spectral analysis of the new schemes is presented in this linear range to evaluate their different numerical properties in particular the dissipative character of the proposed schemes in the high frequency range is fully demonstrated in fact it is shown that the new second order scheme is l stable most remarkably the extension of these ideas to the nonlinear range is accomplished avoiding the use of multi stage formulae given the freedom gained in using general nonlinear relations while preserving the conservation laws of the momenta and the corresponding relative equilibria several representative numerical simulations are presented in the context of nonlinear elastodynamics to evaluate the performance of the newly proposed schemes

no hypersignaling principle a paramount topic in quantum foundations rooted in the study of the einstein podolsky rosen epr paradox and bell inequalities is that of characterizing quantum theory in terms of the spacelike correlations it allows here we show that to focus only on spacelike correlations is not enough we explicitly construct a toy model theory that while not contradicting classical and quantum theories at the level of spacelike correlations still displays an anomalous behavior in its timelike correlations we call this anomaly quantified in terms of a specific communication game the hypersignaling phenomena we hence conclude that the principle of quantumness if it exists cannot be found in spacelike correlations alone nontrivial constraints need to be imposed also on timelike correlations in order to exclude hypersignaling theories

formulation and analysis of two energy consistent methods for nonlinear elastodynamic frictional contact problems energy conserving algorithms are necessary to solve nonlinear elastodynamic problems in order to recover long term time integration accuracy and stability furthermore some physical phenomena such as friction can generate dissipation then in this work we present and analyse two energy consistent algorithms for hyperelastodynamic frictional contact problems which are characterised by a conserving behaviour for frictionless impacts but also by an admissible frictional dissipation phenomenon the first approach permits one to enforce respectively the kuhn tucker and persistency conditions during each time step by combining an adapted continuation of the newton method and a lagrangean formulation in addition the second method which is based on the work in p hauret p le tallec energy controlling time integration methods for nonlinear elastodynamics and low velocity impact comput methods appl mech eng 195 2006 4890 4916 represents a specific penalisation of the unilateral contact conditions some numerical simulations are presented to underscore the conservative or dissipative behaviour of the proposed methods

logarithmic laws for compressible turbulent boundary layers dimensional similarity arguments proposed by millikan are used with the morkovin hypothesis to deduce logarithmic laws for compressible turbulent boundary layers as an alternative to the traditional van driest analysis it is shown that an overlap exists between the wall layer and the defect layer and this leads to logarithmic behavior in the overlap region the von karman constant is found to depend parametrically on the mach number based on the friction velocity the dimensionless total heat flux and the specific heat ratio even though it remains constant at approximately 0 41 for a freestream mach number range of 0 to 4 544 with adiabatic wall boundary conditions it rises sharply as the mach number increases significantly beyond 4 544 the intercept of the logarithmic law of the wall is found to depend on the mach number based on the friction velocity the dimensionless total heat flux the prandtl number evaluated at the wall and the specific heat ratio on the other hand the intercept of the logarithmic defect law is parametric in the pressure gradient parameter and all of the aforementioned dimensionless variables except the prandtl number a skin friction law is also deduced for compressible boundary layers the skin friction coefficientmore is shown to depend on the momentum thickness reynolds number the wall temperature ratio and all of the other parameters already mentioned 26 refs less

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

contact impact by the pinball algorithm with penalty and lagrangian methods contact impact algorithms which are sometimes called slideline algorithms are a computationally time consuming part of many explicit simulations of non linear problems because they involve many branches so they are not amenable to vectorization which is essential for speed on supercomputers the pinball algorithm is a simplified slideline algorithm which is readily vectorized its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs it can be implemented in either a lagrange multiplier or penalty method it is shown that in any lagrange multiplier method no iterations are needed to define the contact surface examples of solutions and running times are given

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

bounding the set of quantum correlations we introduce a hierarchy of conditions necessarily satisfied by any distribution p ensuremath alpha ensuremath beta representing the probabilities for two separate observers to obtain outcomes ensuremath alpha and ensuremath beta when making local measurements on a shared quantum state each condition in this hierarchy is formulated as a semidefinite program among other applications our approach can be used to obtain upper bounds on the quantum violation of an arbitrary bell inequality it yields for instance tight bounds for the violations of the collins et al inequalities

skin friction and velocity profile family for compressible turbulent boundary layers the paper presents a general approach to constructing mean velocity profiles for compressible turbulent boundary layers with isothermal or adiabatic walls the theory is based on a density weighted transformation that allows the extension of the incompressible similarity laws of the wall to the compressible regions the velocity profile family is compared to a range of experimental data and excellent agreement is obtained a self consistent skin friction law which satisfies the proposed velocity profile family is derived and compared with the well known van driest ii theory for boundary layers in zero pressure gradient the results are found to be at least as good as those obtained by using the van driest ii transformation

temporal quantum correlations and leggett garg inequalities in multilevel systems we show that the quantum bound for temporal correlations in a leggett garg test analogous to the tsirelson bound for spatial correlations in a bell test strongly depends on the number of levels n that can be accessed by the measurement apparatus via projective measurements we provide exact bounds for small n that exceed the known bound for the leggett garg inequality and we show that in the limit n the leggett garg inequality can be violated up to its algebraic maximum

sequences of projective measurements in generalized probabilistic models we define a simple rule that allows us to describe sequences of projective measurements for a broad class of generalized probabilistic models this class embraces quantum mechanics and classical probability theory but for example also the hypothetical popescu rohrlich box for quantum mechanics the definition yields the established luders rule which is the standard rule for updating the quantum state after a measurement for the general case it can be seen as being the least disturbing or most coherent way of performing sequential measurements we show as an example that the spekkens toy model spekkens 2007 phys rev a 75 032110 provides an instance of our definition we also demonstrate the possibility of strong postquantum correlations as well as the existence of triple slit correlations for certain nonquantum toy models

how to overcome indetermination and interpenetration in granular systems via nonsmooth contact dynamics an exploratory investigation abstract the present paper is an exploratory investigation to overcome difficulties encountered in the simulation of dense granulates when a nscd approach is used some simple examples permit identification of impulse indetermination as the main cause of the failure or the slowdown of the numerical algorithm we propose to deal directly with the space of impulses with null resulting momentum a prediction correction scheme is detailed and enriched to restrict at best the interpenetration finally sophisticated tools are developed to preserve the sparsity of the matrices and consequently to ensure an efficient implementation of an adapted nonsmooth solver

van driest transformation and compressible wall bounded flows the transformation validity question utilizing resulting data from direct numerical simulations dns of supersonic isothermal cold wall channel flow was investigated the dns results stood for a wide scope of parameter and were suitable for the purpose of examining the generality of van driest transformation the van driest law of the wall can be obtained from the inner layer similarity arguments it was demonstrated that the van driest transformation cannot be incorporated to collapse the sublayer and log layer velocity profiles simultaneously velocity and temperature predictions according to the preceding composite mixing length model were presented despite satisfactory congruity with the dns data the model must be perceived as an engineering guide and not as a rigorous analysis

is a time symmetric interpretation of quantum theory possible without retrocausality huw price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal i e it must involve influences that travel backwards in time one of price s assumptions is that the quantum state is a state of reality however one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no go theorems including recent proofs of the reality of the quantum state here we show that this assumption can be replaced by a different assumption called mediation that plausibly holds independently of the status of the quantum state we also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely we show that our assumptions imply a timelike analogue of bell s local causality criterion and in doing so give a new interpretation of timelike violations of bell inequalities namely they show the impossibility of a non retrocausal time symmetric ontology

a continuum based finite element formulation for the implicit solution of multibody large deformation frictional contact problems in this paper a formulation is presented for the finite element treatment of multibody large deformation frictional contact problems the term multibody is used to mean that when two bodies mechanically contact both may be deformable a novel aspect of the approach advocated is that the equations governing contact are developed in the continuum setting first before deriving the corresponding finite element equations this feature distinguishes the current work from many earlier treatments of contact problems and renders it considerably more general in particular the approach yields a characterization of the frictional constraint assuming a coulomb law suitable for arbitrary discretizations in either two or three dimensions a geometric framework is constructed within which both frictionless and frictional response are naturally described making subsequent finite element discretization a straightforward substitution of finite dimensional solution spaces for their continuum counterparts to our knowledge this general formulation and implementation of the frictional contact problem in a finite element setting has not been reported previously in the literature the development includes exact linearization of the statement of virtual work which enables optimal convergence properties for newton raphson solution strategies and which appears to be highly desirable if not essential for the general robustness of implicit finite element techniques since the theory and subsequent linearization require no limitations on the amount of deformation or relative sliding that can occur the resulting treatment of frictional contact is suitable for a wide range of examples displaying significant non linear behaviour this assertion is substantiated through presentation of a variety of examples in both two and three dimensions

reply by the authors to f motallebi m rightly pointed out the misprints in eqs 8 and 10 ref 1 in addition to these errors introduced in printing there are others that have been reported in the errata that appeared in aiaa journal vol 32 no 11 1993 p 2192 these errors do not change our results and conclusions since our program and analysis are correct the horizontal axis of fig la is labeled correctly although in step 2 of the skin friction algorithm it is referred to as re 2 when discussing fig 1 we considered only incompressible flows and hence the parameter req was used however as we extended the algorithm from incompressible flows to compressible flows an important step was to change the parameter in the n correlation from rcq viscosity evaluated in the freestream to re 2 viscosity evaluated at the wall following fernholz and finley see the discussion following eq 8 this change was stated clearly in the beginning of sec ii we disagree with motallebi s statement that the algorithm is limited to hypersonic flows the current method can be considered as an extension of coles method which was proposed mainly for low speed flows for m 0 the method reproduces the karman schoenherr skin friction formula in the published paper we gave examples only for high mach number flows because this is where the model is most likely to break down supersonic flows are less severe test cases and the model works well figure 1 shows an example where the comparison of the present algorithm with the data of moore and harkness was made for a flow over an

simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized α scheme abstract this paper presents a formalism for the transient simulation of nonsmooth dynamic mechanical systems composed of rigid and flexible bodies kinematic joints and frictionless contact conditions the proposed algorithm guarantees the exact satisfaction of the bilateral and unilateral constraints both at position and velocity levels thus it significantly differs from penalty techniques since no penetration is allowed the numerical scheme is obtained in two main steps firstly a splitting method is used to isolate the contributions of impacts which shall be integrated with only first order accuracy from smooth contributions which can be integrated using a higher order scheme secondly following the idea of gear gupta and leimkuhler the equation of motion is reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels after time discretization the equation of motion involves two complementarity conditions and it can be solved at each time step using a monolithic semi smooth newton method the numerical behavior of the proposed method is studied and compared to other approaches for a number of numerical examples it is shown that the formulation offers a unified and valid approach for the description of contact conditions between rigid bodies as well as between flexible bodies

lagrange constraints for transient finite element surface contact a new approach to enforce surface contact conditions in transient non linear finite element problems is developed in this paper the method is based on the lagrange multiplier concept and is compatible with explicit time integration operators compatibility with explicit operators is established by referencing lagrange multipliers one time increment ahead of associated surface contact displacement constraints however the method is not purely explicit because a coupled system of equations must be solved to obtain the lagrange multipliers an important development herein is the formulation of a highly efficient method to solve the lagrange multiplier equations the equation solving strategy is a modified gauss seidel method in which non linear surface contact force conditions are enforced during iteration the new surface contact method presented has two significant advantages over the widely accepted penalty function method surface contact conditions are satisfied more precisely and the method does not adversely affect the numerical stability of explicit integration transient finite element analysis results are presented for problems involving impact and sliding with friction a brief review of the classical lagrange multiplier method with implicit integration is also included