a unified procedure for construction of theories of deformable media i classical continuum physics a new unified procedure for constructing continuum theories of deformable media is presented and used in this and a companion paper the procedure starts with a balance of energy and derives from it all the relevant balance laws that may also include those that are associated with thermal electrical and magnetic effects the basic energetic ingredients that are included in the balance of energy depend of course on the nature of the particular theory of material behaviour desired the advantage of the new procedure becomes especially apparent when one considers formulation of a new theory of material behaviour for which additional balance laws involving new kinetic quantities are required to accompany any additional basic kinematic and thermal variables additional to those in the classical formulation indeed in the formulation of such new theories usually little or no previous information is available concerning properties of the new kinetic quantities in the additional balance laws and in this connection the unified procedure of this paper provides a simple attractive setting for deriving the basic equations that are automatically consistent with the energy balance in this paper first the basic features of the new procedure are illustrated in the context of classical thermomechanics generalizations of this thermomechanical theory are then discussed in two cases 1 in the presence of an additional kinematic variable and 2 in the presence of full electromagnetic effects both of these generalizations bring out some interesting novel features when new theories are being constructed

discontinuous galerkin finite element methods for second order hyperbolic problems abstract we prove a priori and a posteriori error estimates for a finite element method for linear second order hyperbolic equations based on a space time finite element discretization with the basis functions being continuous in space and discontinuous in time

a characterization of ideal polyhedra in hyperbolic 3 space the goals of this paper are to provide a characterization of dihedral angles of convex ideal those with all vertices on the sphere at infinity polyhedra in h3 and also of those convex polyhedra with some vertices on the sphere at infinity and some in the finite part of h3 these characterizations are given in respectively theorems 0 1 and 10 5 the first theorem is proved in detail while the proof of the second which is similar is only outlined the results of this paper grow out of the general framework of the author s doctoral dissertation 13 as published in 20 a lot of the language and some of the auxilary results come from there as well so familiarity with the latter reference is very helpful the necessity of the conditions postulated in theorem 0 1 has been shown in 14 hence only the sufficiency direction will be shown in the current paper in 1832 jakob steiner asked for a combinatorial characterization of convex polyhedra inscribed in the sphere this was considered intractable it took almost a hundred years to find a single example of an uninscribable combinatorial type by steinitz 24 however theorem 0 1 gives such a characterization section 11 is dedicated to a very brief historical survey and some purely graph theoretic and computational geometric consequences of theorem 0 1 in order to state this theorem suppose that a convex ideal polyhedron p in h3 is given let p denote the poincar dual of p and assign to each edge e of p a weight w e equal to the exterior dihedral angle at the corresponding edge e of p then the following result holds

geometry of integral binary hermitian forms abstract we generalize conway s approach to integral binary quadratic forms to study integral binary hermitian forms over quadratic imaginary extensions of q we show that every indefinite anisotropic form determines a plane ocean in mendoza s spine associated to the corresponding bianchi group in the hyperbolic 3 space the ocean can be used to compute the group of integral transformations preserving the hermitian form

general energy decay in a timoshenko type system of thermoelasticity of type iii with a viscoelastic damping in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove a general decay result from which the exponential and polynomial decays are only special cases

fiducial theory and optimal inference it is shown that the fiducial distribution in a group model or more generally a quasigroup model determines the optimal equivariant frequentist inference procedures the proof does not rely on existence of invariant measures and generalizes results corresponding to the choice of the right haar measure as a bayesian prior classical and more recent examples show that fiducial arguments can be used to give good candidates for exact or approximate confidence distributions it is here suggested that the fiducial algorithm can be considered as an alternative to the bayesian algorithm for the construction of good frequentist inference procedures more generally

a note on discontinuity waves in type iii thermoelasticity two recent nonlinear theories of thermoelasticity developed by green and naghdi are examined it is shown that in type ii theory second sound is permissible and both mechanical and temperature waves may propagate in type iii theory we show that the situation is more analogous to that in classical nonlinear thermoelasticity one wave propagates and a homothermal temperature wave is allowed

arithmetic of arithmetic coxeter groups in the 1990s j h conway published a combinatorial geometric method for analyzing integer valued binary quadratic forms bqfs using a visualization he named the topograph conway revisited the reduction of bqfs and the solution of quadratic diophantine equations such as pell s equation it appears that the crux of his method is the coincidence between the arithmetic group p g l 2 z and the coxeter group of type 3 there are many arithmetic coxeter groups and each may have unforeseen applications to arithmetic we introduce conway s topograph and generalizations to other arithmetic coxeter groups this includes a study of arithmetic flags and variants of binary quadratic forms

strain gradient theory of chiral cosserat thermoelasticity without energy dissipation in this paper we use the green naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of cosserat thermoelastic bodies the theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor the constitutive equations for isotropic chiral thermoelastic materials are presented in this case in contrast with the classical cosserat thermoelasticity a thermal field produces a microrotation of the particles the thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory existence and uniqueness results are established the theory is used to study the effects of a concentrated heat source in an unbounded homogeneous and isotropic chiral solid

a spacetime discontinuous galerkin method for hyperbolic heat conduction non fourier conduction models remedy the paradox of infinite signal speed in the traditional parabolic heat equation for applications involving very short length or time scales hyperbolic conduction models better represent the physical thermal transport processes this paper reviews the maxwell cattaneo vernotte modification of the fourier conduction law and describes its implementation within a spacetime discontinuous galerkin sdg finite element method that admits jumps in the primary variables across element boundaries with arbitrary orientation in space and time a causal advancing front meshing procedure enables a patch wise solution procedure with linear complexity in the number of spacetime elements an h adaptive scheme and a special sdg shock capturing operator accurately resolve sharp solution features in both space and time numerical results for one spatial dimension demonstrate the convergence properties of the sdg method as well as the effectiveness of the shock capturing method simulations in two spatial dimensions demonstrate the proposed method s ability to accurately resolve continuous and discontinuous thermal waves in problems where rapid and localized heating of the conducting medium takes place

a re examination of the basic postulates of thermomechanics this paper is mainly concerned with a re examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics however the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed more specifically after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics the basic postulates of the purely mechanical theory for a continuum including its specialization for a rigid body is re examined this includes some differences from the usual procedure on the subject next thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables a discussion of a theory of heat or a purely thermal theory is provided which differs from the usual development in the classical thermodynamics a detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well motivated constitutive equations special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves the remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject

a new unconditionally stable fractional step method for non linear coupled thermomechanical problems a new class of time stepping algorithms for strongly coupled thermomechanical problems is presented which retains the computational convenience of traditional staggered algorithms without upsetting the unconditional stability property characteristic of fully implicit monolithic schemes 11 the proposed schemes are fractional step methods associated with a two phase operator split of the full non linear system of thermoelasticity into an adiabatic elastodynamics phase followed by a heat conduction phase at fixed configuration this operator split is shown to inherit the contractivity property of the full problem of evolution thus leading to unconditionally b stable product formula algorithms in sharp contrast with this stability result traditional staggered algorithms based on an isothermal mechanical phase followed by a heat conduction phase with an effective heat source are shown to lead at best to conditionally stable schemes it is further shown that the actual implementation of these two classes of schemes is essentially identical the numerical simulations presented include both dynamic and quasi static problems and are shown to closely replicate the stability estimates and non linear stability results derived for these two classes of staggered schemes

an unconditionally stable algorithm for generalized thermoelasticity based on operator splitting and time discontinuous galerkin finite element methods an efficient time stepping algorithm is proposed based on operator splitting and the space time discontinuous galerkin finite element method for problems in the non classical theory of thermoelasticity the non classical theory incorporates three models the classical theory based on fourier s law of heat conduction resulting in a hyperbolic parabolic coupled system a non classical theory of a fully hyperbolic extension and a combination of the two the general problem is split into two contractive sub problems namely the mechanical phase and the thermal phase each sub problem is discretized using the space time discontinuous galerkin finite element method the sub problems are stable which then leads to unconditional stability of the global product algorithm a number of numerical examples are presented to demonstrate the performance and capability of the method

on timoshenko type systems with type iii thermoelasticity asymptotic behavior abstract in this study we consider a thermoelastic beam system where the oscillations are defined by the timoshenko model and heat conduction is given by the green and naghdi theories we provide an explicit characterization of the decay rate which can be exponential or polynomial depending on the relationship between the coefficients of the wave propagation speed

partitioned coupling of advection diffusion reaction systems and brinkman flows we present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection diffusion reaction systems and incompressible viscous flow the space discretisation of the governing equations is based on mixed finite element methods defined on unstructured meshes whereas the time integration hinges on an operator splitting strategy that exploits the differences in scales between the reaction advection and diffusion processes considering the global system as a number of sequentially linked sets of partial differential and algebraic equations the flow solver presents the advantage that all unknowns in the system here vorticity velocity and pressure can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective the robustness of the proposed method is illustrated with a series of numerical tests in 2d and 3d relevant in the modelling of bacterial bioconvection and boussinesq systems

stabilisation of a thermo elastic system under nonuniformly bounded disturbances in the boundary input abstractwe consider the exponential stabilisation for a thermo elastic system of type ii with nonuniformly bounded external disturbances in the boundary control we begin with finding feedback controls for the system without disturbances by lyapunov function approach then based on the resulting feedback control we give new dynamic feedback control laws that make the system exponentially stable by tracking disturbances exponentially through a time varying high gain observer we apply the linear operator semi group theory to prove the well posedness of the resulting closed system finally we prove that the solution of the closed loop system can approach zero polynomially or exponentially by the lyapunov function approach