integral representation and green s functions for 3d time dependent thermo piezoelectricity abstract a boundary integral method is developed for 3d time dependent quasistatic thermo piezoelectricity this time domain formulation involves only surface quantities as a result volume discretization is completely avoided green s functions are derived by resorting to radon transform and presented in integral form reductions to the case of isotropic dielectric solid have been worked out in detail and its corresponding solutions expressed in explicit form are consistent with the existing solutions

a simple level set method for solving stefan problems a simple level set method for solving stefan problems is presented this method can be applied to problems involving dendritic solidification our method consists of an implicit finite difference scheme for solving the heat equation and a level set approach for capturing the front between solid and liquid phases of a pure substance our method is accurate with respect to some exact solutions of the stefan problem results indicate that this method can handle topology changes and complicated interfacial shapes and that it can numerically simulate many of the physical features of dendritic solidification

on uniform fields in heterogeneous media uniform elastic strain fields are found in two phase fibrous media of arbitrary transverse geometry and in two phase media of any phase geometry in initially stress free fibrous solids a single uniform field can be created by certain proportionally changing tractions derived from a uniform overall stress in the presence of phase eigenstrains many overall stress states can be superimposed to create uniform strain fields in fibrous media the existence of such fields is exploited to establish a number of exact results for two phase fibre systems these include universal connections between phase and overall moduli and between components of phase stress and strain fields expressions for new transformation influence functions and concentration factors in terms of their mechanical counterparts and also expressions for the overall stresses and strains caused by phase eigenstrains examples are presented for macroscopically monoclinic fibrous composites with transversely isotropic phases in two phase media of arbitrary phase geometry there is only a single uniform stress and strain field for each non vanishing eigenstrain state the existence of this field is utilized in derivation of exact connections between transformation and mechanical influence functions and concentration factors

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

exact relations between the thermoelectroelastic moduli of heterogeneous materials exact relations are obtained between the effective thermoelectroelastic moduli of two phase heterogeneous media and their corresponding isothermal effective electroelastic moduli the relations are obtained by generalizing the results of v m levin and b w rosen and z hashin to the inherently anisotropic coupling between the electric and elastic fields in thermoelectroelastic composites the explicit expressions that are obtained can be used to obtain the effective thermal expansion and pyroelectric coefficients of the composite when the effective electroelastic elastic piezoelectric and dielectric moduli are known either by theory or experiment the results also provide a means to assess the internal consistency of any micromechanics model that is proposed to estimate the thermoelectroelastic and electroelastic moduli of the composite it is verified that when piezoelectric coupling is absent the expressions reduce to those of b w rosen and z hashin for thermoelastic composite media finally the resulting exact relations are exploited to prove the interesting phenomena that two phase heterogeneous media can exhibit a net pyroelectric response even though neither of the individual phases exhibits pyroelectricity

sofic groups and direct finiteness abstract we construct an analogue of von neumann s affiliated algebras for sofic group algebras over arbitrary fields consequently we settle kaplansky s direct finiteness conjecture for sofic groups

capturing the behavior of bubbles and drops using the variational level set approach we reproduce the general behavior of complicated bubble and droplet motions using the variational level set formulation introduced by the authors earlier our approach here ignores inertial effects thus the motion is only correct as an approximation for very viscous problems however the steady states are true equilibrium solutions inertial forces will be added in future work the problems include soap bubbles colliding and merging drops falling or remaining attached to a generally irregular ceiling and liquid penetrating through a funnel in both two and three dimensions each phase is identified with a particular level set function the zero level set of this function is that particular phase boundary the level set functions all evolve in time through a constrained gradient descent procedure so as to minimize an energy functional the functions are coupled through physical constraints and through the requirements that different phases do not overlap and vacuum regions do not develop both boundary conditions and inequality constraints are cast in terms of either local or global equality constraints the gradient projection method leads to a system of perturbed by curvature if surface tension is involved hamilton jacobi equations coupled through a constraint the coupling is enforced using the lagrange multiplier associated with this constraint the numerical implementation requires much of the modern level set technology in particular we achieve a significant speed up by using the fast localization algorithm of h k zhao m kang b merriman d peng and s osher

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

the amenability of affine algebras abstract we introduce the notion of amenability for affine algebras we characterize amenability by folner sequences paradoxicality and the existence of finitely invariant dimension measures then we extend the results of rowen on ranks from affine algebras of subexponential growth to amenable affine algebras

exact relations for effective tensors of composites necessary conditions and sufficient conditions typically the elastic and electrical properties of composite materials are strongly microstructure dependent so it comes as a nice surprise to come across exact formulae for effective moduli that are universally valid no matter what the microstructure such exact formulae provide useful benchmarks for testing numerical and actual experimental data and for evaluating the merit of various approximation schemes they can also be regarded as fundamental invariances existing in a given physical context classic examples include hill s formulae for the effective bulk modulus of a two phase mixture when the phases have equal shear moduli levin s formulae linking the effective thermal expansion coefficient and effective bulk modulus of two phase mixtures and dykhne s result for the effective conductivity of an isotropic two dimensional polycrystalline material here we present a systematic theory of exact relations embracing the known exact relations and establishing new ones the search for exact relations is reduced to a search for matrix subspaces having a structure of special jordan algebras one of many new exact relations is for the effective shear modulus of a class of three dimensional polycrystalline materials we present complete lists of exact relations for three dimensional thermoelectricity and for three dimensional thermopiezoelectric composites that include all exact relations for elasticity thermoelasticity and piezoelectricity as particular cases 2000 john wiley sons inc

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

from microstructure independent formulas for composite materials to rank one convex non quasiconvex functions examples of non quasiconvex functions that are rank one convex are rare in this paper we construct a family of such functions by means of the algebraic methods of the theory of exact relations for polycrystalline composite materials developed to identify g closed sets of positive codimensions the algebraic methods are used to construct a set of materials of positive codimension that is closed under lamination but is not g closed the well known link between g closed sets and quasiconvex functions and sets closed under lamination and rank one convex functions is then used to construct a family of rotationally invariant nonnegative and 2 homogeneous rank one convex functions that are not quasiconvex

sofic groups and profinite topology on free groups abstract we give a definition of weakly sofic groups w sofic groups our definition is a rather natural extension of the definition of sofic groups where instead of the hamming metric on symmetric groups we use general bi invariant metrics on finite groups the existence of non w sofic groups is equivalent to some conjecture about profinite topology on free groups

approximations of groups characterizations of sofic groups and equations over groups we give new characterizations of sofic groups a group g is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups a group g is sofic if and only if any system of equations solvable in all alternating groups is solvable over g the last characterization allows to express soficity of an existentially closed group by sentences

linear sofic groups and algebras we introduce and systematically study linear sofic groups and linear sofic algebras this generalizes amenable and lef groups and algebras we prove that a group is linear sofic if and only if its group algebra is linear sofic we show that linear soficity for groups is a priori weaker than soficity but stronger than weak soficity we also provide an alternative proof of a result of elek and szabo which states that sofic groups satisfy kaplansky s direct finiteness conjecture

high order essentially nonsocillatory schemes for hamilton jacobi equations hamilton jacobi h j equations are frequently encountered in applications e g in control theory and differential games h j equations are closely related to hyperbolic conservation laws in one space dimension the former is simply the integrated version of the latter similarity also exists for the multidimensional case and this is helpful in the design of difference approximations in this paper high order essentially nonoscillatory eno schemes for h j equations are investigated which yield uniform high order accuracy in smooth regions and sharply resolve discontinuities in the derivatives the eno scheme construction procedure is adapted from that for hyperbolic conservation laws the schemes are numerically tested on a variety of one dimensional and two dimensional problems including a problem related to control optimization and high order accuracy in smooth regions good resolution of discontinuities in the derivatives and convergence to viscosity solutions are observed

temperature related effective properties and exact relations for thermo magneto electro elastic fibrous composites based on the asymptotic homogenization method a three dimensional boundary value problem for two phase periodic thermo magneto electro elastic composites is presented we consider composite materials consisting of identical parallel cylindrical fibers periodically distributed in a matrix both constituents are transversely isotropic and the unit cell has rhombohedral shape the derivation of the corresponding homogenized problem effective coefficients and local problems is summarized exact relations are derived without imposing any restriction on the global behavior of such fibrous composite materials in particular proportionality relations linking the temperature related effective coefficients are obtained simple analytical formulae are obtained for these temperature related effective coefficients as a function of four effective elastic coefficients and they show the existence of pyroelectric and pyromagnetic product properties in the composite material when these effects are not present at the constituents level moreover the formulae are valid for any fiber cross section geometry and periodicity an analytical formula of the fiber area fraction for which the effective pyroelectric and pyromagnetic coefficients are maximal is given some numerical examples are considered in order to illustrate the relevance of the combination of the exact relations with homogenization methods comparisons with analytical and numerical results are included