Implementation of MCA in the framework of LIGGGHTS

We describe the implementation of the Movable Cellular Automata Method (MCA) within the framework of the open-source code LIGGGHTS to simulate complex solid behaviour; most importantly plastic deformation, on different scales. The developed code extends the capabilities of the MCA method, as well as that of LIGGGHTS software; which simulates granular behaviour and is based on the discrete element method. The main difference between MCA and DEM is that the interaction between the particles is based on a many-body forces form of inter-automata interactions, similar to the embedded atom method used in molecular dynamics, because pair-wise interactions between elements used in DEM are insufficient to simulate irreversible strain accumulation (plasticity) in ductile consolidated materials. We first give an overview of the MCA method and its significance, followed by the implementation approach. The code has been successfully verified against analytical data

Representation of SU(infinity) Algebra for Matrix Models

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N^2-1) times (N^2-1) matrices of the SU(N) generators go to those of the Poisson algebra in the large N limit. However, it is not the case for the N times N matrices in the fundamental representation.Comment: 8 page

Numerical simulation of mechanical behaviour and prediction of effective properties of metal matrix composites with consideration for structural evolution under shock wave loading

Mechanical behaviour of stochastic metal-ceramic composite materials under shock wave loading was numerically simulated on mesoscopic scale level. Deformation of mesoscopic volumes of composites whose structure consisted of a metal matrix and randomly distributed ceramic inclusions was simulated. The results of numerical simulation were used for numerical evaluation of effective elastic and strength properties of metal-ceramic materials with different values of volume concentration of ceramic inclusions. The values of the effective mechanical characteristics of investigated materials were obtained, and the character of the dependence of the effective elastic and strength properties on the structure of composites was determined. It is shown that the dependence of the values of the effective elastic moduli on the volume concentration of ceramic inclusions is nonlinear and monotonically increasing. The values of the effective elastic limits increase with increasing concentration of the inclusions, however, for the considered composites, this dependence is not monotonic

Black Hole Configurations with Total Entropy Less than A/4

If one surrounds a black hole with a perfectly reflecting shell and adiabatically squeezes the shell inward, one can increase the black hole area A to exceed four times the total entropy S, which stays fixed during the process. A can be made to exceed 4S by a factor of order unity before the one enters the Planck regime where the semiclassical approximation breaks down. One interpretation is that the black hole entropy resides in its thermal atmosphere, and the shell restricts the atmosphere so that its entropy is less than A/4.Comment: 31 pages, LaTe

Regularization of the Hamiltonian constraint and the closure of the constraint algebra

In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An important issue considered in the paper is the closure of the constraint algebra. The main result we obtain is that the Poisson bracket between the regulated Hamiltonian constraint and the Diffeomorphism constraint is equal to a sum of regulated Hamiltonian constraints with appropriately redefined regulating functions.Comment: 23 pages, epsfig.st

Study of effect of damage accumulation on stress distribution parameters in mesovolume of biocomposite and its performance characteristics

Abstract—A numerical study of mechanical properties of zirconium ceramic–cortical bone tissue biocomposite has been fulfilled using a multiple-scale approach. Evolution of mesoscopic stress distribution in the components of biocomposite during its deformation has been studied with the assumption of damage accumulation until the macrostrength criterion is fulfilled. It has been shown that the parameters of the laws of distribution change with damage accumulation

Anthropic reasoning in multiverse cosmology and string theory

Anthropic arguments in multiverse cosmology and string theory rely on the weak anthropic principle (WAP). We show that the principle, though ultimately a tautology, is nevertheless ambiguous. It can be reformulated in one of two unambiguous ways, which we refer to as WAP_1 and WAP_2. We show that WAP_2, the version most commonly used in anthropic reasoning, makes no physical predictions unless supplemented by a further assumption of "typicality", and we argue that this assumption is both misguided and unjustified. WAP_1, however, requires no such supplementation; it directly implies that any theory that assigns a non-zero probability to our universe predicts that we will observe our universe with probability one. We argue, therefore, that WAP_1 is preferable, and note that it has the benefit of avoiding the inductive overreach characteristic of much anthropic reasoning.Comment: 7 pages. Expanded discussion of selection effects and some minor clarifications, as publishe

Asymptotic Flatness in Rainbow Gravity

A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented.Comment: 11 page

Quantum symmetry, the cosmological constant and Planck scale phenomenology

We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant, not under the Poincare group, but under a deformation of it parameterized by a dimensional parameter proportional to the Planck mass. Such deformations, called kappa-Poincare algebras, imply modified energy-momentum relations of a type that may be observable in near future experiments. Our argument applies in both 2+1 and 3+1 dimensions and assumes only 1) that the low energy limit of a quantum theory of gravity must involve also a limit in which the cosmological constant is taken very small with respect to the Planck scale and 2) that in 3+1 dimensions the physical energy and momenta of physical elementary particles is related to symmetries of the full quantum gravity theory by appropriate renormalization depending on Lambda l^2_{Planck}. The argument makes use of the fact that the cosmological constant results in the symmetry algebra of quantum gravity being quantum deformed, as a consequence when the limit \Lambda l^2_{Planck} -> 0 is taken one finds a deformed Poincare invariance. We are also able to isolate what information must be provided by the quantum theory in order to determine which presentation of the kappa-Poincare algebra is relevant for the physical symmetry generators and, hence, the exact form of the modified energy-momentum relations. These arguments imply that Lorentz invariance is modified as in proposals for doubly special relativity, rather than broken, in theories of quantum gravity, so long as those theories behave smoothly in the limit the cosmological constant is taken to be small.Comment: LaTex, 19 page