The mechanics of solids in the plastically-deformable state

The mechanics of continua, which is based on the general stress model of Cauchy, up to the present has almost exclusively been applied to liquid and solid elastic bodies. Saint-Venant has developed a theory for the plastic or remaining form changes of solids, but it does not give the required number of equations for determining motion. A complete set of equations of motion for plastic deformable bodies is derived. This is done within the framework of Cauch mechanics. And it is supported by certain experimental facts which characterize the range of applications

Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals.Comment: 30 page

High shock release in ultrafast laser irradiated metals: Scenario for material ejection

We present one-dimensional numerical simulations describing the behavior of solid matter exposed to subpicosecond near infrared pulsed laser radiation. We point out to the role of strong isochoric heating as a mechanism for producing highly non-equilibrium thermodynamic states. In the case of metals, the conditions of material ejection from the surface are discussed in a hydrodynamic context, allowing correlation of the thermodynamic features with ablation mechanisms. A convenient synthetic representation of the thermodynamic processes is presented, emphasizing different competitive pathways of material ejection. Based on the study of the relaxation and cooling processes which constrain the system to follow original thermodynamic paths, we establish that the metal surface can exhibit several kinds of phase evolution which can result in phase explosion or fragmentation. An estimation of the amount of material exceeding the specific energy required for melting is reported for copper and aluminum and a theoretical value of the limit-size of the recast material after ultrashort laser irradiation is determined. Ablation by mechanical fragmentation is also analysed and compared to experimental data for aluminum subjected to high tensile pressures and ultrafast loading rates. Spallation is expected to occur at the rear surface of the aluminum foils and a comparison with simulation results can determine a spall strength value related to high strain rates

Pure-radiation gravitational fields with a simple twist and a Killing vector

Pure-radiation solutions are found, exploiting the analogy with the Euler- Darboux equation for aligned colliding plane waves and the Euler-Tricomi equation in hydrodynamics of two-dimensional flow. They do not depend on one of the spacelike coordinates and comprise the Hauser solution as a special subcase.Comment: revtex, 9 page

Multimode solutions of first-order elliptic quasilinear systems obtained from Riemann invariants

Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links between two techniques, that of the symmetry reduction method and of the generalized method of characteristics. A variant of the conditional symmetry method for constructing this type of solution is proposed. A specific feature of that approach is an algebraic-geometric point of view, which allows the introduction of specific first-order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method for solving elliptic homogeneous systems of PDEs. A further generalization of the Riemann invariants method to the case of inhomogeneous systems, based on the introduction of specific rotation matrices, enables us to weaken the integrability condition. It allows us to establish a connection between the structure of the set of integral elements and the possibility of constructing specific classes of simple mode solutions. These theoretical considerations are illustrated by the examples of an ideal plastic flow in its elliptic region and a system describing a nonlinear interaction of waves and particles. Several new classes of solutions are obtained in explicit form, including the general integral for the latter system of equations

Generalized probabilities taking values in non-Archimedean fields and topological groups

We develop an analogue of probability theory for probabilities taking values in topological groups. We generalize Kolmogorov's method of axiomatization of probability theory: main distinguishing features of frequency probabilities are taken as axioms in the measure-theoretic approach. We also present a review of non-Kolmogorovian probabilistic models including models with negative, complex, and $p$-adic valued probabilities. The latter model is discussed in details. The introduction of $p$-adic (as well as more general non-Archimedean) probabilities is one of the main motivations for consideration of generalized probabilities taking values in topological groups which are distinct from the field of real numbers. We discuss applications of non-Kolmogorovian models in physics and cognitive sciences. An important part of this paper is devoted to statistical interpretation of probabilities taking values in topological groups (and in particular in non-Archimedean fields)

Probabilities from Entanglement, Born's Rule from Envariance

I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly entangled ``Bell-like'' states can be used to rigorously justify complete ignorance of the observer about the outcome of any measurement on either of the members of the entangled pair. For more general states, envariance leads to Born's rule, $p_k \propto |\psi_k|^2$ for the outcomes associated with Schmidt states. Probabilities derived in this manner are an objective reflection of the underlying state of the system -- they represent experimentally verifiable symmetries, and not just a subjective ``state of knowledge'' of the observer. Envariance - based approach is compared with and found superior to pre-quantum definitions of probability including the {\it standard definition} based on the `principle of indifference' due to Laplace, and the {\it relative frequency approach} advocated by von Mises. Implications of envariance for the interpretation of quantum theory go beyond the derivation of Born's rule: Envariance is enough to establish dynamical independence of preferred branches of the evolving state vector of the composite system, and, thus, to arrive at the {\it environment - induced superselection (einselection) of pointer states}, that was usually derived by an appeal to decoherence. Envariant origin of Born's rule for probabilities sheds a new light on the relation between ignorance (and hence, information) and the nature of quantum states.Comment: Figure and an appendix (Born's rule for continuous spectra) added. Presentation improved. (Comments still welcome...

Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.Comment: 21 page

Atomistic Studies of Defect Nucleation during Nanoindentation of Au (001)

Atomistic studies are carried out to investigate the formation and evolution of defects during nanoindentation of a gold crystal. The results in this theoretical study complement the experimental investigations [J. D. Kiely and J. E. Houston, Phys. Rev. B, v57, 12588 (1998)] extremely well. The defects are produced by a three step mechanism involving nucleation, glide and reaction of Shockley partials on the {111} slip planes noncoplanar with the indented surface. We have observed that slip is in the directions along which the resolved shear stress has reached the critical value of approximately 2 GPa. The first yield occurs when the shear stresses reach this critical value on all the {111} planes involved in the formation of the defect. The phenomenon of strain hardening is observed due to the sessile stair-rods produced by the zipping of the partials. The dislocation locks produced during the second yield give rise to permanent deformation after retraction.Comment: 11 pages, 13 figures, submitted to Physical Review

Commensurability and beyond: from Mises and Neurath to the future of the socialist calculation debate

Mises' 'calculation argument' against socialism argues that monetary calculation is indispensable as a commensurable unit for evaluating factors of production. This is not due to his conception of rationality being purely 'algorithmic,' for it accommodates non-monetary, incommensurable values. Commensurability is needed, rather, as an aid in the face of economic complexity. The socialist Neurath's response to Mises is unsatisfactory in rejecting the need to explore possible non-market techniques for achieving a certain degree of commensurability. Yet Neurath's contribution is valuable in emphasizing the need for a balanced, comparative approach to the question of market versus non-market that puts the commensurability question in context. These central issues raised by adversaries in the early socialist calculation debate have continued relevance for the contemporary discussion