806 research outputs found
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
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
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
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
Identifying Near Earth Object Families
The study of asteroid families has provided tremendous insight into the
forces that sculpted the main belt and continue to drive the collisional and
dynamical evolution of asteroids. The identification of asteroid families
within the NEO population could provide a similar boon to studies of their
formation and interiors. In this study we examine the purported identification
of NEO families by Drummond (2000) and conclude that it is unlikely that they
are anything more than random fluctuations in the distribution of NEO
osculating orbital elements. We arrive at this conclusion after examining the
expected formation rate of NEO families, the identification of NEO groups in
synthetic populations that contain no genetically related NEOs, the orbital
evolution of the largest association identified by Drummond (2000), and the
decoherence of synthetic NEO families intended to reproduce the observed
members of the same association. These studies allowed us to identify a new
criterion that can be used to select real NEO families for further study in
future analyses, based on the ratio of the number of pairs and the size of
strings to the number of objects in an identified association.Comment: Accepted for publication in Icarus. 19 pages including 11 figure
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 -adic valued probabilities. The latter model is discussed in details.
The introduction of -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)
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
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
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