1,723 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
On a class of linearizable Monge-Amp\`ere equations
Monge-Amp\`ere equations of the form,
arise in many areas of fluid and solid mechanics. Here it is shown that in the
special case , where denotes an arbitrary function,
the Monge-Amp\`ere equation can be linearized by using a sequence of Amp\`ere,
point, Legendre and rotation transformations. This linearization is a
generalization of three examples from finite elasticity, involving plane strain
and plane stress deformations of the incompressible perfectly elastic Varga
material and also relates to a previous linearization of this equation due to
Khabirov [7]
The importance of temporal stress variation and dynamic disequilibrium for the initiation of plate tectonics
We use 1-D thermal history models and 3-D numerical experiments to study the impact of dynamic thermal disequilibrium and large temporal variations of normal and shear stresses on the initiation of plate tectonics. Previous models that explored plate tectonics initiation from a steady state, single plate mode of convection concluded that normal stresses govern the initiation of plate tectonics, which based on our 1-D model leads to plate yielding being more likely with increasing interior heat and planet mass for a depth-dependent Byerlee yield stress. Using 3-D spherical shell mantle convection models in an episodic regime allows us to explore larger temporal stress variations than can be addressed by considering plate failure from a steady state stagnant lid configuration. The episodic models show that an increase in convective mantle shear stress at the lithospheric base initiates plate failure, which leads with our 1-D model to plate yielding being less likely with increasing interior heat and planet mass. In this out-of-equilibrium and strongly time-dependent stress scenario, the onset of lithospheric overturn events cannot be explained by boundary layer thickening and normal stresses alone. Our results indicate that in order to understand the initiation of plate tectonics, one should consider the temporal variation of stresses and dynamic disequilibrium
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
Mobility induces global synchronization of oscillators in periodic extended systems
We study synchronization of locally coupled noisy phase oscillators which
move diffusively in a one-dimensional ring. Together with the disordered and
the globally synchronized states, the system also exhibits several wave-like
states which display local order. We use a statistical description valid for a
large number of oscillators to show that for any finite system there is a
critical spatial diffusion above which all wave-like solutions become unstable.
Through Langevin simulations, we show that the transition to global
synchronization is mediated by the relative size of attractor basins associated
to wave-like states. Spatial diffusion disrupts these states and paves the way
for the system to attain global synchronization
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
Extreme fluctuations in noisy task-completion landscapes on scale-free networks
We study the statistics and scaling of extreme fluctuations in noisy
task-completion landscapes, such as those emerging in synchronized
distributed-computing networks, or generic causally-constrained queuing
networks, with scale-free topology. In these networks the average size of the
fluctuations becomes finite (synchronized state) and the extreme fluctuations
typically diverge only logarithmically in the large system-size limit ensuring
synchronization in a practical sense. Provided that local fluctuations in the
network are short-tailed, the statistics of the extremes are governed by the
Gumbel distribution. We present large-scale simulation results using the exact
algorithmic rules, supported by mean-field arguments based on a coarse-grained
description.Comment: 16 pages, 6 figures, revte
Facts, Values and Quanta
Quantum mechanics is a fundamentally probabilistic theory (at least so far as
the empirical predictions are concerned). It follows that, if one wants to
properly understand quantum mechanics, it is essential to clearly understand
the meaning of probability statements. The interpretation of probability has
excited nearly as much philosophical controversy as the interpretation of
quantum mechanics. 20th century physicists have mostly adopted a frequentist
conception. In this paper it is argued that we ought, instead, to adopt a
logical or Bayesian conception. The paper includes a comparison of the orthodox
and Bayesian theories of statistical inference. It concludes with a few remarks
concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late
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