1,090 research outputs found
Reflection of plane waves from the flat boundary of a micropolar elastic halfspace
Microstructure effect on wave propagation, and plane wave reflection from stress free flat surface in micropolar elastic half-spac
Extension the Noether's theorem to Lagrangian formulation with nonlocality
A Lagrangian formulation with nonlocality is investigated in this paper. The
nonlocality of the Lagrangian is introduced by a new nonlocal argument that is
defined as a nonlocal residual satisfying the zero mean condition. The nonlocal
Euler-Lagrangian equation is derived from the Hamilton's principle. The
Noether's theorem is extended to this Lagrangian formulation with nonlocality.
With the help of the extended Noether's theorem, the conservation laws relevant
to energy, linear momentum, angular momentum and the Eshelby tensor are
determined in the nonlocal elasticity associated with the mechanically based
constitutive model. The results show that the conservation laws exist only in
the form of the integral over the whole domain occupied by body. The
localization of the conservation laws is discussed in detail. We demonstrate
that not every conservation law corresponds to a local equilibrium equation.
Only when the nonlocal residual of conservation current exists, can a
conservation law be transformed into a local equilibrium equation by
localization.Comment: 13 page
A mixture theory for geophysical fluids
International audienceA continuum theory is developed for a geophysical fluid consisting of two species. Balance laws are given for the individual components of the mixture, modeled as micropolar viscous fluids. The continua allow independent rotational degrees of freedom, so that the fluids can exhibit couple stresses and a non-symmetric stress tensor. The second law of thermodynamics is used to develop constitutive equations. Linear constitutive equations are constituted for a heat conducting mixture, each species possessing separate viscosities. Field equations are obtained and boundary and initial conditions are stated. This theory is relevant to an atmospheric mixture consisting of any two species from rain, snow and/or sand. Also, this is a continuum theory for oceanic mixtures, such as water and silt, or water and oil spills, etc
Bifurcation analysis of rotating axially compressed imperfect nano-rod
Static stability problem for axially compressed rotating nano-rod clamped at
one and free at the other end is analyzed by the use of bifurcation theory. It
is obtained that the pitchfork bifurcation may be either super- or
sub-critical. Considering the imperfections in rod's shape and loading, it is
proved that they constitute the two-parameter universal unfolding of the
problem. Numerical analysis also revealed that for non-locality parameters
having higher value than the critical one interaction curves have two branches,
so that for a single critical value of angular velocity there exist two
critical values of horizontal force
Solitary and compact-like shear waves in the bulk of solids
We show that a model proposed by Rubin, Rosenau, and Gottlieb [J. Appl. Phys.
77 (1995) 4054], for dispersion caused by an inherent material characteristic
length, belongs to the class of simple materials. Therefore, it is possible to
generalize the idea of Rubin, Rosenau, and Gottlieb to include a wide range of
material models, from nonlinear elasticity to turbulence. Using this insight,
we are able to fine-tune nonlinear and dispersive effects in the theory of
nonlinear elasticity in order to generate pulse solitary waves and also bulk
travelling waves with compact support
Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter
Torsional degrees of freedom play an important role in modern gravity
theories as well as in condensed matter systems where they can be modeled by
defects in solids. Here we isolate a class of torsion models that support
torsion configurations with a localized, conserved charge that adopts integer
values. The charge is topological in nature and the torsional configurations
can be thought of as torsional `monopole' solutions. We explore some of the
properties of these configurations in gravity models with non-vanishing
curvature, and discuss the possible existence of such monopoles in condensed
matter systems. To conclude, we show how the monopoles can be thought of as a
natural generalization of the Cartan spiral staircase.Comment: 4+epsilon, 1 figur
Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids
Transformation elasticity, by analogy with transformation acoustics and
optics, converts material domains without altering wave properties, thereby
enabling cloaking and related effects. By noting the similarity between
transformation elasticity and the theory of incremental motion superimposed on
finite pre-strain it is shown that the constitutive parameters of
transformation elasticity correspond to the density and moduli of
small-on-large theory. The formal equivalence indicates that transformation
elasticity can be achieved by selecting a particular finite (hyperelastic)
strain energy function, which for isotropic elasticity is semilinear strain
energy. The associated elastic transformation is restricted by the requirement
of statically equilibrated pre-stress. This constraint can be cast as \tr
{\mathbf F} = constant, where is the deformation gradient,
subject to symmetry constraints, and its consequences are explored both
analytically and through numerical examples of cloaking of anti-plane and
in-plane wave motion.Comment: 20 pages, 5 figure
On the origin dependence of multipole moments in electromagnetism
The standard description of material media in electromagnetism is based on
multipoles. It is well known that these moments depend on the point of
reference chosen, except for the lowest order. It is shown that this "origin
dependence" is not unphysical as has been claimed in the literature but forms
only part of the effect of moving the point of reference. When also the
complementary part is taken into account then different points of reference
lead to different but equivalent descriptions of the same physical reality.
This is shown at the microscopic as well as at the macroscopic level. A similar
interpretation is valid regarding the "origin dependence" of the reflection
coefficients for reflection on a semi infinite medium. We show that the
"transformation theory" which has been proposed to remedy this situation (and
which is thus not needed) is unphysical since the transformation considered
does not leave the boundary conditions invariant.Comment: 14 pages, 0 figure
Vibrations of amorphous, nanometric structures: When does continuum theory apply?
Structures involving solid particles of nanometric dimensions play an
increasingly important role in material sciences. These structures are often
characterized through the vibrational properties of their constituent
particles, which can be probed by spectroscopic methods. Interpretation of such
experimental data requires an extension of continuum elasticity theory down to
increasingly small scales. Using numerical simulation and exact diagonalization
for simple models, we show that continuum elasticity, applied to disordered
system, actually breaks down below a length scale of typically 30 to 50
molecular sizes. This length scale is likely related to the one which is
generally invoked to explain the peculiar vibrational properties of glassy
systems.Comment: 4 pages, 5 figures, LATEX, Europhysics Letters accepte
Non-minimal Wu-Yang wormhole
We discuss exact solutions of three-parameter non-minimal Einstein-Yang-Mills
model, which describe the wormholes of a new type. These wormholes are
considered to be supported by SU(2)-symmetric Yang-Mills field, non-minimally
coupled to gravity, the Wu-Yang ansatz for the gauge field being used. We
distinguish between regular solutions, describing traversable non-minimal
Wu-Yang wormholes, and black wormholes possessing one or two event horizons.
The relation between the asymptotic mass of the regular traversable Wu-Yang
wormhole and its throat radius is analysed.Comment: 9 pages, 2 figures, typos corrected, 2 references adde
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