88 research outputs found
A Generalized Electrowetting Equation: Its Derivation and Consequences
The thermodynamics of electrowetting is treated. A general equation of
electrowetting is derived from the first principles. It is demonstrated that
the well-known Lippmann Equation describes a particular case of electrowetting
when the radial derivative of the capacitance of the double layer is constant.
The apparent contact angle of electrowetting depends on the gradient of
capacity of a double layer in the vicinity of the triple line. The role of the
area adjacent to the triple line in constituting the equilibrium apparent
contact angle of electrowetting is emphasized.Comment: 11 pages, 3 Figure
Localization in Coupled Finite Vibro-Impact Chains: Discrete Breathers and Multibreathers
We examine the dynamics of strongly localized periodic solutions (discrete
breathers) in two-dimensional array of coupled finite one-dimensional chains of
oscillators. Localization patterns with both single and multiple localization
sites (multibreathers) are considered. The model is scalar, i.e. each particle
can move only parallel to the axis of the chain it belongs to. The model
involves symmetric parabolic on-site potential with rigid constraints (the
displacement domain of each particle is finite) and a linear nearest-neighbor
coupling in the chain, and also between the neighbors in adjacent chains. When
the particle approaches the constraint, it undergoes an elastic Newtonian
impact. The rigid impact constraints are the only source of nonlinearity in the
system. The model allows easy computation of highly accurate approximate
solutions for the breathers and multibreathers with an arbitrary set of
localization sites in conservative setting. The vibro-impact nonlinearity
permits explicit derivation of a monodromy matrix for the breather and
multi-breather solutions. Consequently, the stability of the derived breather
and multibreather solutions can be studied in the framework of simple methods
of linear algebra, without additional approximations. It is shown that due to
the coupling of the chains, the breather solutions can undergo the symmetry
breaking.Comment: 6 pages, 6 figure
Discrete Breathers and Multi-Breathers in Finite Vibro-Impact Chain
We explore dynamics of discrete breathers and multi-breathers in finite
one-dimensional chain. The model involves parabolic on-site potential with
rigid constraints and linear nearest-neighbor coupling. The rigid non-ideal
impact constraints are the only source of nonlinearity and damping in the
model. The model allows derivation of exact analytic solutions for the
breathers and multi-breathers with arbitrary set of localization sites, both in
conservative and forced-damped settings. We choose periodic boundary
conditions; exact solutions for other types of the boundary conditions are also
possible. Local character of the nonlinearity allows explicit derivation of a
monodromy matrix for the breather solutions. Consequently, a stability of the
derived breather and multi-breather solutions can be efficiently studied in the
framework of simple methods of linear algebra, and with rather moderate
computational efforts. We demonstrate that finitness of the chain fragment and
proximity of the localization sites strongly effect existence and stability
patterns of these localized solutions
Mechanical control of heat conductivity in microscopic models of dielectrics
We discuss a possibility to control a heat conductivity in simple
one-dimensional models of dielectrics by means of external mechanical loads. To
illustrate such possibilities we consider first a well-studied chain with
degenerate double-well potential of the interparticle interaction. Contrary to
previous studies, we consider varying length of the chain with fixed number of
particles. Number of possible energetically degenerate ground states strongly
depends on the overall length of the chain, or, in other terms, on average
length of the link between neighboring particles. These degenerate states
correspond to mechanical equilibrium, therefore one can say that the transition
between them mimics to some extent a process of plastic deformation. We
demonstrate that such modification of the chain length can lead to quite
profound (almost five-fold) reduction of the heat conduction coefficient. Even
more profound effect is revealed for a model with single-well non-convex
potential. It is demonstrated that in certain range of constant external
forcing this model becomes "effectively"\ double-well, and has a multitude of
possible states of equilibrium for the same value of the external load. Thus,
the heat conduction coefficient can be reduced by two orders of magnitude. We
suggest a mechanical model of a chain with periodic double-well potential,
which allows control over the heat conduction. The models considered may be
useful for description of heat transport in biological macromolecules and for
control of the heat transport in microsystems.Comment: 10 pages, 16 figure
Determining the Inter-Particle Force-Laws in Amorphous Solids from a Visual Image
We consider the problem of how to determine the force laws in an amorphous
system of interacting particles. Given the positions of the centers of mass of
the constituent particles we propose a new algorithm to determine the
inter-particle force-laws. Having different types of constituents we
determine the coefficients in the Laurent polynomials for the
possibly different force-laws. A visual providing the particle positions in
addition to a measurement of the pressure is all that is required. The
algorithm proposed includes a part that can correct for experimental errors in
the positions of the particles. Such a correction of unavoidable measurement
errors is expected to benefit many experiments in the field.Comment: Very slight changes from original version. Mostly visual improvement
and clarification
Heat conduction in diatomic chains with correlated disorder
The paper considers heat transport in diatomic one-dimensional lattices,
containing equal amounts of particles with different masses. Ordering of the
particles in the chain is governed by single correlation parameter -- the
probability for two neighboring particles to have the same mass. As this
parameter grows from zero to unity, the structure of the chain varies from
regular staggering chain to completely random configuration, and then -- to
very long clusters of particles with equal masses. Therefore, this correlation
parameter allows a control of typical cluster size in the chain. In order to
explore different regimes of the heat transport, two interatomic potentials are
considered. The first one is an infinite potential wall, corresponding to
instantaneous elastic collisions between the neighboring particles. In
homogeneous chains such interaction leads to an anomalous heat transport. The
other one is classical Lennard-Jones interatomic potential, which leads to a
normal heat transport. The simulations demonstrate that the correlated disorder
of the particle arrangement does not change the convergence properties of the
heat conduction coefficient, but essentially modifies its value. For the
collision potential, one observes essential growth of the coefficient for fixed
chain length as the limit of large homogeneous clusters is approached. The
thermal transport in these models remains superdiffusive. In the Lennard-Jones
chain the effect of correlation appears to be not monotonous in the limit of
low temperatures. This behavior stems from the competition between formation of
long clusters mentioned above, and Anderson localization close to the
staggering ordered state.Comment: 9 pages, 10 figure
Atomistic theory of the shear band direction in amorphous solids
One of the major theoretical riddles in shear banding instabilities is the
angle that the shear band chooses spontaneously with respect to the principal
stress axis. Here we employ our recent atomistic theory to compute analytically
the angle in terms of the characteristics of the Eshelby inclusion that models
faithfully the eigenfunction of the Hessian matrix that goes soft at the
plastic instability. We show that loading protocols that do not conserve volume
result in shear bands at angles different from 45 to the strain axis; only
when the external strains preserve volume like in pure shear, the shear bands
align precisely at 45 to the strain axis. We compute an analytic formula
for the angle of the shear band in terms of the characteristics of the loading
protocol; quantitative agreement with computer simulations is demonstrated.Comment: 4 page
On the Effect of Micro-alloying on the Mechanical Properties of Metallic Glasses
"Micro-alloying", referring to the addition of small concentration of a
foreign metal to a given metallic glass, was used extensively in recent years
to attempt to improve the mechanical properties of the latter. The results are
haphazard and nonsystematic. In this paper we provide a microscopic theory of
the effect of micro-alloying, exposing the delicate consequences of this
procedure and the large parameter space which needs to be controlled. In
particular we consider two very similar models which exhibit opposite trends
for the change of the shear modulus, and explain the origins of the difference
as displayed in the different microscopic structure and properties
Escape of a forced-damped particle from weakly nonlinear truncated potential well
Escape from a potential well is an extreme example of transient behavior. We
consider the escape of the harmonically forced particle under viscous damping
from the benchmark truncated weakly nonlinear potential well. Main attention is
paid to most interesting case of primary 1:1 resonance. The treatment is based
on multiple-scales analysis and exploration of the slow-flow dynamics. Contrary
to Hamiltonian case described in earlier works, in the case with damping the
slow-flow equations are not integrable. However, if the damping is small
enough, it is possible to analyze the perturbed slow-flow equations. The effect
of the damping on the escape threshold is evaluated in the explicit analytic
form. Somewhat unexpectedly, the escape mechanisms in terms of the slow flow
are substantially different for the linear and weakly nonlinear cases
Internal resonances and dynamic responses in equivalent mechanical model of partially liquid-filled vessel
The paper treats oscillations of a liquid in partially filled vessel under
horizontal harmonic ground excitation. Such excitation may lead to hydraulic
impacts. The liquid sloshing mass is modeled by equivalent pendulum, which can
impact the vessel walls. We use parameters of the equivalent pendulum for
well-explored case of cylindrical vessels. The hydraulic impacts are modeled by
high-power potential function. Conditions for internal resonances are
presented. A non-resonant behavior and dynamic response related to 3:1 internal
resonance are explored. When the excitation amplitude exceeds a critical value,
the system exhibits multiple steady state solutions. Quasi-periodic solutions
appear in relatively narrow range of parameters. Numerical continuation links
between resonant regimes found asymptotically for small excitation amplitude,
and high-amplitude responses with intensive impacts.Comment: 40 pages, 17 figure
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