2,886 research outputs found
The Velocity of the Propagating Wave for General Coupled Scalar Systems
We consider spatially coupled systems governed by a set of scalar density
evolution equations. Such equations track the behavior of message-passing
algorithms used, for example, in coding, sparse sensing, or
constraint-satisfaction problems. Assuming that the "profile" describing the
average state of the algorithm exhibits a solitonic wave-like behavior after
initial transient iterations, we derive a formula for the propagation velocity
of the wave. We illustrate the formula with two applications, namely
Generalized LDPC codes and compressive sensing.Comment: 5 pages, 5 figures, submitted to the Information Theory Workshop
(ITW) 2016 in Cambridge, U
On the thermodynamic framework of generalized coupled thermoelastic-viscoplastic-damage modeling
A complete potential based framework using internal state variables is put forth for the derivation of reversible and irreversible constitutive equations. In this framework, the existence of the total (integrated) form of either the (Helmholtz) free energy or the (Gibbs) complementary free energy are assumed a priori. Two options for describing the flow and evolutionary equations are described, wherein option one (the fully coupled form) is shown to be over restrictive while the second option (the decoupled form) provides significant flexibility. As a consequence of the decoupled form, a new operator, i.e., the Compliance operator, is defined which provides a link between the assumed Gibb's and complementary dissipation potential and ensures a number of desirable numerical features, for example the symmetry of the resulting consistent tangent stiffness matrix. An important conclusion reached, is that although many theories in the literature do not conform to the general potential framework outlined, it is still possible in some cases, by slight modifications of the used forms, to restore the complete potential structure
Modeling and analysis of a phase field system for damage and phase separation processes in solids
In this work, we analytically investigate a multi-component system for
describing phase separation and damage processes in solids. The model consists
of a parabolic diffusion equation of fourth order for the concentration coupled
with an elliptic system with material dependent coefficients for the strain
tensor and a doubly nonlinear differential inclusion for the damage function.
The main aim of this paper is to show existence of weak solutions for the
introduced model, where, in contrast to existing damage models in the
literature, different elastic properties of damaged and undamaged material are
regarded. To prove existence of weak solutions for the introduced model, we
start with an approximation system. Then, by passing to the limit, existence
results of weak solutions for the proposed model are obtained via suitable
variational techniques.Comment: Keywords: Cahn-Hilliard system, phase separation, elliptic-parabolic
systems, doubly nonlinear differential inclusions, complete damage, existence
results, energetic solutions, weak solutions, linear elasticity,
rate-dependent system
Periodic travelling waves in convex Klein-Gordon chains
We study Klein-Gordon chains with attractive nearest neighbour forces and
convex on-site potential, and show that there exists a two-parameter family of
periodic travelling waves (wave trains) with unimodal and even profile
functions. Our existence proof is based on a saddle-point problem with
constraints and exploits the invariance properties of an improvement operator.
Finally, we discuss the numerical computation of wave trains.Comment: 12 pages, 3 figure
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