1,889 research outputs found
A Minimal Mechanosensing Model Predicts Keratocyte Evolution on Flexible Substrates
A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behaviour of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and travelling waves in the lamellipodium leading edge, (iii) response to remote mechanical stress externally applied to the substrate (tensotaxis) and (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis)
Numerical simulation of model problems in plasticity based on field dislocation mechanics
The aim of this paper is to investigate the numerical implementation of the field dislocation mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006 J. Mech. Phys. Solids 54 1687-710) is recalled which permits to express the set of equations under the form of a static problem, corresponding to the determination of the local stress field for a given dislocation density distribution, complemented by an evolution problem, corresponding to the transport of the dislocation density. The static problem is solved using FFT-based techniques (Brenner et al 2014 Phil. Mag. 94 1764-87). The main contribution of the present study is an efficient numerical scheme based on high resolution Godunov-type solvers to solve the evolution problem. Model problems of dislocation-mediated plasticity are finally considered in a simplified layer case. First, uncoupled problems with uniform velocity are considered, which permits to reproduce annihilation of dislocations and expansion of dislocation loops. Then, the FDM theory is applied to several problems of dislocation microstructures subjected to a mechanical loading
Optimal Control of Quantum Dynamics : A New Theoretical Approach
A New theoretical formalism for the optimal quantum control has been
presented. The approach stems from the consideration of describing the
time-dependent quantum system in terms of the real physical observables, viz.,
the probability density rho(x,t) and the quantum current j(x,t) which is well
documented in the Bohm's hydrodynamical formulation of quantum mechanics. The
approach has been applied for manipulating the vibrational motion of HBr in its
ground electronic state under an external electric field.Comment: 4 figure
Nambu mechanics, -ary operations and their quantization
We start with an overview of the "generalized Hamiltonian dynamics"
introduced in 1973 by Y. Nambu, its motivations, mathematical background and
subsequent developments -- all of it on the classical level. This includes the
notion (not present in Nambu's work) of a generalization of the Jacobi identity
called Fundamental Identity. We then briefly describe the difficulties
encountered in the quantization of such -ary structures, explain their
reason and present the recently obtained solution combining deformation
quantization with a "second quantization" type of approach on . The
solution is called "Zariski quantization" because it is based on the
factorization of (real) polynomials into irreducibles. Since we want to
quantize composition laws of the determinant (Jacobian) type and need a Leibniz
rule, we need to take care also of derivatives and this requires going one step
further (Taylor developments of polynomials over polynomials). We also discuss
a (closer to the root, "first quantized") approach in various circumstances,
especially in the case of covariant star products (exemplified by the case of
su(2)). Finally we address the question of equivalence and triviality of such
deformation quantizations of a new type (the deformations of algebras are more
general than those considered by Gerstenhaber).Comment: 23 pages, LaTeX2e with the LaTeX209 option. To be published in the
proceedings of the Ascona meeting. Mathematical Physics Studies, volume 20,
Kluwe
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