98 research outputs found
The ves hypothesis and protein misfolding
Proteins function by changing conformation. These conformational changes, which involve the concerted motion of a large number of atoms are classical events but, in many cases, the triggers are quantum mechani-
cal events such as chemical reactions. Here the initial quantum states after
the chemical reaction are assumed to be vibrational excited states, something
that has been designated as the VES hypothesis. While the dynamics under
classical force fields fail to explain the relatively lower structural stability of
the proteins associated with misfolding diseases, the application of the VES hy-
pothesis to two cases can provide a new explanation for this phenomenon. This explanation relies on the transfer of vibrational energy from water molecules to proteins, a process whose viability is also examined
From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states
The self-consistent propagation of generalized [coherent-product]
states and of a class of gaussian density matrix generalizations is examined,
at both zero and finite-temperature, for arbitrary interactions between the
localized lattice (electronic or vibronic) excitations and the phonon modes. It
is shown that in all legitimate cases, the evolution of states reduces
to the disentangled evolution of the component states. The
self-consistency conditions for the latter amount to conditions for
decoherence-free propagation, which complement the Davydov soliton
equations in such a way as to lift the nonlinearity of the evolution for the
on-site degrees of freedom. Although it cannot support Davydov solitons, the
coherent-product ansatz does provide a wide class of exact density-matrix
solutions for the joint evolution of the lattice and phonon bath in compatible
systems. Included are solutions for initial states given as a product of a
[largely arbitrary] lattice state and a thermal equilibrium state of the
phonons. It is also shown that external pumping can produce self-consistent
Frohlich-like effects. A few sample cases of coherent, albeit not solitonic,
propagation are briefly discussed.Comment: revtex3, latex2e; 22 pages, no figs.; to appear in Phys.Rev.E
(Nov.2001
Stochastic Lagrangian Particle Approach to Fractal Navier-Stokes Equations
In this article we study the fractal Navier-Stokes equations by using
stochastic Lagrangian particle path approach in Constantin and Iyer
\cite{Co-Iy}. More precisely, a stochastic representation for the fractal
Navier-Stokes equations is given in terms of stochastic differential equations
driven by L\'evy processes. Basing on this representation, a self-contained
proof for the existence of local unique solution for the fractal Navier-Stokes
equation with initial data in \mW^{1,p} is provided, and in the case of two
dimensions or large viscosity, the existence of global solution is also
obtained. In order to obtain the global existence in any dimensions for large
viscosity, the gradient estimates for L\'evy processes with time dependent and
discontinuous drifts is proved.Comment: 19 page
Multi-soliton energy transport in anharmonic lattices
We demonstrate the existence of dynamically stable multihump solitary waves
in polaron-type models describing interaction of envelope and lattice
excitations. In comparison with the earlier theory of multihump optical
solitons [see Phys. Rev. Lett. {\bf 83}, 296 (1999)], our analysis reveals a
novel physical mechanism for the formation of stable multihump solitary waves
in nonintegrable multi-component nonlinear models.Comment: 4 pages, 4 figure
Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise
The Primitive Equations are a basic model in the study of large scale Oceanic
and Atmospheric dynamics. These systems form the analytical core of the most
advanced General Circulation Models. For this reason and due to their
challenging nonlinear and anisotropic structure the Primitive Equations have
recently received considerable attention from the mathematical community.
In view of the complex multi-scale nature of the earth's climate system, many
uncertainties appear that should be accounted for in the basic dynamical models
of atmospheric and oceanic processes. In the climate community stochastic
methods have come into extensive use in this connection. For this reason there
has appeared a need to further develop the foundations of nonlinear stochastic
partial differential equations in connection with the Primitive Equations and
more generally.
In this work we study a stochastic version of the Primitive Equations. We
establish the global existence of strong, pathwise solutions for these
equations in dimension 3 for the case of a nonlinear multiplicative noise. The
proof makes use of anisotropic estimates, estimates on the
pressure and stopping time arguments.Comment: To appear in Nonlinearit
Burgers' Flows as Markovian Diffusion Processes
We analyze the unforced and deterministically forced Burgers equation in the
framework of the (diffusive) interpolating dynamics that solves the so-called
Schr\"{o}dinger boundary data problem for the random matter transport. This
entails an exploration of the consistency conditions that allow to interpret
dispersion of passive contaminants in the Burgers flow as a Markovian diffusion
process. In general, the usage of a continuity equation , where stands for the
Burgers field and is the density of transported matter, is at variance
with the explicit diffusion scenario. Under these circumstances, we give a
complete characterisation of the diffusive transport that is governed by
Burgers velocity fields. The result extends both to the approximate description
of the transport driven by an incompressible fluid and to motions in an
infinitely compressible medium. Also, in conjunction with the Born statistical
postulate in quantum theory, it pertains to the probabilistic (diffusive)
counterpart of the Schr\"{o}dinger picture quantum dynamics.Comment: Latex fil
Energy localization and shape transformations in semiflexible polymer rings
Shape transformations in driven and damped molecular chains are considered. Closed chains of weakly coupled molecular subunits under the action of spatially homogeneous time-periodic external field are studied. The coupling between the internal excitations and the bending degrees of freedom of the chain modifies the local bending rigidity of the chain. In the absence of driving the array takes a circular shape.When the energy pumped into the system exceeds some critical value the chain undergoes a nonequilibrium phase transition: The circular shape of the aggregate becomes unstable and the chain takes the shape of an ellipse or, in general, of a polygon. The excitation energy distribution becomes spatially nonuniform: It localizes in such places where the chain is more flat. The weak interaction of the chain with a flat surface restricts the dynamics to a flat manifold.Y.B.G. acknowledges partial financial support from a special program of the National Academy of Sciences of Ukraine, and is thankful to the Department of Applied Mathematics and Computer Science and the Department of Physics, Technical University of Denmark as well as the University of Seville for hospitality. J.F.R.A acknowledges Grant No. 2011/FQM-280 from CEICE, Junta de Andalucia Spain. J.F.R.A. and V.J.S.-M. acknowledge financial support from Project No. FIS2015-65998-C2-2-P from MINECO, Spain.Gaididei, YB.; Archilla, JFR.; Sánchez Morcillo, VJ.; Gorria, C. (2016). Energy localization and shape transformations in semiflexible polymer rings. Physical Review E. 93(6):062227-1-062227-9. https://doi.org/10.1103/PhysRevE.93.062227S062227-1062227-993
Natural boundaries for the Smoluchowski equation and affiliated diffusion processes
The Schr\"{o}dinger problem of deducing the microscopic dynamics from the
input-output statistics data is known to admit a solution in terms of Markov
diffusions. The uniqueness of solution is found linked to the natural
boundaries respected by the underlying random motion. By choosing a reference
Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential
and the field of local accelerations it induces. We generate the family of
affiliated diffusions with the same local dynamics, but different inaccessible
boundaries on finite, semi-infinite and infinite domains. For each diffusion
process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet
boundary data) Wiener path integration.As a by-product of the discussion, we
give an overview of the problem of inaccessible boundaries for the diffusion
and bring together (sometimes viewed from unexpected angles) results which are
little known, and dispersed in publications from scarcely communicating areas
of mathematics and physics.Comment: Latex file, Phys. Rev. E 49, 3815-3824, (1994
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