2,115 research outputs found
Transition Matrix Monte Carlo Reweighting and Dynamics
We study an induced dynamics in the space of energy of single-spin-flip Monte
Carlo algorithm. The method gives an efficient reweighting technique. This
dynamics is shown to have relaxation times proportional to the specific heat.
Thus, it is plausible for a logarithmic factor in the correlation time of the
standard 2D Ising local dynamics.Comment: RevTeX, 5 pages, 3 figure
Exact Markovian kinetic equation for a quantum Brownian oscillator
We derive an exact Markovian kinetic equation for an oscillator linearly
coupled to a heat bath, describing quantum Brownian motion. Our work is based
on the subdynamics formulation developed by Prigogine and collaborators. The
space of distribution functions is decomposed into independent subspaces that
remain invariant under Liouville dynamics. For integrable systems in
Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled,
renormalized particles. In contrast for non-integrable systems, the invariant
subspaces follow a dynamics with broken-time symmetry, involving generalized
functions. This result indicates that irreversibility and stochasticity are
exact properties of dynamics in generalized function spaces. We comment on the
relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.Comment: A few typos in the published version are correcte
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
The analytic continuation of the Lippmann-Schwinger bras and kets is obtained
and characterized. It is shown that the natural mathematical setting for the
analytic continuation of the solutions of the Lippmann-Schwinger equation is
the rigged Hilbert space rather than just the Hilbert space. It is also argued
that this analytic continuation entails the imposition of a time asymmetric
boundary condition upon the group time evolution, resulting into a semigroup
time evolution. Physically, the semigroup time evolution is simply a (retarded
or advanced) propagator.Comment: 32 pages, 3 figure
Antigen receptor repertoires of one of the smallest known vertebrates
The rules underlying the structure of antigen receptor repertoires are not yet fully defined, despite their enormous importance for the understanding of adaptive immunity. With current technology, the large antigen receptor repertoires of mice and humans cannot be comprehensively studied. To circumvent the problems associated with incomplete sampling, we have studied the immunogenetic features of one of the smallest known vertebrates, the cyprinid fish Paedocypris sp. “Singkep” (“minifish”). Despite its small size, minifish has the key genetic facilities characterizing the principal vertebrate lymphocyte lineages. As described for mammals, the frequency distributions of immunoglobulin and T cell receptor clonotypes exhibit the features of fractal systems, demonstrating that self-similarity is a fundamental property of antigen receptor repertoires of vertebrates, irrespective of body size. Hence, minifish achieve immunocompetence via a few thousand lymphocytes organized in robust scale-free networks, thereby ensuring immune reactivity even when cells are lost or clone sizes fluctuate during immune responses
On the Thermal Symmetry of the Markovian Master Equation
The quantum Markovian master equation of the reduced dynamics of a harmonic
oscillator coupled to a thermal reservoir is shown to possess thermal symmetry.
This symmetry is revealed by a Bogoliubov transformation that can be
represented by a hyperbolic rotation acting on the Liouville space of the
reduced dynamics. The Liouville space is obtained as an extension of the
Hilbert space through the introduction of tilde variables used in the
thermofield dynamics formalism. The angle of rotation depends on the
temperature of the reservoir, as well as the value of Planck's constant. This
symmetry relates the thermal states of the system at any two temperatures. This
includes absolute zero, at which purely quantum effects are revealed. The
Caldeira-Leggett equation and the classical Fokker-Planck equation also possess
thermal symmetry. We compare the thermal symmetry obtained from the Bogoliubov
transformation in related fields and discuss the effects of the symmetry on the
shape of a Gaussian wave packet.Comment: Eqs.(64a), (65a)-(68) are correcte
Predictability of large future changes in a competitive evolving population
The dynamical evolution of many economic, sociological, biological and
physical systems tends to be dominated by a relatively small number of
unexpected, large changes (`extreme events'). We study the large, internal
changes produced in a generic multi-agent population competing for a limited
resource, and find that the level of predictability actually increases prior to
a large change. These large changes hence arise as a predictable consequence of
information encoded in the system's global state.Comment: 10 pages, 3 figure
Isostatic phase transition and instability in stiff granular materials
In this letter, structural rigidity concepts are used to understand the
origin of instabilities in granular aggregates. It is shown that: a) The
contact network of a noncohesive granular aggregate becomes exactly isostatic
in the limit of large stiffness-to-load ratio. b) Isostaticity is responsible
for the anomalously large susceptibility to perturbation of these systems, and
c) The load-stress response function of granular materials is critical
(power-law distributed) in the isostatic limit. Thus there is a phase
transition in the limit of intinitely large stiffness, and the resulting
isostatic phase is characterized by huge instability to perturbation.Comment: RevTeX, 4 pages w/eps figures [psfig]. To appear in Phys. Rev. Let
Dynamics of Fluid Vesicles in Oscillatory Shear Flow
The dynamics of fluid vesicles in oscillatory shear flow was studied using
differential equations of two variables: the Taylor deformation parameter and
inclination angle . In a steady shear flow with a low viscosity
of internal fluid, the vesicles exhibit steady tank-treading
motion with a constant inclination angle . In the oscillatory flow
with a low shear frequency, oscillates between or
around for zero or finite mean shear rate ,
respectively. As shear frequency increases, the vesicle
oscillation becomes delayed with respect to the shear oscillation, and the
oscillation amplitude decreases. At high with , another limit-cycle oscillation between and
is found to appear. In the steady flow, periodically rotates
(tumbling) at high , and and the vesicle shape
oscillate (swinging) at middle and high shear rate. In the
oscillatory flow, the coexistence of two or more limit-cycle oscillations can
occur for low in these phases. For the vesicle with a fixed shape,
the angle rotates back to the original position after an oscillation
period. However, it is found that a preferred angle can be induced by small
thermal fluctuations.Comment: 11 pages, 13 figure
Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids
In this review, we describe and analyze a mesoscale simulation method for
fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now
called multi-particle collision dynamics (MPC) or stochastic rotation dynamics
(SRD). The method consists of alternating streaming and collision steps in an
ensemble of point particles. The multi-particle collisions are performed by
grouping particles in collision cells, and mass, momentum, and energy are
locally conserved. This simulation technique captures both full hydrodynamic
interactions and thermal fluctuations. The first part of the review begins with
a description of several widely used MPC algorithms and then discusses
important features of the original SRD algorithm and frequently used
variations. Two complementary approaches for deriving the hydrodynamic
equations and evaluating the transport coefficients are reviewed. It is then
shown how MPC algorithms can be generalized to model non-ideal fluids, and
binary mixtures with a consolute point. The importance of angular-momentum
conservation for systems like phase-separated liquids with different
viscosities is discussed. The second part of the review describes a number of
recent applications of MPC algorithms to study colloid and polymer dynamics,
the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of
viscoelastic fluids
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