3,218 research outputs found
Modeling Adaptive Regulatory T-Cell Dynamics during Early HIV Infection
Regulatory T-cells (Tregs) are a subset of CD4+ T-cells that have been found to suppress the immune response. During HIV viral infection, Treg activity has been observed to have both beneficial and deleterious effects on patient recovery; however, the extent to which this is regulated is poorly understood. We hypothesize that this dichotomy in behavior is attributed to Treg dynamics changing over the course of infection through the proliferation of an ‘adaptive’ Treg population which targets HIV-specific immune responses. To investigate the role Tregs play in HIV infection, a delay differatial equation model was constructed to examine (1) the possible existence of two distinct Treg populations, normal (nTregs) and adaptive (aTregs), and (2) their respective effects in limiting viral load. Sensitivity analysis was performed to test parameter regimes that show the proportionality of viral load with adaptive regulatory populations and also gave insight into the importance of downregulation of CD4+ cells by normal Tregs on viral loads. Through the inclusion of Treg populations in the model, a diverse array of viral dynamics was found. Specifically, oscillatory and steady state behaviors were both witnessed and it was seen that the model provided a more accurate depiction of the effector cell population as compared with previous models. Through further studies of adaptive and normal Tregs, improved treatments for HIV can be constructed for patients and the viral mechanisms of infection can be further elucidated
A rigorous real time Feynman Path Integral and Propagator
We will derive a rigorous real time propagator for the Non-relativistic
Quantum Mechanic transition probability amplitude and for the
Non-relativistic wave function. The propagator will be explicitly given in
terms of the time evolution operator. The derivation will be for all
self-adjoint nonvector potential Hamiltonians. For systems with potential that
carries at most a finite number of singularity and discontinuities, we will
show that our propagator can be written in the form of a rigorous real time,
time sliced Feynman path integral via improper Riemann integrals. We will also
derive the Feynman path integral in Nonstandard Analysis Formulation. Finally,
we will compute the propagator for the harmonic oscillator using the
Nonstandard Analysis Feynman path integral formuluation; we will compute the
propagator without using any knowledge of classical properties of the harmonic
oscillator
First order phase transition of the vortex lattice in twinned YBa2Cu3O7 single crystals in tilted magnetic fields
We present an exhaustive analysis of transport measurements performed in
twinned YBa2Cu3O7 single crystals which stablishes that the vortex solid-liquid
transition is first order when the magnetic field H is applied at an angle
theta away from the direction of the twin planes. We show that the resistive
transitions are hysteretic and the V-I curves are non-linear, displaying a
characteristic s-shape at the melting line Hm(T), which scales as
epsilon(theta)Hm(T,theta). These features are gradually lost when the critical
point H*(theta) is approached. Above H*(theta) the V-I characteristics show a
linear response in the experimentally accessible V-I window, and the transition
becomes reversible. Finally we show that the first order phase transition takes
place between a highly correlated vortex liquid in the field direction and a
solid state of unknown symmetry. As a consequence, the available data support
the scenario for a vortex-line melting rather than a vortex sublimation as
recently suggested [T.Sasagawa et al. PRL 80, 4297 (1998)].Comment: 10 pages, 8 figures, submitted to PR
Effective dynamics for particles coupled to a quantized scalar field
We consider a system of N non-relativistic spinless quantum particles
(``electrons'') interacting with a quantized scalar Bose field (whose
excitations we call ``photons''). We examine the case when the velocity v of
the electrons is small with respect to the one of the photons, denoted by c
(v/c= epsilon << 1). We show that dressed particle states exist (particles
surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow
Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic
energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and
the velocity dependent Darwin interaction and a mass renormalization at order
(v/c)^{2}. Beyond that order the effective dynamics are expected to be
dissipative.
The main mathematical tool we use is adiabatic perturbation theory. However,
in the present case there is no eigenvalue which is separated by a gap from the
rest of the spectrum, but its role is taken by the bottom of the absolutely
continuous spectrum, which is not an eigenvalue.
Nevertheless we construct approximate dressed electrons subspaces, which are
adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln
(v/c)^{-1}}. We also give an explicit expression for the non adiabatic
transitions corresponding to emission of free photons. For the radiated energy
we obtain the quantum analogue of the Larmor formula of classical
electrodynamics.Comment: 67 pages, 2 figures, version accepted for publication in
Communications in Mathematical Physic
Asymptotic analysis for the generalized langevin equation
Various qualitative properties of solutions to the generalized Langevin
equation (GLE) in a periodic or a confining potential are studied in this
paper. We consider a class of quasi-Markovian GLEs, similar to the model that
was introduced in \cite{EPR99}. Geometric ergodicity, a homogenization theorem
(invariance principle), short time asymptotics and the white noise limit are
studied. Our proofs are based on a careful analysis of a hypoelliptic operator
which is the generator of an auxiliary Markov process. Systematic use of the
recently developed theory of hypocoercivity \cite{Vil04HPI} is made.Comment: 27 pages, no figures. Submitted to Nonlinearity
Vortex Flow and Transverse Flux Screening at the Bose Glass Transition
We investigate the vortex phase diagram in untwinned YBaCuO single crystals
with columnar defects. These randomly distributed defects, produced by heavy
ion irradiation, are expected to induce a ``Bose Glass'' phase of localized
vortices characterized by a vanishing resistance and a Meissner effect for
magnetic fields transverse to the defect axis. We directly observe the
transverse Meissner effect using an array of Hall probe magnetometers. As
predicted, the Meissner state breaks down at temperatures Ts that decrease
linearly with increasing transverse magnetic field. However, Ts falls well
below the conventional melting temperature Tm determined by a vanishing
resistivity, suggesting an intermediate regime where flux lines are effectively
localized even when rotated off the columnar defects.Comment: 15 pages, 5 figure
Non-commutative Geometry and Kinetic Theory of Open Systems
The basic mathematical assumptions for autonomous linear kinetic equations
for a classical system are formulated, leading to the conclusion that if they
are differential equations on its phase space , they are at most of the 2nd
order. For open systems interacting with a bath at canonical equilibrium they
have a particular form of an equation of a generalized Fokker-Planck type. We
show that it is possible to obtain them as Liouville equations of Hamiltonian
dynamics on with a particular non-commutative differential structure,
provided certain geometric in character, conditions are fulfilled. To this end,
symplectic geometry on is developped in this context, and an outline of the
required tensor analysis and differential geometry is given. Certain questions
for the possible mathematical interpretation of this structure are also
discussed.Comment: 22 pages, LaTe
Anderson Localization, Non-linearity and Stable Genetic Diversity
In many models of genotypic evolution, the vector of genotype populations
satisfies a system of linear ordinary differential equations. This system of
equations models a competition between differential replication rates (fitness)
and mutation. Mutation operates as a generalized diffusion process on genotype
space. In the large time asymptotics, the replication term tends to produce a
single dominant quasispecies, unless the mutation rate is too high, in which
case the populations of different genotypes becomes de-localized. We introduce
a more macroscopic picture of genotypic evolution wherein a random replication
term in the linear model displays features analogous to Anderson localization.
When coupled with non-linearities that limit the population of any given
genotype, we obtain a model whose large time asymptotics display stable
genotypic diversityComment: 25 pages, 8 Figure
Imprints of the Quantum World in Classical Mechanics
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics
are much more numerous than is usually believed. We show Using no physical
hypotheses) that the Schroedinger equation for a nonrelativistic system of
spinless particles is a classical equation which is equivalent to Hamilton's
equations.Comment: Paper submitted to Foundations of Physic
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