99 research outputs found
Observing Brownian motion in vibration-fluidized granular matter
At the beginning of last century, Gerlach and Lehrer observed the rotational
Brownian motion of a very fine wire immersed in an equilibrium environment, a
gas. This simple experiment eventually permitted the full development of one of
the most important ideas of equilibrium statistical mechanics: the very
complicated many-particle problem of a large number of molecules colliding with
the wire, can be represented by two macroscopic parameters only, namely
viscosity and the temperature. Can this idea, mathematically developed in the
so-called Langevin model and the fluctuation-dissipation theorem be used to
describe systems that are far from equilibrium? Here we address the question
and reproduce the Gerlach and Lehrer experiment in an archetype non-equilibrium
system, by immersing a sensitive torsion oscillator in a granular system of
millimetre-size grains, fluidized by strong external vibrations. The
vibro-fluidized granular medium is a driven environment, with continuous
injection and dissipation of energy, and the immersed oscillator can be seen as
analogous to an elastically bound Brownian particle. We show, by measuring the
noise and the susceptibility, that the experiment can be treated, in first
approximation, with the same formalism as in the equilibrium case, giving
experimental access to a ''granular viscosity'' and an ''effective
temperature'', however anisotropic and inhomogeneous, and yielding the
surprising result that the vibro-fluidized granular matter behaves as a
''thermal'' bath satisfying a fluctuation-dissipation relation
Non-Perturbative Renormalization Group for Simple Fluids
We present a new non perturbative renormalization group for classical simple
fluids. The theory is built in the Grand Canonical ensemble and in the
framework of two equivalent scalar field theories as well. The exact mapping
between the three renormalization flows is established rigorously. In the Grand
Canonical ensemble the theory may be seen as an extension of the Hierarchical
Reference Theory (L. Reatto and A. Parola, \textit{Adv. Phys.}, \textbf{44},
211 (1995)) but however does not suffer from its shortcomings at subcritical
temperatures. In the framework of a new canonical field theory of liquid state
developed in that aim our construction identifies with the effective average
action approach developed recently (J. Berges, N. Tetradis, and C. Wetterich,
\textit{Phys. Rep.}, \textbf{363} (2002))
A Brownian particle in a microscopic periodic potential
We study a model for a massive test particle in a microscopic periodic
potential and interacting with a reservoir of light particles. In the regime
considered, the fluctuations in the test particle's momentum resulting from
collisions typically outweigh the shifts in momentum generated by the periodic
force, and so the force is effectively a perturbative contribution. The
mathematical starting point is an idealized reduced dynamics for the test
particle given by a linear Boltzmann equation. In the limit that the mass ratio
of a single reservoir particle to the test particle tends to zero, we show that
there is convergence to the Ornstein-Uhlenbeck process under the standard
normalizations for the test particle variables. Our analysis is primarily
directed towards bounding the perturbative effect of the periodic potential on
the particle's momentum.Comment: 60 pages. We reorganized the article and made a few simplifications
of the conten
Action Potential Initiation in the Hodgkin-Huxley Model
A recent paper of B. Naundorf et al. described an intriguing negative correlation between variability of the onset potential at which an action potential occurs (the onset span) and the rapidity of action potential initiation (the onset rapidity). This correlation was demonstrated in numerical simulations of the Hodgkin-Huxley model. Due to this antagonism, it is argued that Hodgkin-Huxley-type models are unable to explain action potential initiation observed in cortical neurons in vivo or in vitro. Here we apply a method from theoretical physics to derive an analytical characterization of this problem. We analytically compute the probability distribution of onset potentials and analytically derive the inverse relationship between onset span and onset rapidity. We find that the relationship between onset span and onset rapidity depends on the level of synaptic background activity. Hence we are able to elucidate the regions of parameter space for which the Hodgkin-Huxley model is able to accurately describe the behavior of this system
Rotation and Spin in Physics
We delineate the role of rotation and spin in physics, discussing in order
Newtonian classical physics, special relativity, quantum mechanics, quantum
electrodynamics and general relativity. In the latter case, we discuss the
generalization of the Kepler formula to post-Newtonian order )
including spin effects and two-body effects. Experiments which verify the
theoretical results for general relativistic spin-orbit effects are discussed
as well as efforts being made to verify the spin-spin effects
Persistent Cell Motion in the Absence of External Signals: A Search Strategy for Eukaryotic Cells
Eukaryotic cells are large enough to detect signals and then orient to them
by differentiating the signal strength across the length and breadth of the
cell. Amoebae, fibroblasts, neutrophils and growth cones all behave in this
way. Little is known however about cell motion and searching behavior in the
absence of a signal. Is individual cell motion best characterized as a random
walk? Do individual cells have a search strategy when they are beyond the range
of the signal they would otherwise move toward? Here we ask if single,
isolated, Dictyostelium and Polysphondylium amoebae bias their motion in the
absence of external cues. We placed single well-isolated Dictyostelium and
Polysphondylium cells on a nutrient-free agar surface and followed them at 10
sec intervals for ~10 hr, then analyzed their motion with respect to velocity,
turning angle, persistence length, and persistence time, comparing the results
to the expectation for a variety of different types of random motion. We find
that amoeboid behavior is well described by a special kind of random motion:
Amoebae show a long persistence time (~10 min) beyond which they start to lose
their direction; they move forward in a zig-zag manner; and they make turns
every 1-2 min on average. They bias their motion by remembering the last turn
and turning away from it. Interpreting the motion as consisting of runs and
turns, the duration of a run and the amplitude of a turn are both found to be
exponentially distributed. We show that this behavior greatly improves their
chances of finding a target relative to performing a random walk. We believe
that other eukaryotic cells may employ a strategy similar to Dictyostelium when
seeking conditions or signal sources not yet within range of their detection
system.Comment: 15 pages, 11 figures, accepted for publication in PLOS On
On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data
Convergence of density expansions of correlation functions and the Ornstein-Zernike equation
We prove absolute convergence of the multi-body correlation functions as a power series in the density uniformly in their arguments. This is done by working in the context of the cluster expansion in the canonical ensemble and by expressing the correlation functions as the derivative of the logarithm of an appropriately extended partition function. In the thermodynamic limit, due to combinatorial cancellations, we show that the coeffi- cients of the above series are expressed by sums over some class of two-connected graphs. Furthermore, we prove the convergence of the density expansion of the “direct correlation function” which is based on a completely different approach and it is valid only for some inte- gral norm. Precisely, this integral norm is suitable to derive the Ornstein-Zernike equation. As a further outcome, we obtain a rigorous quantification of the error in the Percus-Yevick approximation
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