8,918 research outputs found
Langevin equation for the extended Rayleigh model with an asymmetric bath
In this paper a one-dimensional model of two infinite gases separated by a
movable heavy piston is considered. The non-linear Langevin equation for the
motion of the piston is derived from first principles for the case when the
thermodynamic parameters and/or the molecular masses of gas particles on left
and right sides of the piston are different. Microscopic expressions involving
time correlation functions of the force between bath particles and the piston
are obtained for all parameters appearing in the non-linear Langevin equation.
It is demonstrated that the equation has stationary solutions corresponding to
directional fluctuation-induced drift in the absence of systematic forces. In
the case of ideal gases interacting with the piston via a quadratic repulsive
potential, the model is exactly solvable and explicit expressions for the
kinetic coefficients in the non-linear Langevin equation are derived. The
transient solution of the non-linear Langevin equation is analyzed
perturbatively and it is demonstrated that previously obtained results for
systems with the hard-wall interaction are recovered.Comment: 10 pages. To appear in Phys. Rev.
Proof of phase separation in the binary-alloy problem: the one-dimensional spinless Falicov-Kimball model
The ground states of the one-dimensional Falicov-Kimball model are
investigated in the small-coupling limit, using nearly degenerate perturbation
theory. For rational electron and ion densities, respectively equal to
, , with relatively prime to and
close enough to , we find that in the ground state
the ion configuration has period . The situation is analogous to the Peierls
instability where the usual arguments predict a period- state that produces
a gap at the Fermi level and is insulating. However for far
enough from , this phase becomes unstable against phase
separation. The ground state is a mixture of a period- ionic configuration
and an empty (or full) configuration, where both configurations have the same
electron density to leading order. Combining these new results with those
previously obtained for strong coupling, it follows that a phase transition
occurs in the ground state, as a function of the coupling, for ion densities
far enough from .Comment: 22 pages, typeset in ReVTeX and one encapsulated postscript file
embedded in the text with eps
Ground States and Flux Configurations of the Two-dimensional Falicov-Kimball Model
The Falicov-Kimball model is a lattice model of itinerant spinless fermions
("electrons") interacting by an on-site potential with classical particles
("ions"). We continue the investigations of the crystalline ground states that
appear for various filling of electrons and ions, for large coupling. We
investigate the model for square as well as triangular lattices. New ground
states are found and the effects of a magnetic flux on the structure of the
phase diagram is studied. The flux phase problem where one has to find the
optimal flux configurations and the nuclei configurations is also solved in
some cases. Finaly we consider a model where the fermions are replaced by
hard-core bosons. This model also has crystalline ground states. Therefore
their existence does not require the Pauli principle, but only the on-site
hard-core constraint for the itinerant particles.Comment: 42 pages, uuencoded postscript file. Missing pages adde
Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction
We introduce and begin a systematic study of sublinearly contracting
projections. We give two characterizations of Morse quasi-geodesics in an
arbitrary geodesic metric space. One is that they are sublinearly contracting;
the other is that they have completely superlinear divergence. We give a
further characterization of sublinearly contracting projections in terms of
projections of geodesic segments.Comment: 24 pages, 5 figures. v2: 22 pages, 5 figures. Correction in proof of
Thm 7.1. Proof of Prop 4.2 revised for improved clarity. Other minor changes
per referee comments. To appear in Documenta Mathematic
Negative curvature in graphical small cancellation groups
We use the interplay between combinatorial and coarse geometric versions of
negative curvature to investigate the geometry of infinitely presented
graphical small cancellation groups. In particular, we characterize
their 'contracting geodesics', which should be thought of as the geodesics that
behave hyperbolically.
We show that every degree of contraction can be achieved by a geodesic in a
finitely generated group. We construct the first example of a finitely
generated group containing an element that is strongly contracting with
respect to one finite generating set of and not strongly contracting with
respect to another. In the case of classical small cancellation
groups we give complete characterizations of geodesics that are Morse and that
are strongly contracting.
We show that many graphical small cancellation groups contain
strongly contracting elements and, in particular, are growth tight. We
construct uncountably many quasi-isometry classes of finitely generated,
torsion-free groups in which every maximal cyclic subgroup is hyperbolically
embedded. These are the first examples of this kind that are not subgroups of
hyperbolic groups.
In the course of our analysis we show that if the defining graph of a
graphical small cancellation group has finite components, then the
elements of the group have translation lengths that are rational and bounded
away from zero.Comment: 40 pages, 14 figures, v2: improved introduction, updated statement of
Theorem 4.4, v3: new title (previously: "Contracting geodesics in infinitely
presented graphical small cancellation groups"), minor changes, to appear in
Groups, Geometry, and Dynamic
Photographing Bioluminescence, Ethics, and Lessons from a Misguided Ethnographer
The author explores the role of the photograph in science, as well as the implicit and explicit biases associated with each use. Analysis of the various forms of manipulation present in Edward Curtis’ photographs serve to illustrate what ramifications implicit and explicit bias can have on both scientific photography and the way in which science is disseminated through photographs. This historical example highlights existing ambiguity within the scientific community regarding the use of the photograph and the pitfalls such ambiguity may generate
The Tax Exempt Status of Racially Discriminatory Religious Schools - Bob Jones University v. United States
On the Second Law of thermodynamics and the piston problem
The piston problem is investigated in the case where the length of the
cylinder is infinite (on both sides) and the ratio is a very small
parameter, where is the mass of one particle of the gaz and is the mass
of the piston. Introducing initial conditions such that the stochastic motion
of the piston remains in the average at the origin (no drift), it is shown that
the time evolution of the fluids, analytically derived from Liouville equation,
agrees with the Second Law of thermodynamics.
We thus have a non equilibrium microscopical model whose evolution can be
explicitly shown to obey the two laws of thermodynamics.Comment: 29 pages, 9 figures submitted to Journal of Statistical Physics
(2003
Two intracellular and cell type-specific bacterial symbionts in the placozoan Trichoplax H2
Placozoa is an enigmatic phylum of simple, microscopic, marine metazoans(1,2). Although intracellular bacteria have been found in all members of this phylum, almost nothing is known about their identity, location and interactions with their host(3-6). We used metagenomic and metatranscriptomic sequencing of single host individuals, plus metaproteomic and imaging analyses, to show that the placozoan Trichoplax sp. H2 lives in symbiosis with two intracellular bacteria. One symbiont forms an undescribed genus in the Midichloriaceae (Rickettsiales)(7,8) and has a genomic repertoire similar to that of rickettsial parasites(9,10), but does not seem to express key genes for energy parasitism. Correlative image analyses and three-dimensional electron tomography revealed that this symbiont resides in the rough endoplasmic reticulum of its host's internal fibre cells. The second symbiont belongs to the Margulisbacteria, a phylum without cultured representatives and not known to form intracellular associations(11-13). This symbiont lives in the ventral epithelial cells of Trichoplax, probably metabolizes algal lipids digested by its host and has the capacity to supplement the placozoan's nutrition. Our study shows that one of the simplest animals has evolved highly specific and intimate associations with symbiotic, intracellular bacteria and highlights that symbioses can provide access to otherwise elusive microbial dark matter
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