789 research outputs found
On the Fluctuation Relation for Nose-Hoover Boundary Thermostated Systems
We discuss the transient and steady state fluctuation relation for a
mechanical system in contact with two deterministic thermostats at different
temperatures. The system is a modified Lorentz gas in which the fixed
scatterers exchange energy with the gas of particles, and the thermostats are
modelled by two Nos\'e-Hoover thermostats applied at the boundaries of the
system. The transient fluctuation relation, which holds only for a precise
choice of the initial ensemble, is verified at all times, as expected. Times
longer than the mesoscopic scale, needed for local equilibrium to be settled,
are required if a different initial ensemble is considered. This shows how the
transient fluctuation relation asymptotically leads to the steady state
relation when, as explicitly checked in our systems, the condition found in
[D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validity
of the steady state fluctuation relation, is verified. For the steady state
fluctuations of the phase space contraction rate \zL and of the dissipation
function \zW, a similar relaxation regime at shorter averaging times is
found. The quantity \zW satisfies with good accuracy the fluctuation relation
for times larger than the mesoscopic time scale; the quantity \zL appears to
begin a monotonic convergence after such times. This is consistent with the
fact that \zW and \zL differ by a total time derivative, and that the tails
of the probability distribution function of \zL are Gaussian.Comment: Major revision. Fig.10 was added. Version to appear in Journal of
Statistical Physic
Gender and race distribution of dental graduates (1985 - 2004) and first year dental students (2000 - 2005) in South Africa
This paper, written at the close of a decade
of democracy in South Africa, sets
out to analyse the demographic profile
of dental graduates from 1985-2004 at
the five Faculties/Schools of Dentistry in
South Africa. A comparison of the profiles
for the pre-democracy (1985-1994) and
post-apartheid (1995-2004) periods has
been made. The demographic profile of
first year dental students from 2000-2005
is also presented. From 1985-1994, most
dental graduates were male (79%), but
this changed substantially from 1995-2004,
with females comprising 46% of those
graduating. In the pre-democracy period,
more than three-quarters of all graduates
were White (78%), decreasing to 46% in
the post-apartheid period under review.
Black graduates increased from 6% to 24%
across the two study periods. Amongst the
first year dental student intake from 2000-
2005, females comprised 57%. There was
an almost equal distribution across the
White, Black and Asian groups.
Dental faculties/schools have made important
strides in transforming the demographic
profile of their students. The percentage
of Black graduates, however, needs to be
significantly increased if it is to reflect the
national population. Faculties/schools must
further ensure that able students from working
class background are identified and
considered for acceptance into the undergraduate
dental programme, and should
then be offered the necessary academic
and mentoring support to enable success
Enantioselective synthesis of non-proteinogenic 2-arylallyl-α-amino acids via Pd/In catalytic cascades
An efficient synthesis of both R- and S-enantiomers of 2-arylallyl-α-amino acids via a diastereoselective Pd/In mediated catalytic allylation of chiral N-sulfinyl-α-imino esters is described. The potential for further enhancement of molecular complexity and creating contiguous chiral centres by interfacing these processes with catalytic cyclisation–anion capture methodology is demonstrated
Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems
The master equation approach to Lyapunov spectra for many-particle systems is
applied to non-equilibrium thermostatted systems to discuss the conjugate
pairing rule. We consider iso-kinetic thermostatted systems with a shear flow
sustained by an external restriction, in which particle interactions are
expressed as a Gaussian white randomness. Positive Lyapunov exponents are
calculated by using the Fokker-Planck equation to describe the tangent vector
dynamics. We introduce another Fokker-Planck equation to describe the
time-reversed tangent vector dynamics, which allows us to calculate the
negative Lyapunov exponents. Using the Lyapunov exponents provided by these two
Fokker-Planck equations we show the conjugate pairing rule is satisfied for
thermostatted systems with a shear flow in the thermodynamic limit. We also
give an explicit form to connect the Lyapunov exponents with the
time-correlation of the interaction matrix in a thermostatted system with a
color field.Comment: 10 page
Class and rank of differential modules
A differential module is a module equipped with a square-zero endomorphism.
This structure underpins complexes of modules over rings, as well as
differential graded modules over graded rings. We establish lower bounds on the
class--a substitute for the length of a free complex--and on the rank of a
differential module in terms of invariants of its homology. These results
specialize to basic theorems in commutative algebra and algebraic topology. One
instance is a common generalization of the equicharacteristic case of the New
Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning
complexes over noetherian commutative rings, and of a theorem of G. Carlsson on
differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones
Mathematica
Capillary Condensation and Interface Structure of a Model Colloid-Polymer Mixture in a Porous Medium
We consider the Asakura-Oosawa model of hard sphere colloids and ideal
polymers in contact with a porous matrix modeled by immobilized configurations
of hard spheres. For this ternary mixture a fundamental measure density
functional theory is employed, where the matrix particles are quenched and the
colloids and polymers are annealed, i.e. allowed to equilibrate. We study
capillary condensation of the mixture in a tiny sample of matrix as well as
demixing and the fluid-fluid interface inside a bulk matrix. Density profiles
normal to the interface and surface tensions are calculated and compared to the
case without matrix. Two kinds of matrices are considered: (i) colloid-sized
matrix particles at low packing fractions and (ii) large matrix particles at
high packing fractions. These two cases show fundamentally different behavior
and should both be experimentally realizable. Furthermore, we argue that
capillary condensation of a colloidal suspension could be experimentally
accessible. We find that in case (ii), even at high packing fractions, the main
effect of the matrix is to exclude volume and, to high accuracy, the results
can be mapped onto those of the same system without matrix via a simple
rescaling.Comment: 12 pages, 9 figures, submitted to PR
Adsorption of Line Segments on a Square Lattice
We study the deposition of line segments on a two-dimensional square lattice.
The estimates for the coverage at jamming obtained by Monte-Carlo simulations
and by -order time-series expansion are successfully compared. The
non-trivial limit of adsorption of infinitely long segments is studied, and the
lattice coverage is consistently obtained using these two approaches.Comment: 19 pages in Latex+5 postscript files sent upon request ; PTB93_
Mean Field Fluid Behavior of the Gaussian Core Model
We show that the Gaussian core model of particles interacting via a
penetrable repulsive Gaussian potential, first considered by Stillinger (J.
Chem. Phys. 65, 3968 (1976)), behaves like a weakly correlated ``mean field
fluid'' over a surprisingly wide density and temperature range. In the bulk the
structure of the fluid phase is accurately described by the random phase
approximation for the direct correlation function, and by the more
sophisticated HNC integral equation. The resulting pressure deviates very
little from a simple, mean-field like, quadratic form in the density, while the
low density virial expansion turns out to have an extremely small radius of
convergence. Density profiles near a hard wall are also very accurately
described by the corresponding mean-field free-energy functional. The binary
version of the model exhibits a spinodal instability against de-mixing at high
densities. Possible implications for semi-dilute polymer solutions are
discussed.Comment: 13 pages, 2 columns, ReVTeX epsfig,multicol,amssym, 15 figures;
submitted to Phys. Rev. E (change: important reference added
Nonequilibrium statistical mechanics and entropy production in a classical infinite system of rotators
We analyze the dynamics of a simple but nontrivial classical Hamiltonian
system of infinitely many coupled rotators. We assume that this infinite system
is driven out of thermal equilibrium either because energy is injected by an
external force (Case I), or because heat flows between two thermostats at
different temperatures (Case II). We discuss several possible definitions of
the entropy production associated with a finite or infinite region, or with a
partition of the system into a finite number of pieces. We show that these
definitions satisfy the expected bounds in terms of thermostat temperatures and
energy flow.Comment: 36 page
Theory of asymmetric non-additive binary hard-sphere mixtures
We show that the formal procedure of integrating out the degrees of freedom
of the small spheres in a binary hard-sphere mixture works equally well for
non-additive as it does for additive mixtures. For highly asymmetric mixtures
(small size ratios) the resulting effective Hamiltonian of the one-component
fluid of big spheres, which consists of an infinite number of many-body
interactions, should be accurately approximated by truncating after the term
describing the effective pair interaction. Using a density functional treatment
developed originally for additive hard-sphere mixtures we determine the zero,
one, and two-body contribution to the effective Hamiltonian. We demonstrate
that even small degrees of positive or negative non-additivity have significant
effect on the shape of the depletion potential. The second virial coefficient
, corresponding to the effective pair interaction between two big spheres,
is found to be a sensitive measure of the effects of non-additivity. The
variation of with the density of the small spheres shows significantly
different behavior for additive, slightly positive and slightly negative
non-additive mixtures. We discuss the possible repercussions of these results
for the phase behavior of binary hard-sphere mixtures and suggest that
measurements of might provide a means of determining the degree of
non-additivity in real colloidal mixtures
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