3,949 research outputs found
Noninteracting Fermions in infinite dimensions
Usually, we study the statistical behaviours of noninteracting Fermions in
finite (mainly two and three) dimensions. For a fixed number of fermions, the
average energy per fermion is calculated in two and in three dimensions and it
becomes equal to 50 and 60 per cent of the fermi energy respectively. However,
in the higher dimensions this percentage increases as the dimensionality
increases and in infinite dimensions it becomes 100 per cent. This is an
intersting result, at least pedagogically. Which implies all fermions are
moving with Fermi momentum. This result is not yet discussed in standard text
books of quantum statistics. In this paper, this fact is discussed and
explained. I hope, this article will be helpful for graduate students to study
the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010
Discontinuous percolation transitions in real physical systems
We study discontinuous percolation transitions (PT) in the diffusion-limited
cluster aggregation model of the sol-gel transition as an example of real
physical systems, in which the number of aggregation events is regarded as the
number of bonds occupied in the system. When particles are Brownian, in which
cluster velocity depends on cluster size as with
, a larger cluster has less probability to collide with other
clusters because of its smaller mobility. Thus, the cluster is effectively more
suppressed in growth of its size. Then the giant cluster size increases
drastically by merging those suppressed clusters near the percolation
threshold, exhibiting a discontinuous PT. We also study the tricritical
behavior by controlling the parameter , and the tricritical point is
determined by introducing an asymmetric Smoluchowski equation.Comment: 5 pages, 5 figure
A Model for Phase Transition based on Statistical Disassembly of Nuclei at Intermediate Energies
Consider a model of particles (nucleons) which has a two-body interaction
which leads to bound composites with saturation properties. These properties
are : all composites have the same density and the ground state energies of
composites with k nucleons are given by -kW+\sigma k^{2/3} where W and \sigma
are positive constants. W represents a volume term and \sigma a surface tension
term. These values are taken from nuclear physics. We show that in the large N
limit where N is the number of particles such an assembly in a large enclosure
at finite temperature shows properties of liquid-gas phase transition. We do
not use the two-body interaction but the gross properties of the composites
only. We show that (a) the p-\rho isotherms show a region where pressure does
not change as changes just as in Maxwell construction of a Van der Waals
gas, (b) in this region the chemical potential does not change and (c) the
model obeys the celebrated Clausius-Clapeyron relations. A scaling law for the
yields of composites emerges. For a finite number of particles N (upto some
thousands) the problem can be easily solved on a computer. This allows us to
study finite particle number effects which modify phase transition effects. The
model is calculationally simple. Monte-Carlo simulations are not needed.Comment: RevTex file, 21 pages, 5 figure
Negative Interactions in Irreversible Self-Assembly
This paper explores the use of negative (i.e., repulsive) interaction the
abstract Tile Assembly Model defined by Winfree. Winfree postulated negative
interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu,
and Yin explored their power in the context of reversible attachment
operations. We explore the power of negative interactions with irreversible
attachments, and we achieve two main results. Our first result is an
impossibility theorem: after t steps of assembly, Omega(t) tiles will be
forever bound to an assembly, unable to detach. Thus negative glue strengths do
not afford unlimited power to reuse tiles. Our second result is a positive one:
we construct a set of tiles that can simulate a Turing machine with space bound
s and time bound t, while ensuring that no intermediate assembly grows larger
than O(s), rather than O(s * t) as required by the standard Turing machine
simulation with tiles
BLITZEN: A highly integrated massively parallel machine
The architecture and VLSI design of a new massively parallel processing array chip are described. The BLITZEN processing element array chip, which contains 1.1 million transistors, serves as the basis for a highly integrated, miniaturized, high-performance, massively parallel machine that is currently under development. Each processing element has 1K bits of static RAM and performs bit-serial processing with functional elements for arithmetic, logic, and shifting
On black hole thermalization, D0 brane dynamics, and emergent spacetime
When matter falls past the horizon of a large black hole, the expectation
from string theory is that the configuration thermalizes and the information in
the probe is rather quickly scrambled away. The traditional view of a classical
unique spacetime near a black hole horizon conflicts with this picture. The
question then arises as to what spacetime does the probe actually see as it
crosses a horizon, and how does the background geometry imprint its signature
onto the thermal properties of the probe. In this work, we explore these
questions through an extensive series of numerical simulations of D0 branes. We
determine that the D0 branes quickly settle into an incompressible symmetric
state -- thermalized within a few oscillations through a process driven
entirely by internal non-linear dynamics. Surprisingly, thermal background
fluctuations play no role in this mechanism. Signatures of the background
fields in this thermal state arise either through fluxes, i.e. black hole hair;
or if the probe expands to the size of the horizon -- which we see evidence of.
We determine simple scaling relations for the D0 branes' equilibrium size, time
to thermalize, lifetime, and temperature in terms of their number, initial
energy, and the background fields. Our results are consistent with the
conjecture that black holes are the fastest scramblers as seen by Matrix
theory.Comment: 43 pages, 12 figures; v2: added analysis showing that results are
consistent with and confirm Susskind conjecture on black hole thermalization.
Added clarification about strong coupling regime. Citation adde
Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature
Frieden and Soffer conjectured some years ago the existence of a ``Fisher
temperature" T_F that would play, with regards to Fisher's information measure
I, the same role that the ordinary temperature T plays vis-a-vis Shannon's
logarithmic measure. Here we exhibit the existence of reciprocity relations
between T_F and T and provide an interpretation with reference to the meaning
of T_F for the canonical ensemble.Comment: 3 pages, no figure
Carboplatin/taxane-induced gastrointestinal toxicity: a pharmacogenomics study on the SCOTROC1 trial
Carboplatin/taxane combination is first-line therapy for ovarian cancer. However, patients can encounter treatment delays, impaired quality of life, even death because of chemotherapy-induced gastrointestinal (GI) toxicity. A candidate gene study was conducted to assess potential association of genetic variants with GI toxicity in 808 patients who received carboplatin/taxane in the Scottish Randomized Trial in Ovarian Cancer 1 (SCOTROC1). Patients were randomized into discovery and validation cohorts consisting of 404 patients each. Clinical covariates and genetic variants associated with grade III/IV GI toxicity in discovery cohort were evaluated in replication cohort. Chemotherapy-induced GI toxicity was significantly associated with seven single-nucleotide polymorphisms in the ATP7B, GSR, VEGFA and SCN10A genes. Patients with risk genotypes were at 1.53 to 18.01 higher odds to develop carboplatin/taxane-induced GI toxicity (P<0.01). Variants in the VEGF gene were marginally associated with survival time. Our data provide potential targets for modulation/inhibition of GI toxicity in ovarian cancer patients
- …