1,895 research outputs found
W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions
In an attempt to improve on our earlier W3 theory [J. Chem. Phys. {\bf 120},
4129 (2004)] we consider such refinements as more accurate estimates for the
contribution of connected quadruple excitations (), inclusion of
connected quintuple excitations (), diagonal Born-Oppenheimer
corrections (DBOC), and improved basis set extrapolation procedures. Revised
experimental data for validation purposes were obtained from the latest version
of the ATcT (Active Thermochemical Tables) Thermochemical Network. We found
that the CCSDTQCCSDT(Q) difference converges quite rapidly with the basis
set, and that the formula
1.10[CCSDT(Q)/cc-pVTZ+CCSDTQ/cc-pVDZCCSDT(Q)/cc-pVDZ] offers a very reliable
as well as fairly cost-effective estimate of the basis set limit
contribution. The largest contribution found in the present work is
on the order of 0.5 kcal/mol (for ozone). DBOC corrections are significant at
the 0.1 kcal/mol level in hydride systems. . Based on the accumulated
experience, a new computational thermochemistry protocol for first-and
second-row main-group systems, to be known as W4 theory, is proposed. Our W4
atomization energies for a number of key species are in excellent agreement
(better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1
kJ/mol) with the latest experimental data obtained from Active Thermochemical
Tables. A simple {\em a priori} estimate for the importance of post-CCSD(T)
correlation contributions (and hence a pessimistic estimate for the error in a
W2-type calculation) is proposed.Comment: J. Chem. Phys., in press; electronic supporting information available
at http://theochem.weizmann.ac.il/web/papers/w4.htm
Demonstration of the difference Casimir force for samples with different charge carrier densities
A measurement of the Casimir force between a gold coated sphere and two Si
plates of different carrier densities is performed using a high vacuum based
atomic force microscope. The results are compared with the Lifshitz theory and
good agreement is found. Our experiment demonstrates that by changing the
carrier density of the semiconductor plate by several orders of magnitude it is
possible to modify the Casimir interaction. This result may find applications
in nanotechnology.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let
Nonlinear dynamics in one dimension: On a criterion for coarsening and its temporal law
We develop a general criterion about coarsening for a class of nonlinear
evolution equations describing one dimensional pattern-forming systems. This
criterion allows one to discriminate between the situation where a coarsening
process takes place and the one where the wavelength is fixed in the course of
time. An intermediate scenario may occur, namely `interrupted coarsening'. The
power of the criterion lies in the fact that the statement about the occurrence
of coarsening, or selection of a length scale, can be made by only inspecting
the behavior of the branch of steady state periodic solutions. The criterion
states that coarsening occurs if lambda'(A)>0 while a length scale selection
prevails if lambda'(A)<0, where is the wavelength of the pattern and A
is the amplitude of the profile. This criterion is established thanks to the
analysis of the phase diffusion equation of the pattern. We connect the phase
diffusion coefficient D(lambda) (which carries a kinetic information) to
lambda'(A), which refers to a pure steady state property. The relationship
between kinetics and the behavior of the branch of steady state solutions is
established fully analytically for several classes of equations. Another
important and new result which emerges here is that the exploitation of the
phase diffusion coefficient enables us to determine in a rather straightforward
manner the dynamical coarsening exponent. Our calculation, based on the idea
that |D(lambda)|=lambda^2/t, is exemplified on several nonlinear equations,
showing that the exact exponent is captured. Some speculations about the
extension of the present results to higher dimension are outlined.Comment: 16 pages. Only a few minor changes. Accepted for publication in
Physical Review
Comparison of the experimental data for the Casimir pressure with the Lifshitz theory at zero temperature
We perform detailed comparison of the experimental data of the experiment on
the determination of the Casimir pressure between two parallel Au plates with
the theoretical values computed using the Lifshitz formula at zero temperature.
Computations are done using the optical data for the complex index of
refraction of Au extrapolated to low frequencies by means of the Drude model
with both most often used and other suggested Drude parameters. It is shown
that the experimental data exclude the Lifshitz formula at zero temperature at
a 70% confidence level if the Drude model with most often used values of the
parameters is employed. If other values of the Drude parameters are used, the
Lifshitz formula at zero frequency is experimentally excluded at a 95%
confidence level. The Lifshitz formula at zero temperature combined with the
generalized plasma-like model with most often used value of the plasma
frequency is shown to be experimentally consistent. We propose a decisive
experiment which will shed additional light on the role of relaxation
properties of conduction electrons in the Casimir effect.Comment: 22 pages, 6 figures; Phys. Rev. B, to appea
Synchronous Behavior of Two Coupled Electronic Neurons
We report on experimental studies of synchronization phenomena in a pair of
analog electronic neurons (ENs). The ENs were designed to reproduce the
observed membrane voltage oscillations of isolated biological neurons from the
stomatogastric ganglion of the California spiny lobster Panulirus interruptus.
The ENs are simple analog circuits which integrate four dimensional
differential equations representing fast and slow subcellular mechanisms that
produce the characteristic regular/chaotic spiking-bursting behavior of these
cells. In this paper we study their dynamical behavior as we couple them in the
same configurations as we have done for their counterpart biological neurons.
The interconnections we use for these neural oscillators are both direct
electrical connections and excitatory and inhibitory chemical connections: each
realized by analog circuitry and suggested by biological examples. We provide
here quantitative evidence that the ENs and the biological neurons behave
similarly when coupled in the same manner. They each display well defined
bifurcations in their mutual synchronization and regularization. We report
briefly on an experiment on coupled biological neurons and four dimensional ENs
which provides further ground for testing the validity of our numerical and
electronic models of individual neural behavior. Our experiments as a whole
present interesting new examples of regularization and synchronization in
coupled nonlinear oscillators.Comment: 26 pages, 10 figure
Robustness and Enhancement of Neural Synchronization by Activity-Dependent Coupling
We study the synchronization of two model neurons coupled through a synapse
having an activity-dependent strength. Our synapse follows the rules of
Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the
coupling between neurons produces enlarged frequency locking zones and results
in synchronization that is more rapid and much more robust against noise than
classical synchronization arising from connections with constant strength. We
also present a simple discrete map model that demonstrates the generality of
the phenomenon.Comment: 4 pages, accepted for publication in PR
Essential spectra of difference operators on \sZ^n-periodic graphs
Let (\cX, \rho) be a discrete metric space. We suppose that the group
\sZ^n acts freely on and that the number of orbits of with respect to
this action is finite. Then we call a \sZ^n-periodic discrete metric
space. We examine the Fredholm property and essential spectra of band-dominated
operators on where is a \sZ^n-periodic discrete metric space.
Our approach is based on the theory of band-dominated operators on \sZ^n and
their limit operators.
In case is the set of vertices of a combinatorial graph, the graph
structure defines a Schr\"{o}dinger operator on in a natural way. We
illustrate our approach by determining the essential spectra of Schr\"{o}dinger
operators with slowly oscillating potential both on zig-zag and on hexagonal
graphs, the latter being related to nano-structures
A Simple Theory of Condensation
A simple assumption of an emergence in gas of small atomic clusters
consisting of particles each, leads to a phase separation (first order
transition). It reveals itself by an emergence of ``forbidden'' density range
starting at a certain temperature. Defining this latter value as the critical
temperature predicts existence of an interval with anomalous heat capacity
behaviour . The value suggested in literature
yields the heat capacity exponent .Comment: 9 pages, 1 figur
Cyclic Statistics In Three Dimensions
While 2-dimensional quantum systems are known to exhibit non-permutation,
braid group statistics, it is widely expected that quantum statistics in
3-dimensions is solely determined by representations of the permutation group.
This expectation is false for certain 3-dimensional systems, as was shown by
the authors of ref. [1,2,3]. In this work we demonstrate the existence of
``cyclic'', or , {\it non-permutation group} statistics for a system of n
> 2 identical, unknotted rings embedded in . We make crucial use of a
theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch
relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin
Control of the Casimir force by the modification of dielectric properties with light
The experimental demonstration of the modification of the Casimir force
between a gold coated sphere and a single-crystal Si membrane by light pulses
is performed. The specially designed and fabricated Si membrane was irradiated
with 514 nm laser pulses of 5 ms width in high vacuum leading to a change of
the charge-carrier density. The difference in the Casimir force in the presence
and in the absence of laser radiation was measured by means of an atomic force
microscope as a function of separation at different powers of the absorbed
light. The total experimental error of the measured force differences at a
separation of 100 nm varies from 10 to 20% in different measurements. The
experimental results are compared with theoretical computations using the
Lifshitz theory at both zero and laboratory temperatures. The total theoretical
error determined mostly by the uncertainty in the concentration of charge
carriers when the light is incident is found to be about 14% at separations
less than 140 nm. The experimental data are consistent with the Lifshitz theory
at laboratory temperature, if the static dielectric permittivity of
high-resistivity Si in the absence of light is assumed to be finite. If the dc
conductivity of high-resistivity Si in the absence of light is included into
the model of dielectric response, the Lifshitz theory at nonzero temperature is
shown to be experimentally inconsistent at 95% confidence. The demonstrated
phenomenon of the modification of the Casimir force through a change of the
charge-carrier density is topical for applications of the Lifshitz theory to
real materials in fields ranging from nanotechnology and condensed matter
physics to the theory of fundamental interactions.Comment: 30 pages, 10 figures, 2 table
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