33,723 research outputs found
Experimental Comparisons of Derivative Free Optimization Algorithms
In this paper, the performances of the quasi-Newton BFGS algorithm, the
NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution
Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm
Optimizers (PSO) are compared experimentally on benchmark functions reflecting
important challenges encountered in real-world optimization problems.
Dependence of the performances in the conditioning of the problem and
rotational invariance of the algorithms are in particular investigated.Comment: 8th International Symposium on Experimental Algorithms, Dortmund :
Germany (2009
Spatial correlations in sheared isothermal liquids : From elastic particles to granular particles
Spatial correlations for sheared isothermal elastic liquids and granular
liquids are theoretically investigated. Using the generalized fluctuating
hydrodynamics, correlation functions for both the microscopic scale and the
macroscopic scale are obtained. The existence of the long-range correlation
functions obeying power laws has been confirmed. The validity of our
theoretical predictions have been verified from the molecular dynamics
simulation.Comment: 34 pages, 12 figure
On the frequency and remnants of Hypernovae
Under the hypothesis that some fraction of massive stellar core collapses
give rise to unusually energetic events, termed hypernovae, I examine the
required rates assuming some fraction of such events yield gamma ray bursts. I
then discuss evidence from studies of pulsars and r-process nucleosynthesis
that independently suggests the existence of a class of unusually energetic
events. Finally I describe a scenario which links these different lines of
evidence as supporting the hypernova hypothesis.Comment: TeX, To appear in ApJ Letter
Partly Occupied Wannier Functions
We introduce a scheme for constructing partly occupied, maximally localized
Wannier functions (WFs) for both molecular and periodic systems. Compared to
the traditional occupied WFs the partly occupied WFs posses improved symmetry
and localization properties achieved through a bonding-antibonding closing
procedure. We demonstrate the equivalence between bonding-antibonding closure
and the minimization of the average spread of the WFs in the case of a benzene
molecule and a linear chain of Pt atoms. The general applicability of the
method is demonstrated through the calculation of WFs for a metallic system
with an impurity: a Pt wire with a hydrogen molecular bridge.Comment: 5 pages, 4 figure
Nonlinear Screening and Effective Electrostatic Interactions in Charge-Stabilized Colloidal Suspensions
A nonlinear response theory is developed and applied to electrostatic
interactions between spherical macroions, screened by surrounding microions, in
charge-stabilized colloidal suspensions. The theory describes leading-order
nonlinear response of the microions (counterions, salt ions) to the
electrostatic potential of the macroions and predicts microion-induced
effective many-body interactions between macroions. A linear response
approximation [Phys. Rev. E 62, 3855 (2000)] yields an effective pair potential
of screened-Coulomb (Yukawa) form, as well as a one-body volume energy, which
contributes to the free energy. Nonlinear response generates effective
many-body interactions and essential corrections to both the effective pair
potential and the volume energy. By adopting a random-phase approximation (RPA)
for the response functions, and thus neglecting microion correlations,
practical expressions are derived for the effective pair and triplet potentials
and for the volume energy. Nonlinear screening is found to weaken repulsive
pair interactions, induce attractive triplet interactions, and modify the
volume energy. Numerical results for monovalent microions are in good agreement
with available ab initio simulation data and demonstrate that nonlinear effects
grow with increasing macroion charge and concentration and with decreasing salt
concentration. In the dilute limit of zero macroion concentration,
leading-order nonlinear corrections vanish. Finally, it is shown that nonlinear
response theory, when combined with the RPA, is formally equivalent to the
mean-field Poisson-Boltzmann theory and that the linear response approximation
corresponds, within integral-equation theory, to a linearized hypernetted-chain
closure.Comment: 30 pages, 8 figures, Phys. Rev. E (in press
A maximum-likelihood method for improving faint source flux and color estimates
Flux estimates for faint sources or transients are systematically biased high
because there are far more truly faint sources than bright. Corrections which
account for this effect are presented as a function of signal-to-noise ratio
and the (true) slope of the faint-source number-flux relation. The corrections
depend on the source being originally identified in the image in which it is
being photometered. If a source has been identified in other data, the
corrections are different; a prescription for calculating the corrections is
presented. Implications of these corrections for analyses of surveys are
discussed; the most important is that sources identified at signal-to-noise
ratios of four or less are practically useless.Comment: 9 pp., accepted for publication in PAS
Quasi-Optimal Filtering in Inverse Problems
A way of constructing a nonlinear filter close to the optimal Kolmogorov -
Wiener filter is proposed within the framework of the statistical approach to
inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions,
produces stable and efficient solutions by relying solely on the internal
resources of the inverse theory. The exact representation is given of the
Feasible Region for inverse solutions that follows from the statistical
consideration.Comment: 9 pages, 240 K
Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: Comparison of accurate simulation results with theory
We report a detailed study, using state-of-the-art simulation and theoretical
methods, of the depletion potential between a pair of big hard spheres immersed
in a reservoir of much smaller hard spheres, the size disparity being measured
by the ratio of diameters q=\sigma_s/\sigma_b. Small particles are treated
grand canonically, their influence being parameterized in terms of their
packing fraction in the reservoir, \eta_s^r. Two specialized Monte Carlo
simulation schemes --the geometrical cluster algorithm, and staged particle
insertion-- are deployed to obtain accurate depletion potentials for a number
of combinations of q\leq 0.1 and \eta_s^r. After applying corrections for
simulation finite-size effects, the depletion potentials are compared with the
prediction of new density functional theory (DFT) calculations based on the
insertion trick using the Rosenfeld functional and several subsequent
modifications. While agreement between the DFT and simulation is generally
good, significant discrepancies are evident at the largest reservoir packing
fraction accessible to our simulation methods, namely \eta_s^r=0.35. These
discrepancies are, however, small compared to those between simulation and the
much poorer predictions of the Derjaguin approximation at this \eta_s^r. The
recently proposed morphometric approximation performs better than Derjaguin but
is somewhat poorer than DFT for the size ratios and small sphere packing
fractions that we consider. The effective potentials from simulation, DFT and
the morphometric approximation were used to compute the second virial
coefficient B_2 as a function of \eta_s^r. Comparison of the results enables an
assessment of the extent to which DFT can be expected to correctly predict the
propensity towards fluid fluid phase separation in additive binary hard sphere
mixtures with q\leq 0.1.Comment: 16 pages, 9 figures, revised treatment of morphometric approximation
and reordered some materia
Towards first-principles understanding of the metal-insulator transition in fluid alkali metals
By treating the electron-ion interaction as perturbation in the
first-principles Hamiltonian, we have calculated the density response functions
of a fluid alkali metal to find an interesting charge instability due to
anomalous electronic density fluctuations occurring at some finite wave vector
{\bi Q} in a dilute fluid phase above the liquid-gas critical point. Since
|{\bi Q}| is smaller than the diameter of the Fermi surface, this instability
necessarily impedes the electric conduction, implying its close relevance to
the metal-insulator transition in fluid alkali metals.Comment: 11 pages, 5 figure
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