3,066 research outputs found
A Criterion for the Critical Number of Fermions and Chiral Symmetry Breaking in Anisotropic QED(2+1)
By analyzing the strength of a photon-fermion coupling using basic scattering
processes we calculate the effect of a velocity anisotropy on the critical
number of fermions at which mass is dynamically generated in planar QED. This
gives a quantitative criterion which can be used to locate a quantum critical
point at which fermions are gapped and confined out of the physical spectrum in
a phase diagram of various condensed matter systems. We also discuss the
mechanism of relativity restoration within the symmetric, quantum-critical
phase of the theory.Comment: To appear in Physical Review
Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study
We perform a comparative study of the free energies and the density
distributions in hard sphere crystals using Monte Carlo simulations and density
functional theory (employing Fundamental Measure functionals). Using a recently
introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009))
we obtain crystal free energies to a high precision. The free energies from
Fundamental Measure theory are in good agreement with the simulation results
and demonstrate the applicability of these functionals to the treatment of
other problems involving crystallization. The agreement between FMT and
simulations on the level of the free energies is also reflected in the density
distributions around single lattice sites. Overall, the peak widths and
anisotropy signs for different lattice directions agree, however, it is found
that Fundamental Measure theory gives slightly narrower peaks with more
anisotropy than seen in the simulations. Among the three types of Fundamental
Measure functionals studied, only the White Bear II functional (Hansen-Goos and
Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for
the equilibrium vacancy concentration and a physical behavior of the chemical
potential in crystals constrained by a fixed vacancy concentration.Comment: 17 pages, submitted to Phys. Rev.
Extension of PRISM by Synthesis of Optimal Timeouts in Fixed-Delay CTMC
We present a practically appealing extension of the probabilistic model
checker PRISM rendering it to handle fixed-delay continuous-time Markov chains
(fdCTMCs) with rewards, the equivalent formalism to the deterministic and
stochastic Petri nets (DSPNs). fdCTMCs allow transitions with fixed-delays (or
timeouts) on top of the traditional transitions with exponential rates. Our
extension supports an evaluation of expected reward until reaching a given set
of target states. The main contribution is that, considering the fixed-delays
as parameters, we implemented a synthesis algorithm that computes the
epsilon-optimal values of the fixed-delays minimizing the expected reward. We
provide a performance evaluation of the synthesis on practical examples
Potts-Percolation-Gauss Model of a Solid
We study a statistical mechanics model of a solid. Neighboring atoms are
connected by Hookian springs. If the energy is larger than a threshold the
"spring" is more likely to fail, while if the energy is lower than the
threshold the spring is more likely to be alive. The phase diagram and
thermodynamic quantities, such as free energy, numbers of bonds and clusters,
and their fluctuations, are determined using renormalization-group and
Monte-Carlo techniques.Comment: 10 pages, 12 figure
An Euler-type formula for and closed-form expressions for a class of zeta series
In a recent work, Dancs and He found an Euler-type formula for
, being a positive integer, which contains a series
they could not reduce to a finite closed-form. This open problem reveals a
greater complexity in comparison to , which is a rational multiple
of . For the Dirichlet beta function, the things are `inverse':
is a rational multiple of and no closed-form
expression is known for . Here in this work, I modify the Dancs-He
approach in order to derive an Euler-type formula for ,
including , the Catalan's constant. I also convert the
resulting series into zeta series, which yields new exact closed-form
expressions for a class of zeta series involving and a finite
number of odd zeta values. A closed-form expression for a certain zeta series
is also conjectured.Comment: 11 pages, no figures. A few small corrections. ACCEPTED for
publication in: Integral Transf. Special Functions (09/11/2011
Rocky core solubility in Jupiter and giant exoplanets
Gas giants are believed to form by the accretion of hydrogen-helium gas
around an initial protocore of rock and ice. The question of whether the rocky
parts of the core dissolve into the fluid H-He layers following formation has
significant implications for planetary structure and evolution. Here we use ab
initio calculations to study rock solubility in fluid hydrogen, choosing MgO as
a representative example of planetary rocky materials, and find MgO to be
highly soluble in H for temperatures in excess of approximately 10000 K,
implying significant redistribution of rocky core material in Jupiter and
larger exoplanets
Plasticization and antiplasticization of polymer melts diluted by low molar mass species
An analysis of glass formation for polymer melts that are diluted by
structured molecular additives is derived by using the generalized entropy
theory, which involves a combination of the Adam-Gibbs model and the direct
computation of the configurational entropy based on a lattice model of polymer
melts that includes monomer structural effects. Antiplasticization is
accompanied by a "toughening" of the glass mixture relative to the pure
polymer, and this effect is found to occur when the diluents are small species
with strongly attractive interactions with the polymer matrix. Plasticization
leads to a decreased glass transition temperature T_g and a "softening" of the
fragile host polymer in the glass state. Plasticization is prompted by small
additives with weakly attractive interactions with the polymer matrix. The
shifts in T_g of polystyrene diluted by fully flexible short oligomers are
evaluated from the computations, along with the relative changes in the
isothermal compressibility at T_g to characterize the extent to which the
additives act as antiplasticizers or plasticizers. The theory predicts that a
decreased fragility can accompany both antiplasticization and plasticization of
the glass by molecular additives. The general reduction in the T_g and
fragility of polymers by these molecular additives is rationalized by analyzing
the influence of the diluent's properties (cohesive energy, chain length, and
stiffness) on glass formation in diluted polymer melts. The description of
glass formation at fixed temperature that is induced upon change the fluid
composition directly implies the Angell equation for the structural relaxation
time as function of the polymer concentration, and the computed "zero mobility
concentration" scales linearly with the inverse polymerization index N.Comment: 12 pages, 15 figure
Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms
Continuous-time Markov chains with alarms (ACTMCs) allow for alarm events
that can be non-exponentially distributed. Within parametric ACTMCs, the
parameters of alarm-event distributions are not given explicitly and can be
subject of parameter synthesis. An algorithm solving the -optimal
parameter synthesis problem for parametric ACTMCs with long-run average
optimization objectives is presented. Our approach is based on reduction of the
problem to finding long-run average optimal strategies in semi-Markov decision
processes (semi-MDPs) and sufficient discretization of parameter (i.e., action)
space. Since the set of actions in the discretized semi-MDP can be very large,
a straightforward approach based on explicit action-space construction fails to
solve even simple instances of the problem. The presented algorithm uses an
enhanced policy iteration on symbolic representations of the action space. The
soundness of the algorithm is established for parametric ACTMCs with
alarm-event distributions satisfying four mild assumptions that are shown to
hold for uniform, Dirac and Weibull distributions in particular, but are
satisfied for many other distributions as well. An experimental implementation
shows that the symbolic technique substantially improves the efficiency of the
synthesis algorithm and allows to solve instances of realistic size.Comment: This article is a full version of a paper accepted to the Conference
on Quantitative Evaluation of SysTems (QEST) 201
Optimizing Performance of Continuous-Time Stochastic Systems using Timeout Synthesis
We consider parametric version of fixed-delay continuous-time Markov chains
(or equivalently deterministic and stochastic Petri nets, DSPN) where
fixed-delay transitions are specified by parameters, rather than concrete
values. Our goal is to synthesize values of these parameters that, for a given
cost function, minimise expected total cost incurred before reaching a given
set of target states. We show that under mild assumptions, optimal values of
parameters can be effectively approximated using translation to a Markov
decision process (MDP) whose actions correspond to discretized values of these
parameters
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