Precursor phenomena in frustrated systems

To understand the origin of the dynamical transition, between high temperature exponential relaxation and low temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in presence of disorder) or fully frustrated Ising (in absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case.Comment: Completely rewritten. New data. New result

The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at T=TcT=T_c

The form factor bootstrap approach is used to compute the exact contributions in the large distance expansion of the correlation function $<\sigma(x) \sigma(0)>$ of the two-dimensional Ising model in a magnetic field at $T=T_c$. The matrix elements of the magnetization operator $\sigma(x)$ present a rich analytic structure induced by the (multi) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.Comment: 53 pages, latex, 15 figure

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

Fibonacci-Lucas SIC-POVMs

We present a conjectured family of SIC-POVMs which have an additional symmetry group whose size is growing with the dimension. The symmetry group is related to Fibonacci numbers, while the dimension is related to Lucas numbers. The conjecture is supported by exact solutions for dimensions d=4,8,19,48,124,323, as well as a numerical solution for dimension d=844.Comment: The fiducial vectors can be obtained from http://sicpovm.markus-grassl.de as well as from the source files. v2: precision for the numerical solution in dimension 844 increased to 150 digits and new exact solution for dimension 323 adde

Stability of a Spherical Accretion Shock with Nuclear Dissociation

We examine the stability of a standing shock wave within a spherical accretion flow onto a gravitating star, in the context of core-collapse supernova explosions. Our focus is on the effect of nuclear dissociation below the shock on the linear growth, and non-linear saturation, of non-radial oscillations of the shocked fluid. We combine two-dimensional, time-dependent hydrodynamic simulations using FLASH2.5 with a solution to the linear eigenvalue problem, and demonstrate the consistency of the two approaches. Previous studies of this `Standing Accretion Shock Instability' (SASI) have focused either on zero-energy accretion flows without nuclear dissociation, or made use of a detailed finite-temperature nuclear equation of state and included strong neutrino heating. Our main goal in this and subsequent papers is to introduce equations of state of increasing complexity, in order to isolate the various competing effects. In this work we employ an ideal gas equation of state with a constant rate of nuclear dissociation below the shock, and do not include neutrino heating. We find that a negative Bernoulli parameter below the shock significantly lowers the real frequency, growth rate, and saturation amplitude of the SASI. A decrease in the adiabatic index has similar effects. The non-linear development of the instability is characterized by an expansion of the shock driven by turbulent kinetic energy at nearly constant internal energy. Our results also provide further insight into the instability mechanism: the rate of growth of a particular mode is fastest when the radial advection time from the shock to the accretor overlaps with the period of a standing lateral sound wave. The fastest-growing mode can therefore be modified by nuclear dissociation.Comment: Version accepted by ApJ. Consistent parameter range, and additional plots with eigenfrequencies in units of inverse postshock advection timescale. Minor changes otherwis

Towards a Reformulation Based Approach for Efficient Numeric Planning: Numeric Outer Entanglements

Restricting the search space has shown to be an effective approach for improving the performance of automated planning systems. A planner-independent technique for pruning the search space is domain and problem reformulation. Recently, Outer Entanglements, which are relations between planning operators and initial or goal predicates, have been introduced as a reformulation technique for eliminating potential undesirable instances of planning operators, and thus restricting the search space. Reformulation techniques, however, have been mainly applied in classical planning, although many real-world planning applications require to deal with numerical information. In this paper, we investigate the usefulness of reformulation approaches in planning with numerical fluents. In particular, we propose and extension of the notion of outer entanglements for handling numeric fluents. An empirical evaluation, which involves 150 instances from 5 domains, shows promising results

Coarse Molecular Dynamics of a Peptide Fragment: Free Energy, Kinetics, and Long-Time Dynamics Computations

We present a ``coarse molecular dynamics'' approach and apply it to studying the kinetics and thermodynamics of a peptide fragment dissolved in water. Short bursts of appropriately initialized simulations are used to infer the deterministic and stochastic components of the peptide motion parametrized by an appropriate set of coarse variables. Techniques from traditional numerical analysis (Newton-Raphson, coarse projective integration) are thus enabled; these techniques help analyze important features of the free-energy landscape (coarse transition states, eigenvalues and eigenvectors, transition rates, etc.). Reverse integration of (irreversible) expected coarse variables backward in time can assist escape from free energy minima and trace low-dimensional free energy surfaces. To illustrate the ``coarse molecular dynamics'' approach, we combine multiple short (0.5-ps) replica simulations to map the free energy surface of the ``alanine dipeptide'' in water, and to determine the ~ 1/(1000 ps) rate of interconversion between the two stable configurational basins corresponding to the alpha-helical and extended minima.Comment: The article has been submitted to "The Journal of Chemical Physics.

Constrained MC for QCD evolution with rapidity ordering and minimum kT

With the imminent start of LHC experiments, development of phenomenological tools, and in particular the Monte Carlo programs and algorithms, becomes urgent. A new algorithm for the generation of a parton shower initiated by the single initial hadron beam is presented. The new algorithm is of the class of the so called ``constrained MC'' type algorithm (an alternative to the backward evolution MC algorithm), in which the energy and the type of the parton at the end of the parton shower are constrained (predefined). The complete kinematics configurations with explicitly constructed four momenta are generated and tested. Evolution time is identical with rapidity and minimum transverse momentum is used as an infrared cut-off. All terms of the leading-logarithmic approximation in the DGLAP evolution are properly accounted for. In addition, the essential improvements towards the so-called CCFM/BFKL models are also properly implemented. The resulting parton distributions are cross-checked up to the 0.1% precision level with the help of a multitude of comparisons with other MC and non-MC programs. We regard these tests as an important asset to be exploited at the time when the presented MC will enter as a building block in a larger MC program for W/Z production process at LHC.Comment: Submitted to Computer Physics Communication

Correlation factor for diffusion in cubic crystals with solute-vacancy interactions of arbitrary range

A formalism using a double Laplace Fourier transform of the transport equation yields the return probabilities of the vacancy in the vicinity of the tracer atom in the presence of solute-vacancy interactions of arbitrary extension. Studying model cases, it is shown that taking into account the full range of the interaction may change noticeably the correlation factor. The latter depends tightly on the pattern of migration barriers which is chosen to describe the vacancy jumps around the tracer atom. A thorough ab initio evaluation of all barriers is rarely available in the literature. It is shown that approximations often used to overcome this lack of information can be misleading. The examination of dilute systems recently studied shows that the interactions within the first three neighbour shells dictate the final value with a good precision. The main improvement of the modelling comes from dropping the restrictive assumption which impose an equal value to the jump frequencies leading to a dissociation of the solute-vacancy pair.Comment: 45 pages; 8 figure