24,427 research outputs found
Stieltjes-Bethe equations in higher genus and branched coverings with even ramifications
We describe projective structures on a Riemann surface corresponding to
monodromy groups which have trivial monodromies around singularities
and trivial monodromies along homologically non-trivial loops on a
Riemann surface. We propose a natural higher genus analog of Stieltjes-Bethe
equations. Links with branched projective structures and with Hurwitz spaces
with ramifications of even order are established. We find a higher genus analog
of the genus zero Yang-Yang function (the function generating accessory
parameters) and describe its similarity and difference with Bergman
tau-function on the Hurwitz spaces
Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems
In "equation-free" multiscale computation a dynamic model is given at a fine,
microscopic level; yet we believe that its coarse-grained, macroscopic dynamics
can be described by closed equations involving only coarse variables. These
variables are typically various low-order moments of the distributions evolved
through the microscopic model. We consider the problem of integrating these
unavailable equations by acting directly on kinetic Monte Carlo microscopic
simulators, thus circumventing their derivation in closed form. In particular,
we use projective multi-step integration to solve the coarse initial value
problem forward in time as well as backward in time (under certain conditions).
Macroscopic trajectories are thus traced back to unstable, source-type, and
even sometimes saddle-like stationary points, even though the microscopic
simulator only evolves forward in time. We also demonstrate the use of such
projective integrators in a shooting boundary value problem formulation for the
computation of "coarse limit cycles" of the macroscopic behavior, and the
approximation of their stability through estimates of the leading "coarse
Floquet multipliers".Comment: Submitted to Journal of Computational Physic
Equation-free modeling of evolving diseases: Coarse-grained computations with individual-based models
We demonstrate how direct simulation of stochastic, individual-based models
can be combined with continuum numerical analysis techniques to study the
dynamics of evolving diseases. % Sidestepping the necessity of obtaining
explicit population-level models, the approach analyzes the (unavailable in
closed form) `coarse' macroscopic equations, estimating the necessary
quantities through appropriately initialized, short `bursts' of
individual-based dynamic simulation. % We illustrate this approach by analyzing
a stochastic and discrete model for the evolution of disease agents caused by
point mutations within individual hosts. % Building up from classical SIR and
SIRS models, our example uses a one-dimensional lattice for variant space, and
assumes a finite number of individuals. % Macroscopic computational tasks
enabled through this approach include stationary state computation, coarse
projective integration, parametric continuation and stability analysis.Comment: 16 pages, 8 figure
A thread calculus with molecular dynamics
We present a theory of threads, interleaving of threads, and interaction
between threads and services with features of molecular dynamics, a model of
computation that bears on computations in which dynamic data structures are
involved. Threads can interact with services of which the states consist of
structured data objects and computations take place by means of actions which
may change the structure of the data objects. The features introduced include
restriction of the scope of names used in threads to refer to data objects.
Because that feature makes it troublesome to provide a model based on
structural operational semantics and bisimulation, we construct a projective
limit model for the theory.Comment: 47 pages; examples and results added, phrasing improved, references
replace
Enhanced Symmetries in Multiparameter Flux Vacua
We give a construction of type IIB flux vacua with discrete R-symmetries and
vanishing superpotential for hypersurfaces in weighted projective space with
any number of moduli. We find that the existence of such vacua for a given
space depends on properties of the modular group, and for Fermat models can be
determined solely by the weights of the projective space. The periods of the
geometry do not in general have arithmetic properties, but live in a vector
space whose properties are vital to the construction.Comment: 32 pages, LaTeX. v2: references adde
Coarse Grained Computations for a Micellar System
We establish, through coarse-grained computation, a connection between
traditional, continuum numerical algorithms (initial value problems as well as
fixed point algorithms) and atomistic simulations of the Larson model of
micelle formation. The procedure hinges on the (expected) evolution of a few
slow, coarse-grained mesoscopic observables of the MC simulation, and on
(computational) time scale separation between these and the remaining "slaved",
fast variables. Short bursts of appropriately initialized atomistic simulation
are used to estimate the (coarse-grained, deterministic) local dynamics of the
evolution of the observables. These estimates are then in turn used to
accelerate the evolution to computational stationarity through traditional
continuum algorithms (forward Euler integration, Newton-Raphson fixed point
computation). This "equation-free" framework, bypassing the derivation of
explicit, closed equations for the observables (e.g. equations of state) may
provide a computational bridge between direct atomistic / stochastic simulation
and the analysis of its macroscopic, system-level consequences
- âŠ