37,401 research outputs found
Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoids
Numerical continuation methods for deterministic dynamical systems have been
one of the most successful tools in applied dynamical systems theory.
Continuation techniques have been employed in all branches of the natural
sciences as well as in engineering to analyze ordinary, partial and delay
differential equations. Here we show that the deterministic continuation
algorithm for equilibrium points can be extended to track information about
metastable equilibrium points of stochastic differential equations (SDEs). We
stress that we do not develop a new technical tool but that we combine results
and methods from probability theory, dynamical systems, numerical analysis,
optimization and control theory into an algorithm that augments classical
equilibrium continuation methods. In particular, we use ellipsoids defining
regions of high concentration of sample paths. It is shown that these
ellipsoids and the distances between them can be efficiently calculated using
iterative methods that take advantage of the numerical continuation framework.
We apply our method to a bistable neural competition model and a classical
predator-prey system. Furthermore, we show how global assumptions on the flow
can be incorporated - if they are available - by relating numerical
continuation, Kramers' formula and Rayleigh iteration.Comment: 29 pages, 7 figures [Fig.7 reduced in quality due to arXiv size
restrictions]; v2 - added Section 9 on Kramers' formula, additional
computations, corrected typos, improved explanation
Dynamics of the critical Casimir force for a conserved order parameter after a critical quench
Fluctuation-induced forces occur generically when long-ranged correlations
(e.g., in fluids) are confined by external bodies. In classical systems, such
correlations require specific conditions, e.g., a medium close to a critical
point. On the other hand, long-ranged correlations appear more commonly in
certain non-equilibrium systems with conservation laws. Consequently, a variety
of non-equilibrium fluctuation phenomena, including fluctuation-induced forces,
have been discovered and explored recently. Here, we address a long-standing
problem of non-equilibrium critical Casimir forces emerging after a quench to
the critical point in a confined fluid with order-parameter-conserving dynamics
and non-symmetry-breaking boundary conditions. The interplay of inherent
(critical) fluctuations and dynamical non-local effects (due to density
conservation) gives rise to striking features, including correlation functions
and forces exhibiting oscillatory time-dependences. Complex transient regimes
arise, depending on initial conditions and the geometry of the confinement. Our
findings pave the way for exploring a wealth of non-equilibrium processes in
critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In
certain regimes, our results are applicable to active matter.Comment: 38 pages, 11 figure
Constraints on split-UED from Electroweak Precision Tests
We present strongly improved electroweak precision constraints on the
split-UED model. We find that the dominating effect arises from contributions
to the muon decay rate by the exchange of even-numbered W-boson Kaluza-Klein
modes at tree-level, which so far have not been discussed in the context of UED
models. The constraints on the split-UED parameter space are translated into
bounds on the mass difference of the first Kaluza-Klein mode of fermions and
the lightest Kaluza-Klein mode, which will be tested is the LHC.Comment: 4 pages, 2 figure
A bijection between unicellular and bicellular maps
In this paper we present a combinatorial proof of a relation between the
generating functions of unicellular and bicellular maps. This relation is a
consequence of the Schwinger-Dyson equation of matrix theory. Alternatively it
can be proved using representation theory of the symmetric group. Here we give
a bijective proof by rewiring unicellular maps of topological genus
into bicellular maps of genus and pairs of unicellular maps of lower
topological genera. Our result has immediate consequences for the folding of
RNA interaction structures, since the time complexity of folding the
transformed structure is , where are the lengths of the
respective backbones, while the folding of the original structure has
time complexity, where is the length of the longer sequence.Comment: 18 pages, 13 figure
K-ras and p53 mutations in colonic lavage fluid of patients with colorectal neoplasias
Background: The adenoma-carcinoma sequence has its molecular basis in several gene mutations of which K-ras and p53 are of paramount importance. The aims of this study were to evaluate whether these genetic alterations can be detected in colonic lavage fluid from patients with colorectal adenomas and carcinomas. Methods: In 45 patients with adenomas, 20 patients with colorectal carcinomas and 38 patients with non-neoplastic and noninflammatory diseases of the colon p53 and K-ras mutations were evaluated in colonic lavage fluid employing single-strand confirmation polymorphism analysis and dot-blot hybridization, respectively. Results: Mutations of the K-ras and the p53 gene were found in 15.6% (p = 0.065) of patients with adenomas, in 25.0% (p = 0.016) of patients with carcinomas and in 2.6% in the control group. Conclusion: Genetic alterations in the colonic lavage fluid could be an additional diagnostic tool for the surveillance of patients with colorectal neoplasias. Copyright (C) 2001 S. Karger AG, Basel
Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
We present a shortened and simplified version of our proof
\cite{Fischer:2006vf} of the uniqueness of the scaling solution for the
infrared asymptotics of Green functions in Landau gauge Yang-Mills theory. The
simplification relates to a new RG-invariant arrangement of Green functions
applicable to general theories. As before the proof relies on the necessary
consistency between Dyson-Schwinger equations (DSEs) and functional
renormalisation group equations (FRGs). We also demonstrate the existence of a
specific scaling solution for both, DSEs and FRGs, that displays uniform and
soft kinematic singularities.Comment: 12 pages, 10 figure
Spontaneous spatial fractal pattern formation in absorptive systems
We predict, for the first time to our knowledge, that purely-absorptive nonlinearity can support spontaneous spatial fractal pattern formation. A passive optical ring cavity with a thin slice of saturable absorber is analyzed. Linear stability analysis yields threshold curves for Turing (static) instabilities with features proposed as characteristics of potential fractal pattern formation. Numerical simulations of the fully-nonlinear dynamics, with both one and two transverse dimensions, confirm theoretical predictions
Dynamic wetting with two competing adsorbates
We study the dynamic properties of a model for wetting with two competing
adsorbates on a planar substrate. The two species of particles have identical
properties and repel each other. Starting with a flat interface one observes
the formation of homogeneous droplets of the respective type separated by
nonwet regions where the interface remains pinned. The wet phase is
characterized by slow coarsening of competing droplets. Moreover, in 2+1
dimensions an additional line of continuous phase transition emerges in the
bound phase, which separates an unordered phase from an ordered one. The
symmetry under interchange of the particle types is spontaneously broken in
this region and finite systems exhibit two metastable states, each dominated by
one of the species. The critical properties of this transition are analyzed by
numeric simulations.Comment: 11 pages, 12 figures, final version published in PR
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