6,965 research outputs found
Euler characteristic and quadrilaterals of normal surfaces
Let be a compact 3-manifold with a triangulation . We give an
inequality relating the Euler characteristic of a surface normally embedded
in with the number of normal quadrilaterals in . This gives a relation
between a topological invariant of the surface and a quantity derived from its
combinatorial description. Secondly, we obtain an inequality relating the
number of normal triangles and normal quadrilaterals of , that depends on
the maximum number of tetrahedrons that share a vertex in .Comment: 7 pages, 1 figur
On the unsteady behavior of turbulence models
Periodically forced turbulence is used as a test case to evaluate the
predictions of two-equation and multiple-scale turbulence models in unsteady
flows. The limitations of the two-equation model are shown to originate in the
basic assumption of spectral equilibrium. A multiple-scale model based on a
picture of stepwise energy cascade overcomes some of these limitations, but the
absence of nonlocal interactions proves to lead to poor predictions of the time
variation of the dissipation rate. A new multiple-scale model that includes
nonlocal interactions is proposed and shown to reproduce the main features of
the frequency response correctly
Random walk approach to the d-dimensional disordered Lorentz gas
A correlated random walk approach to diffusion is applied to the disordered
nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length
distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic
expression for the diffusion constant in arbitrary number of dimensions d is
obtained. The result corresponds to an Enskog-like correction to the Boltzmann
prediction, being exact in the dilute limit, and better or nearly exact in
comparison to renormalized kinetic theory predictions for all allowed densities
in d=2,3. Extensive numerical simulations were also performed to elucidate the
role of the approximations involved.Comment: 5 pages, 5 figure
Dynamic multilateral markets
We study dynamic multilateral markets, in which players' payoffs result from intra-coalitional bargaining. The latter is modeled as the ultimatum game with exogenous (time-invariant) recognition probabilities and unanimity acceptance rule. Players in agreeing coalitions leave the market and are replaced by their replicas, which keeps the pool of market participants constant over time. In this infinite game, we establish payoff uniqueness of stationary equilibria and the emergence of endogenous cooperation structures when traders experience some degree of (heterogeneous) bargaining frictions. When we focus on market games with different player types, we derive, under mild conditions, an explicit formula for each type's equilibrium payoff as the market frictions vanish
Heavy Tails, Importance Sampling and Cross-Entropy
We consider the problem of estimating P (Y1+ ... +Yn > x) by importance sampling when the Yi are i.i.d. and heavy-tailed. The idea is to exploit the cross-entropy method as a tool for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y1+ ... +Yn > x,) n-1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some parametric examples (Pareto and Weibull) how this leads to precise answers, which as demonstrated numerically, are close to being variance minimal within the parametric class under consideration. Related problems for M/G/1 and GI/G/1 queues are also discussed
Boundary conditions associated with the Painlev\'e III' and V evaluations of some random matrix averages
In a previous work a random matrix average for the Laguerre unitary ensemble,
generalising the generating function for the probability that an interval at the hard edge contains eigenvalues, was evaluated in terms of
a Painlev\'e V transcendent in -form. However the boundary conditions
for the corresponding differential equation were not specified for the full
parameter space. Here this task is accomplished in general, and the obtained
functional form is compared against the most general small behaviour of
the Painlev\'e V equation in -form known from the work of Jimbo. An
analogous study is carried out for the the hard edge scaling limit of the
random matrix average, which we have previously evaluated in terms of a
Painlev\'e \IIId transcendent in -form. An application of the latter
result is given to the rapid evaluation of a Hankel determinant appearing in a
recent work of Conrey, Rubinstein and Snaith relating to the derivative of the
Riemann zeta function
Quadrilateral-octagon coordinates for almost normal surfaces
Normal and almost normal surfaces are essential tools for algorithmic
3-manifold topology, but to use them requires exponentially slow enumeration
algorithms in a high-dimensional vector space. The quadrilateral coordinates of
Tollefson alleviate this problem considerably for normal surfaces, by reducing
the dimension of this vector space from 7n to 3n (where n is the complexity of
the underlying triangulation). Here we develop an analogous theory for
octagonal almost normal surfaces, using quadrilateral and octagon coordinates
to reduce this dimension from 10n to 6n. As an application, we show that
quadrilateral-octagon coordinates can be used exclusively in the streamlined
3-sphere recognition algorithm of Jaco, Rubinstein and Thompson, reducing
experimental running times by factors of thousands. We also introduce joint
coordinates, a system with only 3n dimensions for octagonal almost normal
surfaces that has appealing geometric properties.Comment: 34 pages, 20 figures; v2: Simplified the proof of Theorem 4.5 using
cohomology, plus other minor changes; v3: Minor housekeepin
Topological analysis of polymeric melts: Chain length effects and fast-converging estimators for entanglement length
Primitive path analyses of entanglements are performed over a wide range of
chain lengths for both bead spring and atomistic polyethylene polymer melts.
Estimators for the entanglement length N_e which operate on results for a
single chain length N are shown to produce systematic O(1/N) errors. The
mathematical roots of these errors are identified as (a) treating chain ends as
entanglements and (b) neglecting non-Gaussian corrections to chain and
primitive path dimensions. The prefactors for the O(1/N) errors may be large;
in general their magnitude depends both on the polymer model and the method
used to obtain primitive paths. We propose, derive and test new estimators
which eliminate these systematic errors using information obtainable from the
variation of entanglement characteristics with chain length. The new estimators
produce accurate results for N_e from marginally entangled systems. Formulas
based on direct enumeration of entanglements appear to converge faster and are
simpler to apply.Comment: Major revisions. Developed near-ideal estimators which operate on
multiple chain lengths. Now test these on two very different model polymers
Energy spectra of finite temperature superfluid helium-4 turbulence
A mesoscopic model of finite temperature superfluid helium-4 based on coupled Langevin-Navier-Stokes dynamics is proposed. Drawing upon scaling arguments and available numerical results, a numerical method for designing well resolved, mesoscopic calculations of finite temperature superfluid turbulence is developed. The application of model and numerical method to the problem of fully developed turbulence decay in helium II, indicates that the spectral structure of normal-fluid and superfluid turbulence is significantly more complex than that of turbulence in simple-fluids. Analysis based on a forced flow of helium-4 at 1.3 K, where viscous dissipation in the normal-fluid is compensated by the Lundgren force, indicate three scaling regimes in the normal-fluid, that include the inertial, low wavenumber, Kolmogorov k?5/3 regime, a sub-turbulence, low Reynolds number, fluctuating k?2.2 regime, and an intermediate, viscous k?6 range that connects the two. The k?2.2 regime is due to normal-fluid forcing by superfluid vortices at high wavenumbers. There are also three scaling regimes in the superfluid, that include a k?3 range that corresponds to the growth of superfluid vortex instabilities due to mutual-friction action, and an adjacent, low wavenumber, k?5/3 regime that emerges during the termination of this growth, as superfluid vortices agglomerate between intense normal-fluid vorticity regions, and weakly polarized bundles are formed. There is also evidence of a high wavenumber k?1 range that corresponds to the probing of individual-vortex velocity fields. The Kelvin waves cascade (the main dynamical effect in zero temperature superfluids) appears to be damped at the intervortex space scale
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