488 research outputs found

### Relaxation for some dynamical problems

In this article, we study the functional Where ÎŠ â Än is a bounded open set and u: ÎŠ Ă(0, T)â Äm and when F: Rnm âR fails to be quasiconvex. We show that with respect to strong convergence of âu/ât and weak convergence of âĂu, the above functional behaves as where QF is the lower quasiconvex envelope of

### Convexity of certain integrals of the calculus of variations

In this paper we study the convexity of the integral over the space . We isolate a necessary condition on f and we find necessary and sufficient conditions in the case where f(x, u, uâ˛) = a(u)uâ˛2n or g(u) + h(uâ˛

### On the different convex hulls of sets involving singular values

We give a representation formula for the convex, polyconvex and rank one convex hulls of a set of n Ă n matrices with prescribed singular value

### On a differential inclusion related to the Born-Infeld equations

We study a partial differential relation that arises in the context of the
Born-Infeld equations (an extension of the Maxwell's equations) by using
Gromov's method of convex integration in the setting of divergence free fields

### Existence and equilibration of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers

We show the existence of global-in-time weak solutions to a general class of
coupled FENE-type bead-spring chain models that arise from the kinetic theory
of dilute solutions of polymeric liquids with noninteracting polymer chains.
The class of models involves the unsteady incompressible Navier-Stokes
equations in a bounded domain in two or three space dimensions for the velocity
and the pressure of the fluid, with an elastic extra-stress tensor appearing on
the right-hand side in the momentum equation. The extra-stress tensor stems
from the random movement of the polymer chains and is defined by the Kramers
expression through the associated probability density function that satisfies a
Fokker-Planck-type parabolic equation, a crucial feature of which is the
presence of a center-of-mass diffusion term. We require no structural
assumptions on the drag term in the Fokker-Planck equation; in particular, the
drag term need not be corotational. With a square-integrable and
divergence-free initial velocity datum for the Navier-Stokes equation and a
nonnegative initial probability density function for the Fokker-Planck
equation, which has finite relative entropy with respect to the Maxwellian of
the model, we prove the existence of a global-in-time weak solution to the
coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the
absence of a body force, the weak solution decays exponentially in time to the
equilibrium solution, at a rate that is independent of the choice of the
initial datum and of the centre-of-mass diffusion coefficient.Comment: 75 page

### Some examples of rank one convex functions in dimension two

We study the rank one convexity of some functions f(Îž) where Îž is a 2 Ă 2 matrix. Examples such as |Îž|2Îą + h(detÎž) and | Îž |2Îą (| Îž |2 â Îłdet Îž) are investigated. Numerical computations are done on the example of Dacorogna and Marcellini, indicating that this function is quasiconve

### Patterns in high-frequency FX data: Discovery of 12 empirical scaling laws

We have discovered 12 independent new empirical scaling laws in foreign
exchange data-series that hold for close to three orders of magnitude and
across 13 currency exchange rates. Our statistical analysis crucially depends
on an event-based approach that measures the relationship between different
types of events. The scaling laws give an accurate estimation of the length of
the price-curve coastline, which turns out to be surprisingly long. The new
laws substantially extend the catalogue of stylised facts and sharply constrain
the space of possible theoretical explanations of the market mechanisms.Comment: 26 pages, 3 figures, 23 tables,2nd version (text made more concise
and readable, algorithm pseudocode, results unchanged), 5-year datasets
(USD-JPY, EUR-USD) provided at http://www.olsen.ch/more/datasets

### Removing zero Lyapunov exponents in volume-preserving flows

Baraviera and Bonatti proved that it is possible to perturb, in the c^1
topology, a volume-preserving and partial hyperbolic diffeomorphism in order to
obtain a non-zero sum of all the Lyapunov exponents in the central direction.
In this article we obtain the analogous result for volume-preserving flows.Comment: 10 page

### Long-range memory model of trading activity and volatility

Earlier we proposed the stochastic point process model, which reproduces a
variety of self-affine time series exhibiting power spectral density S(f)
scaling as power of the frequency f and derived a stochastic differential
equation with the same long range memory properties. Here we present a
stochastic differential equation as a dynamical model of the observed memory in
the financial time series. The continuous stochastic process reproduces the
statistical properties of the trading activity and serves as a background model
for the modeling waiting time, return and volatility. Empirically observed
statistical properties: exponents of the power-law probability distributions
and power spectral density of the long-range memory financial variables are
reproduced with the same values of few model parameters.Comment: 12 pages, 5 figure

- âŚ