Higher-order colored-noise effects in multivariable systems

We extend the partial resummation technique of Fokker-Planck terms for multivariable stochastic differential equations with colored noise. As an example, a model system of a Brownian particle with colored noise is studied. We prove that the asymmetric behavior found in analog simulations is due to higher-order terms which are left out in that technique. On the contrary, the systematic ¿-expansion approach can explain the analog results.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Stochastic multiresonance

We present a class of systems for which the signal-to-noise ratio as a function of the noise level may display a multiplicity of maxima. This phenomenon, referred to as stochastic multiresonance, indicates the possibility that periodic signals may be enhanced at multiple values of the noise level, instead of at a single value which has occurred in systems considered up to now in the framework of stochastic resonance.

Spatiotemporal stochastic resonance in the Swift-Hohenberg equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Stochastic resonance in a suspension of magnetic dipoles under shear flow

We show that a magnetic dipole in a shear flow under the action of an oscillating magnetic field displays stochastic resonance in the linear response regime. To this end, we compute the classical quantifiers of stochastic resonance, i.e., the signal to noise ratio, the escape time distribution, and the mean first passage time. We also discuss the limitations and role of the linear response theory in its applications to the theory of stochastic resonance.

Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seiferts integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

Stochastic resonance in a system of magnetic particles

We show that a dispersion of monodomain ferromagnetic particles in a solid phase exhibits stochastic resonance when a driven linearly polarized magnetic field is applied. By using an adiabatic approach, we calculate the power spectrum, the distribution of residence times, and the mean first passage time. The behavior of these quantities is similar to the behavior of corresponding quantities in other systems where stochastic resonance has also been observed.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Stochastic resonance in a dipole

We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a nonzero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in two different situations, i.e., when the minimum of the potential of the dipole remains fixed in time and when it switches periodically between two equilibrium points. We have also found that the signal-to-noise ratio has a maximum for a certain value of the amplitude of the oscillating field.

Entropic stochastic resonance

We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. The entropic stochastic resonance, characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single molecules and nanodevices.

Jatkuvavaletun teräksen leikkaussuunnitelman optimointi

Teollisuuden tuotannon eri prosessien optimointi on hyvin ajankohtainen aihe. Monet ohjausjärjestelmät ovat ajalta, jolloin tietokoneiden laskentateho oli hyvin vaatimaton nykyisiin verrattuna. Työssä esitetään tuotantoprosessi, joka sisältää teräksen leikkaussuunnitelman muodostamisongelman. Valuprosessi on yksi teräksen valmistuksen välivaiheita. Siinä sopivaan laatuun saatettu sula teräs valetaan linjastoon, jossa se jähmettyy ja leikataan aihioiksi. Myöhemmissä vaiheissa teräsaihioista muokataan pienempiä kokonaisuuksia, tehtaan lopputuotteita. Jatkuvavaletut aihiot voidaan leikata tilauskannasta riippuen monella eri tavalla. Tätä varten tarvitaan leikkaussuunnitelma, jonka muodostamiseksi on ratkaistava sekalukuoptimointiongelma. Sekalukuoptimointiongelmat ovat optimoinnin haastavin muoto. Niitä on tutkittu yksinkertaisempiin optimointiongelmiin nähden vähän. Nykyisten tietokoneiden laskentateho on kuitenkin mahdollistanut raskaampien ja monimutkaisempien optimointialgoritmien käytön ja kehittämisen. Työssä on käytetty ja esitetty eräs stokastisen optimoinnin menetelmä, differentiaalievoluutioalgoritmi. Tässä työssä esitetään teräksen leikkausoptimointialgoritmi. Kehitetty optimointimenetelmä toimii dynaamisesti tehdasympäristössä käyttäjien määrittelemien parametrien mukaisesti. Työ on osa Syncron Tech Oy:n Ovako Bar Oy Ab:lle toimittamaa ohjausjärjestelmää.