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.

Mean field model for spatially extended systems in the presence of multiplicative noise

We present a mean field model that describes the effect of multiplicative noise in spatially extended systems. The model can be solved analytically. For the case of the phi4 potential it predicts that the phase transition is shifted. This conclusion is supported by numerical simulations of this model in two dimensions.

Front dynamics in the presence of spatio-temporal structured noises

Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatiotemporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time, and correlation length appear explicitly. The different effects of these parameters are discussed for the Ginzburg-Landau and Schlögl models. We obtain an analytical expression for the front velocity as a function of the noise parameters. Numerical simulation results are in a good agreement with the theoretical predictions.

Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise

We study the dynamics of reaction-diffusion fronts under the influence of multiplicative noise. An approximate theoretical scheme is introduced to compute the velocity of the front and its diffusive wandering due to the presence of noise. The theoretical approach is based on a multiple scale analysis rather than on a small noise expansion and is confirmed with numerical simulations for a wide range of the noise intensity. We report on the possibility of noise sustained solutions with a continuum of possible velocities, in situations where only a single velocity is allowed without noise.

Nonequilibrium transitions induced by multiplicative noise

A simple model exhibiting a noise-induced ordering transition (NIOT) and a noise-induced disordering transition (NIDT), in which the noise is purely multiplicative, is presented. Both transitions are found in two dimensions as well as in one dimension. We show analytically and numerically that the critical behavior of these two transitions is described by the so called multiplicative noise (MN) universality class. A computation of the set of critical exponents is presented in both d=1 and d=2.

Thermal and back-action noises in dual-sphere gravitational-wave detectors

We study the sensitivity limits of a broadband gravitational-wave detector based on dual resonators such as nested spheres. We determine both the thermal and back-action noises when the resonators displacements are read out with an optomechanical sensor. We analyze the contributions of all mechanical modes, using a new method to deal with the force-displacement transfer functions in the intermediate frequency domain between the two gravitational-wave sensitive modes associated with each resonator. This method gives an accurate estimate of the mechanical response, together with an evaluation of the estimate error. We show that very high sensitivities can be reached on a wide frequency band for realistic parameters in the case of a dual-sphere detector.

Multiplicative noise effects on relaxations from marginal states

Relaxational processes in bistable potentials close to marginal conditions are studied under the combined effect of additive and multiplicative fluctuations. Characteristic time scales associated with the first-passage-time-distribution are analytically obtained. Multiplicative noise introduces large effects on the characteristic decay times, which is particularly significant when relaxations are mediated by fluctuations, i.e., below marginality and for small noise intensity. The relevance of our approach with respect to realistic chemical bistable systems experimentally operated under external noise influences is mentioned.

Affective and physiological responses to environmental noises and music

Research suggests that respiratory patterns may reflect general dimensions of emotional response. In this study, we investigated the relationships between judgments of affective valence (pleasantness) and arousal and respiratory responses to acoustic stimuli. Sixteen environmental noises and 16 musical fragments of 30 s duration were presented to 31 participants, while respiration, skin conductance level and heart rate were recorded. Judgments of valence and arousal were registered using the 9-point Self-Assessment Manikin. For noises, breathing accelerated and minute ventilation augmented with decreases in pleasantness for low-arousal stimuli and with increases in arousal for positive stimuli. For music, breathing accelerated and minute ventilation augmented with increases both in rated valence and arousal. Skin conductance level increased with arousal ratings for music but not for noises, whereas mean heart rate increased with rated arousal for noises but not for music. Although both noises and music are sound-vibrations, differences in the relationships between affective judgments and physiological responses were found suggesting differences in the processing of the two types of acoustic stimuli. [Authors]

Langevin equations with multiplicative noise: Application to domain growth

Langevin Equations of Ginzburg-Landau form, with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hiliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical predictions of the linear analysis. We also present simulation results for spinodal decomposition at large times.

Multiplicative interaction of functional inflammasome genetic variants in determining the risk of gout.

INTRODUCTION: The acute gout flare results from a localised self-limiting innate immune response to monosodium urate (MSU) crystals deposited in joints in hyperuricaemic individuals. Activation of the caspase recruitment domain-containing protein 8 (CARD8) NOD-like receptor pyrin-containing 3 (NLRP3) inflammasome by MSU crystals and production of mature interleukin-1β (IL-1β) is central to acute gouty arthritis. However very little is known about genetic control of the innate immune response involved in acute gouty arthritis. Therefore our aim was to test functional single nucleotide polymorphism (SNP) variants in the toll-like receptor (TLR)-inflammasome-IL-1β axis for association with gout. METHODS: 1,494 gout cases of European and 863 gout cases of New Zealand (NZ) Polynesian (Māori and Pacific Island) ancestry were included. Gout was diagnosed by the 1977 ARA gout classification criteria. There were 1,030 Polynesian controls and 10,942 European controls including from the publicly-available Atherosclerosis Risk in Communities (ARIC) and Framingham Heart (FHS) studies. The ten SNPs were either genotyped by Sequenom MassArray or by Affymetrix SNP array or imputed in the ARIC and FHS datasets. Allelic association was done by logistic regression adjusting by age and sex with European and Polynesian data combined by meta-analysis. Sample sets were pooled for multiplicative interaction analysis, which was also adjusted by sample set. RESULTS: Eleven SNPs were tested in the TLR2, CD14, IL1B, CARD8, NLRP3, MYD88, P2RX7, DAPK1 and TNXIP genes. Nominally significant (P < 0.05) associations with gout were detected at CARD8 rs2043211 (OR = 1.12, P = 0.007), IL1B rs1143623 (OR = 1.10, P = 0.020) and CD14 rs2569190 (OR = 1.08; P = 0.036). There was significant multiplicative interaction between CARD8 and IL1B (P = 0.005), with the IL1B risk genotype amplifying the risk effect of CARD8. CONCLUSION: There is evidence for association of gout with functional variants in CARD8, IL1B and CD14. The gout-associated allele of IL1B increases expression of IL-1β - the multiplicative interaction with CARD8 would be consistent with a synergy of greater inflammasome activity (resulting from reduced CARD8) combined with higher levels of pre-IL-1β expression leading to increased production of mature IL-1β in gout.

Distinguishing schemes and tasks in children's development of multiplicative reasoning

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Office noises and their effect on audiometry

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Detecting non-multiplicative genotype relative risks from transmissions of parental alleles to affected children

The differential transmission of alleles from parents to affected children indicates that the locus under investigation is either directly involved in the occurrence of the disease or that there are allelic associations with other loci that are directly involved. Conditional logistic regression applied to a diallelic locus leads to a test with two degrees of freedom. The power of a single degree of freedom test to detect non-multiplicative allelic effects is discussed here.