In this work we consider the problem of pattern formation modeled by a one dimensional stochastic reaction–diffusion equation with time periodic coefficients. In particular, we apply Large Deviations ...methods to obtain lower bounds on the probability that certain evenly spaced patterns will develop. Our estimates are optimized when the number of interfaces scales as (ϵT)−1, where ϵ is the length-scale and T is the time-scale. For large times T=ρ|lnϵ| our lower bound is of order exp(−ϵ2ρ), suggesting high likelihood for evenly spaced patterns whose number of interfaces is of order (ϵρ|lnϵ|)−1. Numerical simulations provide support to the idea that the more likely number of interfaces, even among unevenly spaced patterns, follows this law.
•Method to obtain bounds on probability of patterns is applied.•Estimates suggest patterns appear under low frequency forcing.•The optimal number of interfaces likely balances opposite effects of diffusion.
λ-cyhalotrin is a pyrethroid pesticide used for protection of crops against various insect pests. Knowledge on behavioural and physiological responses of non-target organisms such as cladocerans is ...very limited. Daphnia is a sensitive organism commonly used in determination of ecotoxicological risk for various substances introduced to aquatic environment, however the main experimental endpoints used such as mortality or immobilisation may not be sufficient to evaluate subtle alterations in zooplankton. The aim of the present study was to evaluate swimming behaviour and physiological parameters of Daphnia magna exposed to λ-cyhalothrin (Karate Zeon 050 CS) at concentrations of 0.05, 0.5, 5 and 50 μg L−1 for 2, 24 and 48 h. The results showed that λ-cyhalothrin affected D. magna swimming behaviour inducing a concentration-dependent inhibition of swimming track density, speed and turning ability. Depression of physiological parameters such as heart rate and thoracic limb activity was also noted. The results suggest that in natural conditions swimming behaviour and physiological endpoints of D. magna may be disturbed by environmental concentrations of λ-cyhalothrin leading to ecological consequences.
•λ-cyhalothrin alters swimming ability of Daphnia magna.•λ-cyhalothrin affects Daphnia heart rate and thoracic limb activity.•Behavioural and physiological parameters of Daphnia magna are sensitive biomarkers of λ-cyhalothrin.
A celebrated conjecture due to De Giorgi states that any bounded solution of the equation Δu + (1 – u²)u = 0 in ℝ N with ∂ yN u > 0 must be such that its level sets {u – λ} are all hyperplanes, at ...least for dimension N ≤ 8. A counterexample for N ≥ 9 has long been believed to exist. Starting from a minimal graph Γ which is not a hyperplane, found by Bombieri, De Giorgi and Giusti in ℝ N , N ≥ 9, we prove that for any small α >0 there is a bounded solution u α (y) with ∂ yN u α > 0, which resembles tanh $\left( {\frac{t}{{\sqrt 2 }}} \right)$ where t = t(y) denotes a choice of signed distance to the blown-up minimal graph Γ α := α⁻¹ Γ. This solution is a counterexample to De Giorgi's conjecture for N ≥ 9.
Matter under different equilibrium conditions of pressure and temperature exhibits different states such as solid, liquid, gas, and plasma. Exotic states of matter, such as Bose-Einstein condensates, ...superfluidity, chiral magnets, superconductivity, and liquid crystalline blue phases are observed in thermodynamic equilibrium. Rather than being a result of an aggregation of matter, their emergence is due to a change of a topological state of the system. These topological states can persist out of thermodynamics equilibrium. Here we investigate topological states of matter in a system with injection and dissipation of energy by means of oscillatory forcing. In an experiment involving a liquid crystal cell under the influence of a low-frequency oscillatory electric field, we observe a transition from a non-vortex state to a state in which vortices persist, topological transition. Depending on the period and the type of the forcing, the vortices self-organise, forming square lattices, glassy states, and disordered vortex structures. The bifurcation diagram is characterised experimentally. A continuous topological transition is observed for the sawtooth and square forcings. The scenario changes dramatically for sinusoidal forcing where the topological transition is discontinuous, which is accompanied by serial transitions between square and glassy vortex lattices. Based on a stochastic amplitude equation, we recognise the origin of the transition as the balance between stochastic creation and deterministic annihilation of vortices. Numerical simulations show topological transitions and the emergence of square vortex lattice. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states.
Let Σ be a surface of constant mean curvature in
with multiple Delaunay ends. Assuming that Σ is non degenerate in this paper we construct new solutions to the Cahn-Hilliard equation
in
such that as
...the zero level set of
approaches Σ. Moreover, on compacts of the connected components of
we have
uniformly.
In this note, we show that for a large class of nonlinear wave equations with
odd
nonlinearities, any globally defined odd solution which is small in the energy space decays to 0 in the local energy ...norm. In particular, this result shows nonexistence of small, odd breathers for some classical nonlinear Klein Gordon equations, such as the sine-Gordon equation and
ϕ
4
and
ϕ
6
models. It also partially answers a question of Soffer and Weinstein (Invent Math 136(1): 9–74, p 19
1999
) about nonexistence of breathers for the cubic NLKG in dimension one.
In this paper we consider a two component system of coupled non linear Schrödinger equations modeling the phase separation in the binary mixture of Bose–Einstein condensates and other related ...problems. Assuming the existence of solutions in the limit of large interspecies scattering length
β
the system reduces to a couple of scalar problems on subdomains of pure phases (Noris et al. in Commun Pure Appl Math 63:267–302, 2010). Here we show that given a solution to the limiting problem under some additional non degeneracy assumptions there exists a family of solutions parametrized by
β
≫
1
.
(1) Autoimmune thyroiditis (AIT) is the most common cause of primary hypothyroidism and one of the most frequent organ-specific autoimmune diseases. Its pathogenesis is polygenic and still requires ...further research. The aim of the study was to assess, for the first time in the Caucasian population, the role of selected
gene promoter polymorphisms (rs2071399 G/A, rs2071400C/T, rs2071402 A/G, and rs2071403 A/G) in the development of AIT. A total of 237 patients diagnosed with AIT and 130 healthy controls were genotyped for four
gene polymorphisms, and the results were statistically analyzed to check for the role of these polymorphisms. There were no significant differences in the genotype and allele frequencies of the studied
gene promoter polymorphisms between patients and controls (
> 0.05). The haplotype distribution (rs2071400-rs2071402-rs2071403) between the two studied groups was similar for the most common variants (CGA, CAG, TGG). Only a rare haplotype (CGG) occurred more frequently among patients compared to controls (
= 0.04). The studied
gene promoter polymorphisms did not show an association with susceptibility to AIT in the Caucasian Polish population, contrary to the results in Japanese patients.
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