A note on the forced Burgers equation

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. A connection with stretched vortices in hydrodynamic flows is discussed.Comment: 10 page

Switching dynamics of spatial solitary wave pixels

Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by the motion of the (complex) solitary wave amplitude in the phase plane. We report generalization, into the domain of transverse effects, of the pulse area theorem for the switching process and a logarithmic law for the transient dynamics. We also consider, for what is the first time to our knowledge, phase-encoded address of solitary pixels and find that a near-square-wave temporal switching pattern is permitted without (transverse) cross switching

Multiscaling for Classical Nanosystems: Derivation of Smoluchowski and Fokker-Planck Equations

Using multiscale analysis and methods of statistical physics, we show that a solution to the N-atom Liouville Equation can be decomposed via an expansion in terms of a smallness parameter epsilon, wherein the long scale time behavior depends upon a reduced probability density that is a function of slow-evolving order parameters. This reduced probability density is shown to satisfy the Smoluchowski equation up to order epsilon squared for a given range of initial conditions. Furthermore, under the additional assumption that the nanoparticle momentum evolves on a slow time scale, we show that this reduced probability density satisfies a Fokker-Planck equation up to the same order in epsilon. This approach applies to a broad range of problems in the nanosciences.Comment: 23 page

Advancing Workplace Diversity Through the Culturally Responsive Teamwork Framework.

Purpose Diversification of the profession is an important element of combating racism, bias, and prejudice in the speech-language pathology workforce at national and systemic levels. However, national and systemic change needs to be combined with equipping individual speech-language pathologists to adapt to the challenges that they face to engaging in culturally responsive practice. This paper presents four interacting levels of practice within the Culturally Responsive Teamwork Framework (CRTF): (a) intrapersonal practices, (b) interpersonal practices, (c) intraprofessional practices, and (d) the interprofessional practices. Conclusion CRTF is a practical, strengths-based framework that draws on international research and expertise to expand personal and professional practice and describe critical behaviors within the workplace that can be used to promote principles of evidence-based practice and social justice, especially when working with people from nondominant cultural or linguistic groups

37 years of forest monitoring in Switzerland: drought effects on; Fagus sylvatica

European beech is one of the most important deciduous tree species in natural forest ecosystems in Central Europe. Its dominance is now being questioned by the emerging drought damages due to the increased incidence of severe summer droughts. In Switzerland, Fagus sylvatica have been observed in the Intercantonal Forest Observation Program since 1984. The dataset presented here includes 179176 annual observations of beech trees on 102 plots during 37 years. The plots cover gradients in drought, nitrogen deposition, ozone, age, altitude, and soil chemistry. In dry regions of Switzerland, the dry and hot summer of 2018 caused a serious branch dieback, increased mortality in Fagus sylvatica and increased yellowing of leaves. Beech trees recovered less after 2018 than after the dry summer 2003 which had been similar in drought intensity except that the drought in 2018 started earlier in spring. Our data analyses suggest the importance of drought in subsequent years for crown transparency and mortality in beech. The drought in 2018 followed previous dry years of 2015 and 2017 which pre-weakened the trees. Our long-term data indicate that the drought from up to three previous years were significant predictors for both tree mortality and for the proportion of trees with serious (>60%) crown transparency. The delay in mortality after the weakening event suggests also the importance of weakness parasites. The staining of active vessels with safranine revealed that the cavitation caused by the low tree water potentials in 2018 persisted at least partially in 2019. Thus, the ability of the branches to conduct water was reduced and the branches dried out. Furthermore, photooxidation in light-exposed leaves has increased strongly since 2011. This phenomenon was related to low concentrations of foliar phosphorus (P) and hot temperatures before leaf harvest. The observed drought effects can be categorized as (i) hydraulic failure (branch dieback), (ii) energy starvation as a consequence of closed stomata and P deficiency (photooxidation) and (iii) infestation with weakness parasites (beech bark disease and root rots)

Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement

Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf Characteristic Functional Approach

By employing Hopf's functional method, we find the exact characteristic functional for a simple nonlinear dynamical system introduced by Orszag. Steady-state equal-time statistics thus obtained are compared to direct numerical simulation. The solution is both non-trivial and strongly non-Gaussian.Comment: 6 pages and 2 figure

Amino acid coevolution reveals three-dimensional structure and functional domains of insect odorant receptors.

Insect odorant receptors (ORs) comprise an enormous protein family that translates environmental chemical signals into neuronal electrical activity. These heptahelical receptors are proposed to function as ligand-gated ion channels and/or to act metabotropically as G protein-coupled receptors (GPCRs). Resolving their signalling mechanism has been hampered by the lack of tertiary structural information and primary sequence similarity to other proteins. We use amino acid evolutionary covariation across these ORs to define restraints on structural proximity of residue pairs, which permit de novo generation of three-dimensional models. The validity of our analysis is supported by the location of functionally important residues in highly constrained regions of the protein. Importantly, insect OR models exhibit a distinct transmembrane domain packing arrangement to that of canonical GPCRs, establishing the structural unrelatedness of these receptor families. The evolutionary couplings and models predict odour binding and ion conduction domains, and provide a template for rationale structure-activity dissection

Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+\epsilon dimensions

The statistics of 2-dimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussian like in equilibrium. The skewness \C S \equiv S_3(R)/S^{3/2}_2(R) was measured as \C S_{\text{exp}}\approx 0.03. This contradiction is lifted by understanding that 2-dimensional turbulence is not far from a situation with equi-partition of enstrophy, which exist as true thermodynamic equilibrium with K41 exponents in space dimension of $d=4/3$. We evaluate theoretically the skewness \C S(d) in dimensions ${4/3}\le d\le 2$, show that \C S(d)=0 at $d=4/3$, and that it remains as small as \C S_{\text{exp}} in 2-dimensions.Comment: PRL, submitted, REVTeX 4, 4 page