Variable Energy Fluxes and Exact Relations in Magnetohydrodynamics Turbulence

In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy several exact relations due to conservation of energy. In this paper, using numerical simulations, we quantify the variable energy fluxes of MHD turbulence, as well as verify several exact relations. We also study the energy fluxes of Elsässer variables that are constant in the inertial range.

Trait mindfulness is primarily associated with depression and not with fatigue in multiple sclerosis (MS): implications for mindfulness-based interventions

Objectives Persons with MS (PwMS) often display symptoms of depression and fatigue. Mindfulness-based interventions are known to counteract these symptoms. However, to-date the exact relations between trait mindfulness, depression and fatigue remain to be examined. Fatigue is generally regarded as a symptom immanent to the disease and as a direct neurobiological consequence of increased cytokine levels and cortical atrophy. In depression on the other hand, psychosocial factors in the context of adaptation difficulties are probably of higher relevance. Hence, one may argue that mindfulness, as a trait that promotes successful adaption, may show a strong negative association with depression and a relatively minor negative association with fatigue in PwMS. Methods In the current study, the association between self-reported trait mindfulness, fatigue and depression was examined in a sample of 69 PwMS. Results Trait mindfulness showed highly significant negative correlations with both, depression and fatigue. Mediation analyses however, revealed that depression mediated the relation between mindfulness and fatigue. Conclusion It may be concluded that in PwMS, trait mindfulness shows a genuine negative association with depression, but that it is only secondarily associated with fatigue. Implications for mindfulness-based interventions in MS are discussed. Based on the results of the current study, it may be feasible to promote the acceptance of default fatigue symptoms, instead of an actual reduction of fatigue symptoms.

A Dynamic Study of Biochemical Self-Replication

As it is well understood, in biological systems, small regulatory motifs are present at all scales, thus looking at simple negative feedback loops give us some information of how autocatalytic systems may be affected by regulation. For a single template self-replication, we consider a plausible mechanism, which we reduce to a 2-variable dimensionless set of ordinary differential equations, (ODE). The stability analysis of the steady states allows us to obtain exact relations to describe two-parameter bifurcation diagrams. We include a negative feedback to the reactants input to study the effect of regulation in biochemical self-replication. Surprisingly, the simpler regulation has the largest impact on the parameter space.

Traveling skyrmions in chiral antiferromagnets

Skyrmions in antiferromagnetic (AFM) materials with the Dzyaloshinskii-Moriya (DM) interaction are expected to exist for essentially the same reasons as in DM ferromagnets (FM). It is shown that skyrmions in antiferromagnets with the DM interaction can be traveling as solitary waves with velocities up to a maximum value that depends on the DM parameter. Their configuration is found numerically. The energy and the linear momentum of an AFM skyrmion lead to a proper definition of its mass. We give the details of the energy-momentum dispersion of traveling skyrmions and explore their particle-like character based on exact relations. The skyrmion number, known to be linked to the dynamics of topological solitons in FM, is, here, unrelated to the dynamical behavior. As a result, the solitonic behavior of skyrmions in AFM is in stark contrast to the dynamical behavior of their FM counterparts.

Isoperimetric equalities for rosettes

In this paper, we study the isoperimetric-type equalities for rosettes, i.e. regular closed planar curves with nonvanishing curvature. We find the exact relations between the length and the oriented area of rosettes based on the oriented areas of the Wigner caustic, the Constant Width Measure Set and the Spherical Measure Set. We also study and find new results about the geometry of affine equidistants of rosettes and of the union of rosettes.

Connection-matrix eigenvalues in the Ising model: taking into account interaction with next-nearest neighbors

The connection matrix of the Ising model on a d-dimensional hypercube is investigated. In addition to the interactions between the nearest neighbors, the interactions between the next-nearest neighbors are taken into account. For such a matrix, the exact relations for the eigenvalues and eigenvectors, which are reasonably simply expressed through the corresponding characteristics of the one-dimensional Ising model, are obtained. Both periodic and free boundary conditions are considered.