Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential

We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to $1/r^b$ and arbitrary angular dependence. It is shown exactly that collapse of Bose-Einstein condensate without contact interactions is possible only for $b\ge 2$. Case $b=2$ is critical and requires number of particles to exceed critical value to allow collapse. Critical collapse in that case is strong one trapping into collapsing region a finite number of particles. Case $b>2$ is supercritical with expected weak collapse which traps rapidly decreasing number of particles during approach to collapse. For $b<2$ singularity at $r=0$ is not strong enough to allow collapse but attractive $1/r^b$ interaction admits stable self-trapping even in absence of external trapping potential

Single-cell RNA sequencing of murine islets shows high cellular complexity at all stages of autoimmune diabetes

Tissue-specific autoimmune diseases are driven by activation of diverse immune cells in the target organs. However, the molecular signatures of immune cell populations over time in an autoimmune process remain poorly defined. Using single-cell RNA sequencing, we performed an unbiased examination of diverse islet-infiltrating cells during autoimmune diabetes in the nonobese diabetic mouse. The data revealed a landscape of transcriptional heterogeneity across the lymphoid and myeloid compartments. Memory CD4 and cytotoxic CD8 T cells appeared early in islets, accompanied by regulatory cells with distinct phenotypes. Surprisingly, we observed a dramatic remodeling in the islet microenvironment, in which the resident macrophages underwent a stepwise activation program. This process resulted in polarization of the macrophage subpopulations into a terminal proinflammatory state. This study provides a single-cell atlas defining the staging of autoimmune diabetes and reveals that diabetic autoimmunity is driven by transcriptionally distinct cell populations specialized in divergent biological functions

Strong Collapse Turbulence in Quintic Nonlinear Schr\"odinger Equation

We consider the quintic one dimensional nonlinear Schr\"odinger equation with forcing and both linear and nonlinear dissipation. Quintic nonlinearity results in multiple collapse events randomly distributed in space and time forming forced turbulence. Without dissipation each of these collapses produces finite time singularity but dissipative terms prevents actual formation of singularity. In statistical steady state of the developed turbulence the spatial correlation function has a universal form with the correlation length determined by the modulational instability scale. The amplitude fluctuations at that scale are nearly-Gaussian while the large amplitude tail of probability density function (PDF) is strongly non-Gaussian with power-like behavior. The small amplitude nearly-Gaussian fluctuations seed formation of large collapse events. The universal spatio-temporal form of these events together with the PDF for their maximum amplitudes define the power-like tail of PDF for large amplitude fluctuations, i.e., the intermittency of strong turbulence.Comment: 14 pages, 17 figure

Pancreatic islets communicate with lymphoid tissues via exocytosis of insulin peptides.

Tissue-specific autoimmunity occurs when selected antigens presented by susceptible alleles of the major histocompatibility complex are recognized by T cells. However, the reason why certain specific self-antigens dominate the response and are indispensable for triggering autoreactivity is unclear. Spontaneous presentation of insulin is essential for initiating autoimmune type 1 diabetes in non-obese diabetic mice1,2. A major set of pathogenic CD4 T cells specifically recognizes the 12-20 segment of the insulin B-chain (B:12-20), an epitope that is generated from direct presentation of insulin peptides by antigen-presenting cells3,4. These T cells do not respond to antigen-presenting cells that have taken up insulin that, after processing, leads to presentation of a different segment representing a one-residue shift, B:13-214. CD4 T cells that recognize B:12-20 escape negative selection in the thymus and cause diabetes, whereas those that recognize B:13-21 have only a minor role in autoimmunity3-5. Although presentation of B:12-20 is evident in the islets3,6, insulin-specific germinal centres can be formed in various lymphoid tissues, suggesting that insulin presentation is widespread7,8. Here we use live imaging to document the distribution of insulin recognition by CD4 T cells throughout various lymph nodes. Furthermore, we identify catabolized insulin peptide fragments containing defined pathogenic epitopes in β-cell granules from mice and humans. Upon glucose challenge, these fragments are released into the circulation and are recognized by CD4 T cells, leading to an activation state that results in transcriptional reprogramming and enhanced diabetogenicity. Therefore, a tissue such as pancreatic islets, by releasing catabolized products, imposes a constant threat to self-tolerance. These findings reveal a self-recognition pathway underlying a primary autoantigen and provide a foundation for assessing antigenic targets that precipitate pathogenic outcomes by systemically sensitizing lymphoid tissues

Lie group analysis of a generalized Krichever-Novikov differential-difference equation

The symmetry algebra of the differential--difference equation $$\dot u_n = [P(u_n)u_{n+1}u_{n-1} + Q(u_n)(u_{n+1}+u_{n-1})+ R(u_n)]/(u_{n+1}-u_{n-1}),$$ where $P$, $Q$ and $R$ are arbitrary analytic functions is shown to have the dimension 1 \le \mbox{dim}L \le 5. When $P$, $Q$ and $R$ are specific second order polynomials in $u_n$ (depending on 6 constants) this is the integrable discretization of the Krichever--Novikov equation. We find 3 cases when the arbitrary functions are not polynomials and the symmetry algebra satisfies \mbox{dim}L=2. These cases are shown not to be integrable. The symmetry algebras are used to reduce the equations to purely difference ones. The symmetry group is also used to impose periodicity $u_{n+N}=u_n$ and thus to reduce the differential--difference equation to a system of $N$ coupled ordinary three points difference equations

How much laser power can propagate through fusion plasma?

Propagation of intense laser beams is crucial for inertial confinement fusion, which requires precise beam control to achieve the compression and heating necessary to ignite the fusion reaction. The National Ignition Facility (NIF), where fusion will be attempted, is now under construction. Control of intense beam propagation may be ruined by laser beam self-focusing. We have identified the maximum laser beam power that can propagate through fusion plasma without significant self-focusing and have found excellent agreement with recent experimental data, and suggest a way to increase that maximum by appropriate choice of plasma composition with implication for NIF designs. Our theory also leads to the prediction of anti-correlation between beam spray and backscatter and suggests the indirect control of backscatter through manipulation of plasma ionization state or acoustic damping.Comment: 15 pages, 4 figures, submitted to Plasma Physics and Controlled Fusio

Inertial mechanism: dynamical mass as a source of particle creation

A kinetic theory of vacuum particle creation under the action of an inertial mechanism is constructed within a nonpertrubative dynamical approach. At the semi-phenomenological level, the inertial mechanism corresponds to quantum field theory with a time-dependent mass. At the microscopic level, such a dependence may be caused by different reasons: The non-stationary Higgs mechanism, the influence of a mean field or condensate, the presence of the conformal multiplier in the scalar-tensor gravitation theory etc. In what follows, a kinetic theory in the collisionless approximation is developed for scalar, spinor and massive vector fields in the framework of the oscillator representation, which is an effective tool for transition to the quasiparticle description and for derivation of non-Markovian kinetic equations. Properties of these equations and relevant observables (particle number and energy densities, pressure) are studied. The developed theory is applied here to describe the vacuum matter creation in conformal cosmological models and discuss the problem of the observed number density of photons in the cosmic microwave background radiation. As other example, the self-consistent evolution of scalar fields with non-monotonic self-interaction potentials (the W-potential and Witten - Di Vecchia - Veneziano model) is considered. In particular, conditions for appearance of tachyonic modes and a problem of the relevant definition of a vacuum state are considered.Comment: 51 pages, 18 figures, submitted to PEPAN (JINR, Dubna); v2: added reference

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Photoproduction of D∗±D^{*\pm} mesons associated with a leading neutron

The photoproduction of $D^{*\pm} (2010)$ mesons associated with a leading neutron has been observed with the ZEUS detector in $ep$ collisions at HERA using an integrated luminosity of 80 pb$^{-1}$. The neutron carries a large fraction, {$x_L>0.2$}, of the incoming proton beam energy and is detected at very small production angles, {$\theta_n<0.8$ mrad}, an indication of peripheral scattering. The $D^*$ meson is centrally produced with pseudorapidity {$|\eta| 1.9$ GeV}, which is large compared to the average transverse momentum of the neutron of 0.22 GeV. The ratio of neutron-tagged to inclusive $D^*$ production is $8.85\pm 0.93({\rm stat.})^{+0.48}_{-0.61}({\rm syst.})\%$ in the photon-proton center-of-mass energy range {$130 <W<280$ GeV}. The data suggest that the presence of a hard scale enhances the fraction of events with a leading neutron in the final state.Comment: 28 pages, 4 figures, 2 table