Transient bimodality in interacting particle systems

We consider a system of spins which have values ±1 and evolve according to a jump Markov process whose generator is the sum of two generators, one describing a spin-flipGlauber process, the other aKawasaki (stirring) evolution. It was proven elsewhere that if the Kawasaki dynamics is speeded up by a factor ^–2, then, in the limit 0 (continuum limit), propagation of chaos holds and the local magnetization solves a reaction-diffusion equation. We choose the parameters of the Glauber interaction so that the potential of the reaction term in the reaction-diffusion equation is a double-well potential with quartic maximum at the origin. We assume further that for each the system is in a finite interval ofZ with ^–1 sites and periodic boundary conditions. We specify the initial measure as the product measure with 0 spin average, thus obtaining, in the continuum limit, a constant magnetic profile equal to 0, which is a stationary unstable solution to the reaction-diffusion equation. We prove that at times of the order ^–1/2 propagation of chaos does not hold any more and, in the limit as 0, the state becomes a nontrivial superposition of Bernoulli measures with parameters corresponding to the minima of the reaction potential. The coefficients of such a superposition depend on time (on the scale ^–1/2) and at large times (on this scale) the coefficient of the term corresponding to the initial magnetization vanishes (transient bimodality). This differs from what was observed by De Masi, Presutti, and Vares, who considered a reaction potential with quadratic maximum and no bimodal effect was seen, as predicted by Broggi, Lugiato, and Colombo.     

On the use of surfaces of section in the N-body ring problem

In the N-body ring problem, we investigate the motion of a massless body interacting with N bodies of equal masses at the vertices of a regular polygon that rotates around a central mass. In this paper, we analyze the use of different surfaces of section in the numerical exploration of the escape in the N-body ring problem in order to get some conclusions about the geometry of the basins of escape in the corresponding configuration spaces.     

BODIPY-based Fluorescent Probe for Fast Detection of Hydrogen Sulfide and Lysosome-targeting Applications in Living Cells

Hydrogen sulfide (H₂S) is recognized as an endogenous gaseous signaling agent in many biological activities. Lysosomes are the main metabolic site and play a pivotal role in cells. Herein, we designed and synthesized two new fluorescent probes BDP-DNBS and BDP-DNP with a BODIPY core to distinguish H₂S. The sensing mechanism is based on the inhibition-recovery of the photo-induced electron transfer (PET) process. Through comparing the responsive behaviors of the two probes toward H₂S, BDP-DNBS showed a fast response time (60 s), low limit of detection (LOD, 51 nM), high sensitivity and selectivity. Moreover, the reaction mechanism was demonstrated by mass spectrometry and fluorescence off-on mechanism was proved by density functional theory (DFT). Significantly, confocal fluorescence imaging indicated that BDP-DNBS was successfully used to visualize H₂S in lysosomes in living HeLa cells.     

Opportunities for innovation: Building on the success of lipid nanoparticle vaccines

Lipid nanoparticle (LNP) formulations of messenger RNA (mRNA) have demonstrated high efficacy as vaccines against SARS-CoV-2. The success of these nanoformulations underscores the potential of LNPs as a delivery system for next-generation biological therapies. In this article, we highlight the key considerations necessary for engineering LNPs as a vaccine delivery system and explore areas for further optimisation. There remain opportunities to improve the protection of mRNA, optimise cytosolic delivery, target specific cells, minimise adverse side-effects and control the release of RNA from the particle. The modular nature of LNP formulations and the flexibility of mRNA as a payload provide many pathways to implement these strategies. Innovation in LNP vaccines is likely to accelerate with increased enthusiasm following recent successes; however, any advances will have implications for a broad range of therapeutic applications beyond vaccination such as gene therapy.     

First passage percolation and escape strategies

Consider first passage percolation on with passage times given by i.i.d. random variables with common distribution F. Let be the time from u to v for a path π and the minimal time among all paths from u to v. We ask whether or not there exist points and a semi‐infinite path such that for all n. Necessary and sufficient conditions on F are given for this to occur. When the support of F is unbounded, we also obtain results on the number of edges with large passage time used by geodesics. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 414–423, 2015     

Escape of photo-detached electron from an annular nanomicrocavity

The escaped probability density of the photo-detached electron in an annular nanomicrocavity shows strong oscillations as a function of the length of the escape orbits. We present a semiclassical theory that describes theses oscillations in terms of bundles of escape orbits. Due to the interference effects of the electron waves travelling along different escaped orbits, oscillatory structures appear in the escaped probability density. In addition, the calculation results suggest that the escaped probability density of the photo-detached electron is not only related to the inner radius of the annular microcavity, but also related to the laser polarization. In order to show the correspondence between the escaped probability density and the detached electron’s escaped orbits clearly, we calculate the Fourier transformed semiclassical wave function and find that the peak positions agree well with the length of the detached electron’s orbits. We hope that our results will be useful in understanding the escape and propagation process of particles through semiconductor microjunctions or ballistic microstructure.     

Mathematics of Philosophy or Philosophy of Mathematics?

This article examines recent attempts to gain insight into philosophical paradoxes through using NDS models employing iterated difference equations and resulting phase portraits and escape time diagrams. The temporal nature of such models is contrasted with an alternative approach based on the a-temporal and non-dynamical construct of a lattice. Finally, there is a discussion of how such strategies for understanding paradox transcend the realm of empirical research and enter territory in the philosophy of mathematics.     

Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.     

Transition to escape in a system of coupled oscillators

We study a Hamiltonian system of coupled oscillators derived from two forced pendulums, connected with a torsional spring. The uncoupled limit is described by two identical oscillators, each possessing a homoclinic orbit separating bounded from unbounded motion. We focus on intermediate energy levels which lead to detained motions, defined as trajectories that, though unbounded as t → ∞, oscillate within the region defined by the homoclinic orbit of the unperturbed system for a long but finite time. We analyze the existence and behavior of these motions in terms of equipotential surfaces. These curves provide bounds on the motion of the system and are shown to be closed for low energies. However, above some critical energy level the equipotential curves become open. The detained trajectories are shown to arise from the region of phase space that was, for appropriate energies, stochastic. These motions remain within this region for long times before finally “leaking out” of the opening in the equipotential curves and proceeding to infinity.