Effects of an oscillating field on a diffusion process in the presence of a trap

Consider a diffusion process on an infinite line terminated by a trap and modulated by a periodic field. When the frequency is equal to zero the mean time to trapping will be finite or infinite, depending on the sign of the field. We ask whether this behavior can be changed by an oscillatory field, and show that it cannot for pure Brownian motion. We suggest that transition can appear when the signal propagation velocity is finite as for the telegrapher's equation. We further suggest that the asymptotic time dependence of the survival probability is proportional tot ^–1/2 just as in the case of ordinary diffusion. The same conclusion is shown to hold for a system whose dynamics is governed by the equation , whereL is a constant.     

Phenylene motion in polycarbonate and polycarbonate/additive mixtures

Pulsed deuteron NMR line shapes have been analysed to characterize type and time scale of the phenylene group motion in glassy bisphenol-A polycarbonate. The motional mechanism involves-flips about theC ₁ C ₄ axis augmented by small angle fulctuations about the same axis, reaching a rms amplitude of ±35 at 380 K. The distribution of correlation times for the-flips is heterogeneous in nature and can be described either by a log-Gaussian or an asymmetric distribution with a more rapid decay at high correlation times comparable to the Williams-Watts distribution. From both distributions essentailly the same mean activation energy of 37 kJ/mol is obtained, whereas the temperature dependent width of the highly asymmetric distribution is somewhat smaller compared to the log-Gaussian distribution. Time scale and activation energy of the-flip motion are correlated to secondary mechanical relaxations. Low molecular mass additives, which suppress the mechanical relaxation, also hinder the phenylene motion for a substantial fraction of phenylene groups. The effect of additives is not only to shift the mean value of the distribution of correlation times to higher values but also to increase drastically the width of the distribution. The results of this work strongly suggest that the secondary mechanical relaxation and the large amplitude motions of the phenylene groups in polycarbonate are related.     

Analysis of degradation mechanism of plasticized PVC under artificial aging conditions

A plasticized poly(vinyl chloride) (PVC) has the advantage of low cost, long-term stability and flame resistance among other commodity plastic, and has been in service as a product in railway field. However, the transition of the plasticizer concentration through the degrading condition and its relationship with the mechanical properties, the molecular motion, the appearance of surface and other properties was not clear. These relationships were studied by means of Rheovibron, pulse NMR, GC/MS, GPC, SEM and other methods. The bulk properties show similar change between weathering and thermal aging. In addition, the molecular chain was little influenced, however, the plasticizer concentration shows obviously different transition through each phase of aging conditions. According to the results of the observation of surface and section, different appearances between weathering and thermal aging were indicated and these appearances closely relate to the bulk properties. In conclusion, through the weathering condition, a stepwise flow out of inorganic components and plasticizer was presumable to be a main mechanism of the degradation. On the other hand, through the thermal aging condition, the rearrangement and aggregation of the molecular chain by the annealing effect were conceivable as the main mechanism of the degradation.     

A first passage time problem for random walk occupancy

Two recent studies of diffusion and flow properties of polymers in a melt have suggested the problem of finding the average time form Brownian particles to leave a sphere for the first time, given that exited particles can also reenter the sphere. We prove that the asymptotic density (asm) for the time to first emptiness of the sphere for zero-mean Brownian motion is a delta function, characterized by the exit timea(m/lnm)^2/D ,a being a constant andD being the dimension. The presence of a field leaves the delta-function form for the density, but changes the time dependence toa lnm, with only the constanta depending on the dimension. Simulations of the process suggest that the value ofm needed for the validity of the asymptotic result is orders of magnitude greater than 1000.     

Diffusion approximation forGI/G/1 controlled queues

A queueing model is considered in which a controller can increase the service rate. There is a holding cost represented by functionh and the service cost proportional to the increased rate with coefficientl. The objective is to minimize the total expected discounted cost.Whenh andl are small and the system operates in heavy traffic, the control problem can be approximated by a singular stochastic control problem for the Brownian motion, namely, the so-called reflected follower problem. The optimal policy in this problem is characterized by a single numberz ^* so that the optimal process is a reflected diffusion in [0,z ^*]. To obtainz ^* one needs to solve a free boundary problem for the second order ordinary differential equation. For the original problem the policy which increases to the maximum the service rate when the normalized queue-length exceedsz ^* is approximately optimal.     

Collision‐free poisson motion planning in ultra high‐dimensional molecular conformation spaces

The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three‐dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute joints and noncovalent interactions as holonomic constraints, can accurately characterize these native ensembles. However, sampling biomolecules remains challenging owing to their ultra‐high dimensional configuration spaces, and the requirement to avoid (self‐) collisions, which results in low acceptance rates. Here, we present two novel mechanisms to overcome these limitations. First, we introduce temporary constraints between near‐colliding links. The resulting constraint varieties instantaneously redirect the search for collision‐free conformations, and couple motions between distant parts of the linkage. Second, we adapt a randomized Poisson‐disk motion planner, which prevents local oversampling and widens the search, to ultra‐high dimensions. Tests on several model systems show that the sampling acceptance rate can increase from 16% to 70%, and that the conformational coverage in loop modeling measured as average closeness to existing loop conformations doubled. Correlated protein motions identified with our algorithm agree with those from MD simulations. © 2018 Wiley Periodicals, Inc.     

Photothermal Heating and Cooling of Nanostructures

A vast range of insulating, semiconducting, and metallic nanomaterials have been studied over the past several decades with the aim of understanding how continuous‐wave or pulsed laser radiation can influence their chemical functionality and local environment. Many fascinating observations have been made during laser irradiation including, but not limited to, the superheating of solvents, mass‐transport‐mediated morphology evolution, photodynamic therapy, morphology dependent resonances, and a range of phase transformations. In addition to laser heating, recent experiments have demonstrated the laser cooling of nanoscale materials through the emission of upconverted, anti‐Stokes photons by trivalent rare‐earth ions. This Focus Review outlines the analytical modeling of photothermal heat transport with an emphasis on the experimental validation of anti‐Stokes laser cooling. This general methodology can be applied to a wide range of photothermal applications, including nanomedicine, photocatalysis, and the synthesis of new materials. The review concludes with an overview of recent advances and future directions for anti‐Stokes cooling.     

Optimal attitude control of a rigid body

Being mainly interested in the control of satellites, we investigate the problem of maneuvering a rigid body from a given initial attitude to a desired final attitude at a specified end time in such a way that a cost functional measuring the overall angular velocity is minimized.This problem is solved by applying a recent technique of Jurdjevic in geometric control theory. Essentially, this technique is just the classical calculus of variations approach to optimal control problems without control constraints, but formulated for control problems on arbitrary manifolds and presented in coordinate-free language. We model the state evolution as a differential equation on the nonlinear state spaceG=SO(3), thereby completely circumventing the inevitable difficulties (singularities and ambiguities) associated with the use of parameters such as Euler angles or quaternions. The angular velocities _k about the body's principal axes are used as (unbounded) control variables. Applying Pontryagin's Maximum Principle, we lift any optimal trajectorytg^*(t) to a trajectory onT ^*G which is then revealed as an integral curve of a certain time-invariant Hamiltonian vector field. Next, the calculus of Poisson brackets is applied to derive a system of differential equations for the optimal angular velocitiest _k ^* (t); once these are known the controlling torques which need to be applied are determined by Euler's equations.In special cases an analytical solution in closed form can be obtained. In general, the unknown initial values _k ^* (t₀) can be found by a shooting procedure which is numerically much less delicate than the straightforward transformation of the optimization problem into a two-point boundary-value problem. In fact, our approach completely avoids the explicit introduction of costate (or adjoint) variables and yields a differential equation for the control variables rather than one for the adjoint variables. This has the consequence that only variables with a clear physical significance (namely angular velocities) are involved for which gooda priori estimates of the initial values are available.     

Chaotic Motion Generated by Delayed Negative Feedback Part II: Construction of Nonlinearities

We construct a smooth function g* : IR ? IR with such that the equation has a slowly oscillating periodic solution y, and a slowly oscillating solution z* whose phase curve is homoclinic with respect to the orbit o of y in the space C = C⁰([1,0],IR). For an associated Poincaré map we obtain a transversal homoclinic loop. The proof of transversality employs a criterion which uses oscillation properties of solutions of variational equations. The main result is that the trajectories (ψn)^∞_-∞ of the Poincaré map in a neighbourhood of the homoclinic loop form a hyperbolic set on which the motion is chaotic.     

Some small ball probabilities for Gaussian processes under nonuniform norms

We establish lower and upper bounds for the small ball probability of a centered Gaussian process(X(t)) _t[0,1] ^N under Hölder-type norms as well as upper bounds for some more general functionals. This extends recently established results for the uniform norm. In addition, our proof of the lower bound is considerably simpler. In the special caseN=1 we establish precise estimates under a wider class of norms including in particular the Besov norms.