The mathematical description of the electrosynthesis of composites of oxy-hydroxycompounds cobalt with polypyrrole overooxidazed

The electrosynthesis of the composite with of the overoxidized polypyrrole with cobalt oxy-hydroxide in strongly acidic media has been described mathematically, using linear stability theory and bifurcation analysis. The steadystates stability conditions and oscillatory and monotonic instability requirements have been described too. The system´s behavior was compared with behavior of other systems with overoxidation, electropolymerization of heterocyclic compounds and electrosynthesis of the cobalt oxy-hydroxides

Integral Equations for Heat Kernel in Compound Media

By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$ acquires a certain constant value. At the interface of the media the conditions are imposed which demand the continuity of the `temperature' and the `heat flows'. The integration in the equations is spread out only over the interface of the media. As a result the dimension of the initial problem is reduced by 1. The perturbation series for the integral equations derived are nothing else as the multiple scattering expansions for the relevant heat kernels. Thus a rigorous derivation of these expansions is given. In the one dimensional case the integral equations at hand are solved explicitly (Abel equations) and the exact expressions for the regarding heat kernels are obtained for diverse matching conditions. Derivation of the asymptotic expansion of the integrated heat kernel for a compound media is considered by making use of the perturbation series for the integral equations obtained. The method proposed is also applicable to the configurations when the same medium is divided, by a smooth compact surface, into internal and external regions, or when only the region inside (or outside) this surface is considered with appropriate boundary conditions.Comment: 26 pages, no figures, no tables, REVTeX4; two items are added into the Reference List; a new section is added, a version that will be published in J. Math. Phy

A Study of the \eta \pi^{0} Spectrum and Search for a J^{PC} = 1^{-+} Exotic Meson

A partial wave analysis (PWA) of the of the $\eta \pi ^0$ system (where $\eta \to \gamma \gamma$) produced in the charge exchange reaction $\pi ^-p\to \eta \pi ^0n$ at an incident momentum of 18 GeV$/c$ is presented as a function of ${\eta \pi ^0}$ invariant mass, $m_{\eta\pi^0}$, and momentum transfer squared, $t_{\pi^{-}\to\eta\pi}$, from the incident $\pi^-$ to the outgoing ${\eta\pi ^0}$ system. $S$, $P$ and $D$ waves were included in the PWA. The $a_0(980)$ and $a_2(1320)$ states are clearly observed in the overall ${\eta\pi ^0}$ effective mass distribution as well as in the amplitudes associated with $S$ wave and $D$ waves respectively after partial wave decomposition. The observed distributions in moments (averages of spherical harmonics) were compared to the results from the PWA and the two are consistent. The distribution in $t_{\pi^{-}\to\eta\pi}$ for individual $D$ waves associated with natural and unnatural parity exchange in the $t$-channel are consistent with Regge phenomenology. Of particular interest in this study is the $P$ wave since this leads to an exotic $J^{PC}=1^{-+}$ for the $\eta \pi$ system. A $P$ wave is present in the data, however attempts to describe the mass dependence of the amplitude and phase motion with respect to the $D$ wave as a Breit-Wigner resonance are problematic. This has implications regarding the existence of a reported exotic $J^{PC} = 1^{-+}$ meson decaying into $\eta \pi^0$ with a mass near 1.4 GeV$/c^2$.Comment: 19 pages, 29 figures, to appear in Phys. Rev.

Single-magnet rotary flowmeter for liquid metals

We present a theory of single-magnet flowmeter for liquid metals and compare it with experimental results. The flowmeter consists of a freely rotating permanent magnet, which is magnetized perpendicularly to the axle it is mounted on. When such a magnet is placed close to a tube carrying liquid metal flow, it rotates so that the driving torque due to the eddy currents induced by the flow is balanced by the braking torque induced by the rotation itself. The equilibrium rotation rate, which varies directly with the flow velocity and inversely with the distance between the magnet and the layer, is affected neither by the electrical conductivity of the metal nor by the magnet strength. We obtain simple analytical solutions for the force and torque on slowly moving and rotating magnets due to eddy currents in a layer of infinite horizontal extent. The predicted equilibrium rotation rates qualitatively agree with the magnet rotation rate measured on a liquid sodium flow in stainless steel duct.Comment: 15 pages, 6 figures, revised version, to appear in J. Appl. Phy

Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results

The variance of the local density of the pair contact process with diffusion (PCPD) is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is shown that for lattice dimension d>2 the variance exhibits a phase transition: For high enough diffusion constants, it asymptotically approaches a finite value, while for low diffusion constants the variance diverges exponentially in time. This behavior appears also in the density correlation function, implying that the correlation time is negative. Yet one has dynamical scaling with a dynamical exponent calculated to be z=2.Comment: 20 pages, 5 figure

Aharonov-Bohm Oscillations in a One-Dimensional Wigner Crystal-Ring

We calculate the magnetic moment (`persistent current') in a strongly correlated electron system --- a Wigner crystal --- in a one-dimensional ballistic ring. The flux and temperature dependence of the persistent current in a perfect ring is shown to be essentially the same as for a system of non-interacting electrons. In contrast, by incorporating into the ring geometry a tunnel barrier that pins the Wigner crystal, the current is suppressed and its temperature dependence is drastically changed. The competition between two temperature effects --- the reduced barrier height for macroscopic tunneling and loss of quantum coherence --- may result in a sharp peak in the temperature dependence. The character of the macroscopic quantum tunneling of a Wigner crystal ring is dictated by the strength of pinning. At strong pinning the tunneling of a rigid Wigner crystal chain is highly inhomogeneous, and the persistent current has a well-defined peak at $T\sim 0.5\ \hbar s/L$ independent of the barrier height ($s$ is the sound velocity of the Wigner crystal, $L$ is the length of the ring). In the weak pinning regime, the Wigner crystal tunnels through the barrier as a whole and if $V_p>T_0$ the effect of the barrier is to suppress the current amplitude and to shift the crossover temperature from $T_0$ to $T^*\simeq \sqrt{V_{p}T_{0}}$. ($V_{p}$ is the amplitude of the pinning potential, $T_{0} =\hbar v_{F}/L ,\; v_{F}\sim \hbar/ma$ is the drift velocity of a Wigner crystal ring with lattice spacing $a$). For very weak pinning, $V_p\ll T_0$, the influence of the barrier on the persistent current of a Wigner crystal ring is negligibly small.Comment: 30 pages, RevTeX, 2 figures available on reques

Diffusion in a generalized Rubinstein-Duke model of electrophoresis with kinematic disorder

Using a generalized Rubinstein-Duke model we prove rigorously that kinematic disorder leaves the prediction of standard reptation theory for the scaling of the diffusion constant in the limit for long polymer chains $D \propto L^{-2}$ unaffected. Based on an analytical calculation as well as Monte Carlo simulations we predict kinematic disorder to affect the center of mass diffusion constant of an entangled polymer in the limit for long chains by the same factor as single particle diffusion in a random barrier model.Comment: 29 pages, 3 figures, submitted to PR

The Influence of Macroscopic Pedestrian Structures on Train Boarding Efficiency

A deeper understanding of pedestrian dynamics is essential to improve crowd flows in public spaces such as train stations. It is essential to understand both the physical and the psychological processes present in this context. However, current research on train boarding behavior is limited in scope and mainly focuses on how group level variables such as number of boarders/deboarders influence train boarding efficiency. Viewing pedestrian dynamics through a psychological lens is important for a detailed understanding of the train boarding context and to recognize target areas for improving crowd flows. At Dutch train stations, boarders follow a social norm of waiting at the train door until deboarding is complete. Although people generally adhere to this norm, the way it is executed may not be optimal for deboarding efficiency. We investigate how waiting boarders form a deboarding channel (a corridor where deboarders exit the train) which is a macroscopic structure formed by pedestrians, and how this channel in turn influences the efficiency of deboarding. Analyzing a dataset with 3278 boarding events at Utrecht Centraal Station in the Netherlands from 2017 - 2020 (a subset of a trajectory dataset that captures 100,000 trajectories per day), we found that higher numbers of boarders and a higher ratio of boarders to deboarders, reduced the width of the deboarding channel, and a lower width was associated with lower deboarding efficiency. These results shift the focus from group level variables to identifying macroscopic structures that are formed when pedestrians interact within a social system and provide specific target areas where nudges/behavioral interventions could be implemented

On the universality of the fluctuation-dissipation ratio in non-equilibrium critical dynamics

The two-time nonequilibrium correlation and response functions in 1D kinetic classical spin systems with non-conserved dynamics and quenched to their zero-temperature critical point are studied. The exact solution of the kinetic Ising model with Glauber dynamics for a wide class of initial states allows for an explicit test of the universality of the non-equilibrium limit fluctuation-dissipation ratio X_{\infty}. It is shown that the value of X_{\infty} depends on whether the initial state has finitely many domain walls or not and thus two distinct dynamic universality classes can be identified in this model. Generic 1D kinetic spin systems with non-conserved dynamics fall into the same universality classes as the kinetic Glauber-Ising model provided the dynamics is invariant under the C-symmetry of simultaneous spin and magnetic-field reversal. While C-symmetry is satisfied for magnetic systems, it need not be for lattice gases which may therefore display hitherto unexplored types of non-universal kinetics