Particle interactions and lattice dynamics: Scenarios for efficient bidirectional stochastic transport?

Intracellular transport processes driven by molecular motors can be described by stochastic lattice models of self-driven particles. Here we focus on bidirectional transport models excluding the exchange of particles on the same track. We explore the possibility to have efficient transport in these systems. One possibility would be to have appropriate interactions between the various motors' species, so as to form lanes. However, we show that the lane formation mechanism based on modified attachment/detachment rates as it was proposed previously is not necessarily connected to an efficient transport state and is suppressed when the diffusivity of unbound particles is finite. We propose another interaction mechanism based on obstacle avoidance that allows to have lane formation for limited diffusion. Besides, we had shown in a separate paper that the dynamics of the lattice itself could be a key ingredient for the efficiency of bidirectional transport. Here we show that lattice dynamics and interactions can both contribute in a cooperative way to the efficiency of transport. In particular, lattice dynamics can decrease the interaction threshold beyond which lanes form. Lattice dynamics may also enhance the transport capacity of the system even when lane formation is suppressed.Comment: 25 pages, 17 figures, 2 table

Random l-colourable structures with a pregeometry

We study finite $l$-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are first randomly assigned to all 1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure, where we now forget the specific colouring of the generating process, has a given property. With this measure we get the following results: 1. A zero-one law. 2. The set of sentences with asymptotic probability 1 has an explicit axiomatisation which is presented. 3. There is a formula $\xi(x,y)$ (not directly speaking about colours) such that, with asymptotic probability 1, the relation "there is an $l$-colouring which assigns the same colour to $x$ and $y$" is defined by $\xi(x,y)$. 4. With asymptotic probability 1, an $l$-colourable structure has a unique $l$-colouring (up to permutation of the colours).Comment: 35 page

Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states

We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials. As in the complex case, these polynomials consatitute orthogonal families of vectors in ambient quaternionic $L^2$-spaces. Using these polynomials, we then define regular and anti-regular subspaces of these $L^2$-spaces, the associated reproducing kernels and the ensuing quaternionic coherent states

Magnetoelectric and HR-STEM investigations on eutectic CoFe₂O₄-Ba_1-xSr_xTiO₃ composites

Multiferroic Ba1–xSrxTiO3–CoFe2O4 (x = 0.03, 0.05) composites with rarely investigated 3-3 connectivity were prepared by eutectic crystallization in an optical floating zone furnace. High-resolution scanning transmission electron microscopy investigations of the CoFe2O4–BaTiO3 interface revealed an almost perfect connection between both components. These micrographs also showed that the impact of post-annealing in air was much larger than expected and resulted in formation of small BaTiO3 inclusions in the CoFe2O4 phase. The magnetoelectric coefficient αME was studied in detail with respect to its dependence on the static magnetic field, the frequency of the driving AC-field and temperature. Furthermore, the influence of different growth rates (5, 10 and 20 mm h-1), chemical composition, sample thickness and the alignment of electrical polarization and magnetic field (collinear or vertical) on the magnetoelectric properties were studied. The largest value of αME = 1.3 mV Oe-1 cm-1 was found for a sample grown at 5 mm h-1. For even slower growth rates, a higher Sr content was required to avoid the formation of impurity phases leading to a decrease of αME

Metal-to-insulator transition and magnetic ordering in CaRu_{1-x}Cu_xO_3

CaRuO_3 is perovskite with an orthorhombic distortion and is believed to be close to magnetic ordering. Magnetic studies of single crystal and polycrystalline CaRu_{1-x}Cu_xO_3 (0\le x \le 15 at.%Cu) reveal that spin-glass-like transition develops for x\le 7 at.%Cu and obtained value for effective magnetic moment p_{eff}=3.55 mu_B for x=5 at.% Cu, single crystal, indicates presence of Ru^{5+}. At higher Cu concentrations more complex magnetic behaviors are observed. Electrical resistivity measured on polycrystalline samples shows metal-to-insulator transition (MIT) at 51 K for only 2 at.% Cu. Charge compensation, which is assumed to be present upon Cu^{2+/3+} substitution, induces appearance of Ru^{5+} and/or creation of oxygen vacancies in crystal structure. Since the observed changes in physical properties are completely attributable to the charge compensation, they cannot be related to behaviors of pure compound where no such mechanism is present. This study provides the criterion for "good" chemical probes for studying Ru-based perovskites.Comment: 12 pages, 7 figure

Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic

First we consider a unidirectional flux \omega_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines' in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=\phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time \tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value \omega_bar_c of the control parameter \omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density \rho_bar rather than the flux \omega_bar is the control parameter. Unequal fluxes \omega_bar_A and \omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.Comment: 50 pages, 16 figures; extra references adde

Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model

The non-equilibrium dynamics of the kinetic spherical model, quenched to T<=T_c, with a non-conserved order-parameter is studied at its upper critical dimension d=d*=4. In the scaling limit where both the waiting time s and the observation time t are large and the ratio y=t/s>1 is fixed, the scaling functions of the two-time autocorrelation and autoresponse functions do not contain any logarithmic correction factors and the typical size of correlated domains scales for large times as L(t) ~ t^0.5 .Comment: Latex2e, 12 pages, 2 figures included, (final form

Wakeful rest alleviates interference-based forgetting

Retroactive interference (RI)—the disruptive influence of events occurring after the formation of a new memory—is one of the primary causes of forgetting. Placing individuals within an environment that postpones interference should, therefore, greatly reduce the likelihood of information being lost from memory. For example, a short period of wakeful rest should diminish interference-based forgetting. To test this hypothesis, participants took part in a foreign language learning activity and were shown English translations of 20 Icelandic words for immediate recall. Half of the participants were then given an 8-min rest before completing a similar or dissimilar interfering distractor task. The other half did not receive a rest until after the distractor task, at which point interference had already taken place. All participants were then asked to translate the Icelandic words for a second time. Results revealed that retention was significantly worse at the second recall test, but being allowed a brief rest before completing the distractor task helped reduce the amount of forgetting. Taking a short, passive break can shield new memories from RI and alleviate forgetting.ERAS Scheme, University of Wolverhampto

A model for bidirectional traffic of cytoskeletal motors

We introduce a stochastic lattice gas model including two particle species and two parallel lanes. One lane with exclusion interaction and directed motion and the other lane without exclusion and unbiased diffusion, mimicking a micotubule filament and the surrounding solution. For a high binding affinity to the filament, jam-like situations dominate the system's behaviour. The fundamental process of position exchange of two particles is approximated. In the case of a many-particle system, we were able to identify a regime in which the system is rather homogenous presenting only small accumulations of particles and a regime in which an important fraction of all particles accumulates in the same cluster. Numerical data proposes that this cluster formation will occur at all densities for large system sizes. Coupling of several filaments leads to an enhanced cluster formation compared to the uncoupled system, suggesting that efficient bidirectional transport on one-dimensional filaments relies on long-ranged interactions and track formation.Comment: 20 pages, 9 figure

Frameworks for logically classifying polynomial-time optimisation problems.

We show that a logical framework, based around a fragment of existential second-order logic formerly proposed by others so as to capture the class of polynomially-bounded P-optimisation problems, cannot hope to do so, under the assumption that P ≠ NP. We do this by exhibiting polynomially-bounded maximisation and minimisation problems that can be expressed in the framework but whose decision versions are NP-complete. We propose an alternative logical framework, based around inflationary fixed-point logic, and show that we can capture the above classes of optimisation problems. We use the inductive depth of an inflationary fixed-point as a means to describe the objective functions of the instances of our optimisation problems