Non-intrinsic origin of the Colossal Dielectric Constants in CaCu3Ti4O12

The dielectric properties of CaCu3Ti4O12, a material showing colossal values of the dielectric constant, were investigated in a broad temperature and frequency range extending up to 1.3 GHz. A detailed equivalent circuit analysis of the results and two crucial experiments, employing different types of contacts and varying sample thickness, provide clear evidence that the apparently high values of the dielectric constant in CaCu3Ti4O12 are non-intrinsic and due to electrode polarization effects. The intrinsic properties of CaCu3Ti4O12 are characterized by charge transport via hopping of localized charge carriers and a relatively high dielectric constant of the order of 100.Comment: 4 pages, 4 figure

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

Transport, magnetic, thermodynamic and optical properties in Ti-doped Sr_2RuO_4

We report on electrical resistivity, magnetic susceptibility and magnetization, on heat capacity and optical experiments in single crystals of Sr_2Ru_(1-x)Ti_xO_4. Samples with x=0.1 and 0.2 reveal purely semiconducting resistivity behavior along c and the charge transport is close to localization within the ab-plane. A strong anisotropy in the magnetic susceptibility appears at temperatures below 100 K. Moreover magnetic ordering in c-direction with a moment of order 0.01 mu_B/f.u. occurs at low temperatures. On doping the low-temperature linear term of the heat capacity becomes reduced significantly and probably is dominated by spin fluctuations. Finally, the optical conductivity reveals the anisotropic character of the dc resistance, with the in-plane conductance roughly following a Drude-type behavior and an insulating response along c

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

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

Descriptive Complexity of Deterministic Polylogarithmic Time and Space

We propose logical characterizations of problems solvable in deterministic polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We introduce a novel two-sorted logic that separates the elements of the input domain from the bit positions needed to address these elements. We prove that the inflationary and partial fixed point vartiants of this logic capture PolylogTime and PolylogSpace, respectively. In the course of proving that our logic indeed captures PolylogTime on finite ordered structures, we introduce a variant of random-access Turing machines that can access the relations and functions of a structure directly. We investigate whether an explicit predicate for the ordering of the domain is needed in our PolylogTime logic. Finally, we present the open problem of finding an exact characterization of order-invariant queries in PolylogTime.Comment: Submitted to the Journal of Computer and System Science

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

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