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From Gross-Pitaevskii (GP) theory for ultracold gases it is predicted that phase-segregated three-component Bose-Einstein condensates (BEC) feature a wetting phase diagram that depends only on atomic masses and scattering lengths. This is unique in theories of surface and interfacial phase transitions and provides a new opportunity for experimental observation of wetting phenomena in BEC mixtures. Previous GP theory for two-component BEC relied on an {\it ad hoc} optical wall boundary condition, on which the character and location of the wetting phase transitions depend sensitively. This boundary condition dependence is eliminated by adding a third component and treating the three phases on equal footing. An unequivocal wetting phase diagram is captured, with phase boundaries calculated analytically using an extension of the established double-parabola approximation.

The dihedral contact angles between interfaces in three-fluid-phase equilibria must be continuous functions of the bulk thermodynamic fields. This general argument, which we propose, predicts a nonwetting gap in the phase diagram, challenging the common belief in "critical-point wetting", even for short-range forces. A demonstration is provided by exact solution of a mean-field two-density functional theory for three-phase equilibria near a tricritical point (TCP). Complete wetting is found in a tiny vicinity of the TCP. Away from it, nonwetting prevails and no wetting transition takes place, not even when a critical endpoint is approached. Far from the TCP, reentrant wetting may occur, with a different wetting phase. These findings shed light on hitherto unexplained experiments on ternary water-oil-nonionic amphiphile mixtures in which nonwetting continues to exist as one approaches either one of the two critical endpoints., Comment: to appear in Physical Review Letters

An analytic iteration sequence based on the extension of the BLUES (Beyond Linear Use of Equation Superposition) function method to partial differential equations (PDEs) with second-order time derivatives is studied. The original formulation of the BLUES method is modified by introducing a matrix formalism that takes into account the initial conditions for higher-order time derivatives. The initial conditions of both the solution and its derivatives now play the role of a source vector. The method is tested on a nonlinear telegrapher equation, which can be reduced to a nonlinear wave equation by a suitable choice of parameters. In addition, a comparison is made with three other methods: the Adomian decomposition method, the variational iteration method (with Green function) and the homotopy perturbation method. The matrix BLUES function method is shown to be a worthwhile alternative for the other methods., Comment: 8 pages, 3 figures

Within Gross-Pitaevskii (GP) theory we derive the interface potential V (l) which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance l. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore non-equilibrium properties by using l as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, V (l) for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, V(l) is independent of l. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using V(l) we study the three-phase contact line where the interface meets the wall under a contact angle theta. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension tau. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, tau does not approach a nonzero positive constant for theta going to zero, but instead approaches zero (from below) as would be expected for a critical wetting transition. This hybrid character of tau is a consequence of the absence of a barrier in V(l) at wetting. For a typical V(l) we provide a conjecture for the exact line tension within GP theory., Comment: 18 pages, 15 figures

The Beyond-Linear-Use-of-Equation-Superposition (BLUES) function method is extended to coupled nonlinear ordinary differential equations and applied to the epidemiological SIRS model with vaccination. Accurate analytic approximations are obtained for the time evolution of the susceptible and infected population fractions. The results are compared with those obtained with alternative methods, notably Adomian decomposition, variational iteration and homotopy perturbation. In contrast with these methods, the BLUES iteration converges rapidly, globally, and captures the exact asymptotic behavior for long times. The time of the infection peak is calculated using the BLUES approximants and the results are compared with numerical solutions, which indicate that the method is able to generate useful analytic expressions that coincide with the (numerically) exact ones already for a small number of iterations., Comment: 23 pages, 8 figures. v2: Accepted version

We revisit a known model in which (conducting) blocks are hierarchically and randomly deposited on a $d$-dimensional substrate according to a hyperbolic size law with the block size decreasing by a factor $\lambda \, > 1$ in each subsequent generation. In the first part of the paper the number of coastal points (in $D=1)$ or coastlines (in $D=2)$ is calculated, which are points or lines that separate a region at "sea level" and an elevated region. We find that this number possesses a non-universal character, implying a Euclidean geometry below a threshold value $P_c$ of the deposition probability $P$, and a fractal geometry above this value. Exactly at the threshold, the geometry is logarithmic fractal. The number of coastlines in $D=2$ turns out to be exactly twice the number of coastal points in $D=1$. We comment briefly on the surface morphology and derive a roughness exponent $\alpha$. In the second part, we study the percolation probability for a current in this model and two extensions of it, in which both the scale factor and the deposition probability can take on different values between generations. We find that the percolation threshold $P_c$ is located at exactly the same value for the deposition probability as the threshold probability of the number of coastal points. This coincidence suggests that exactly at the onset of percolation for a conducting path, the number of coastal points exhibits logarithmic fractal behaviour., Comment: 26 pages, 24 figures. v2 -> Corrected author list and added DOI

An iteration sequence based on the BLUES (beyond linear use of equation superposition) function method is presented for calculating analytic approximants to solutions of nonlinear partial differential equations. This extends previous work using this method for nonlinear ordinary differential equations with an external source term. Now, the initial condition plays the role of the source. The method is tested on three examples: a reaction-diffusion-convection equation, the porous medium equation with growth or decay, and the nonlinear Black-Scholes equation. A comparison is made with three other methods: the Adomian decomposition method (ADM), the variational iteration method (VIM), and the variational iteration method with Green function (GVIM). As a physical application, a deterministic differential equation is proposed for interface growth under shear, combining Burgers and Kardar- Parisi-Zhang nonlinearities. Thermal noise is neglected. This model is studied with Gaussian and space-periodic initial conditions. A detailed Fourier analysis is performed and the analytic coefficients are compared with those of ADM, VIM, GVIM, and standard perturbation theory. The BLUES method turns out to be a worthwhile alternative to the other methods. The advantages that it offers ensue from the freedom of choosing judiciously the linear part, with associated Green function, and the residual containing the nonlinear part of the differential operator at hand., Comment: 39 pages, 17 figures. v4: accepted manuscript

The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly reproduce oscillatory behaviour. Next, a fractional differential equation describing heat transfer in a semi-infinite rod with Stefan-Boltzmann cooling is handled. In this case, a detailed comparison is made with the Adomian decomposition method, the outcome of which is favourable for the BLUES method. As a final problem, the Fisher equation from population biology is dealt with. For all cases, it is shown that the solutions converge exponentially fast to the numerically exact solution, either globally or, for the Fisher problem, locally., Comment: 24 pages, 13 figures

A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function method is shown to converge for nonlinear ordinary differential equations. Case studies are presented for solitary wave solutions of the Camassa-Holm equation and for traveling wavefront solutions of the Burgers equation, with source terms. The convergence of the analytical approximations towards the numerically exact solution is exponentially rapid. In practice, the zeroth-order approximation (a simple convolution) is already useful and the first-order approximation is already accurate while still easy to calculate. The type of nonlinearity can be chosen rather freely, which makes the method generally applicable., Comment: 14 pages, 6 figures

A mean-field density-functional model for three-phase equilibria in fluids (or other soft condensed matter) with two spatially varying densities is analyzed analytically and numerically. The interfacial tension between any two out of three thermodynamically coexisting phases is found to be captured by a surprisingly simple analytic expression that has a geometric interpretation in the space of the two densities. The analytic expression is based on arguments involving symmetries and invariances. It is supported by numerical computations of high precision and it agrees with earlier conjectures obtained for special cases in the same model. An application is presented to three-phase equilibria in the vicinity of a tricritical point. Using the interfacial tension expression and employing the field variables compatible with tricritical point scaling, the expected mean-field critical exponent is derived for the vanishing of the critical interfacial tension as a function of the deviation of the noncritical interfacial tension from its limiting value, upon approach to a critical endpoint in the phase diagram. The analytic results are again confirmed by numerical computations of high precision.

We introduce a computational method in physics that goes "beyond linear use of equation superposition" (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green's function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested., Comment: accepted for publication in Journal of Physics A: Mathematical and General

The magnetic response related to paramagnetic Meissner effect (PME) is studied in a high quality single crystal ZrB12 with non-monotonic vortex-vortex interactions. We observe the expulsion and penetration of magnetic flux in the form of vortex clusters with increasing temperature. A vortex phase diagram is constructed which shows that the PME can be explained by considering the interplay among the flux compression, the different temperature dependencies of the vortex-vortex and the vortex-pin interactions, and thermal fluctuations. Such a scenario is in good agreement with the results of the magnetic relaxation measurements., Comment: accepted by New Journal of Physics

The localized low-energy interfacial excitations, or Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically by means of a double-parabola approximation (DPA) to the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. Within this model analytic expressions are obtained for the excitations underlying capillary waves or "ripplons" for arbitrary strength $K\,(>1)$ of the phase segregation. The dispersion relation $\omega \propto k^{3/2}$ is derived directly from the Bogoliubov-de Gennes equations in limit that the wavelength $2\pi/k$ is much larger than the healing length $\xi $. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in $\omega (k)$ of order $k^{5/2}$ is calculated analytically, entailing a finite-wavelength correction factor $(1+\frac{\sqrt{K-1} \,k\xi}{4\sqrt{2}\,(\sqrt{2}+\sqrt{K-1})})$. This prediction may be tested experimentally using (quasi-)uniform optical-box traps. Explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity $\omega/k$ to the sound velocity $c$. For generic asymmetric mixtures consisting of condensates with unequal healing lengths an additional modulation is predicted of the common value of the condensate densities at the interface., Comment: submitted to Physical Review A

It is known that an engine with ideal efficiency ($\eta =1$ for a chemical engine and $e = e_{\rm Carnot}$ for a thermal one) has zero power because a reversible cycle takes an infinite time. However, at least from a theoretical point of view, it is possible to conceive (irreversible) engines with nonzero power that can reach ideal efficiency. Here this is achieved by replacing the usual linear transport law by a sublinear one and taking the step-function limit for the particle current (chemical engine) or heat current (thermal engine) versus the applied force. It is shown that in taking this limit exact thermodynamic inequalities relating the currents to the entropy production are not violated.

Accurate and useful analytic approximations are developed for order parameter profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates. The pure condensates 1 and 2, each of which contains a particular species of atoms, feature healing lengths $\xi_1$ and $\xi_2$. The inter-atomic interactions are repulsive. In particular, the effective inter-species repulsive interaction strength is $K$. A triple-parabola approximation (TPA) is proposed, to represent closely the energy density featured in Gross-Pitaevskii (GP) theory. This TPA allows us to define a model, which is a handy alternative to the full GP theory, while still possessing a simple analytic solution. The TPA offers a significant improvement over the recently introduced double-parabola approximation (DPA). In particular, a more accurate amplitude for the wall energy (of a single condensate) is derived and, importantly, a more correct expression for the interfacial tension (of two condensates) is obtained, which describes better its dependence on $K$ in the strong segregation regime, while also the interface profiles undergo a qualitative improvement., Comment: 25 pages, 8 figures

Interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths $\xi_1$ and $\xi_2$ and by the inter-species repulsive interaction $K$. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case $\xi_2/\xi_1 = 1/2$ and $K = 3/2$. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all $\xi_1, \xi_2$ and $K$. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory., Comment: 24 pages, 6 figures

The global phase diagram of wetting in the two-dimensional (2d) Ising model is obtained through exact calculation of the surface excess free energy. Besides a surface field for inducing wetting, a surface-coupling enhancement is included. The wetting transition is critical (second order) for any finite ratio of surface coupling J_s to bulk coupling J, and turns first order in the limit J_s/J to infinity. However, for J_s/J much larger than 1 the critical region is exponentially small and practically invisible to numerical studies. A distinct pre-asymptotic regime exists in which the transition displays first-order character. Surprisingly, in this regime the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3/2., Comment: This new version presents the exact solution and its properties whereas the older version was based on an approximate numerical study of the model

An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed at an optical wall can undergo a wetting phase transition in which one of the species excludes the other from contact with the wall. Interestingly, while hard-wall boundary conditions entail the wetting transition to be of first order, using Gross-Pitaevskii theory we show that first-order wetting as well as critical wetting can occur when a realistic exponential optical wall potential (evanescent wave) with a finite turn-on length $\lambda$ is assumed. The relevant surface excess energies are computed in an expansion in $\lambda/\xi_i$, where $\xi_i$ is the healing length of condensate $i$. Experimentally, the wetting transition may best be approached by varying the interspecies scattering length $a_{12}$ using Feshbach resonances. In the hard-wall limit, $\lambda \rightarrow 0$, exact results are derived for the prewetting and first-order wetting phase boundaries., Comment: 18 pages, 15 figures

We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals $1/\lambda^n$ in generation $n$, in terms of a rescaling factor $\lambda$. Without interactions between the blocks, this model is described by a logarithmic fractal, studied previously, which is characterized by a constant increment of the length, area or volume upon proliferation. We study to what extent the logarithmic fractality survives, if each block is equipped with an Ising (pseudo-)spin $s=\pm 1$ and the interactions between those spins are switched on (ranging from antiferromagnetic to ferromagnetic). It turns out that the dependence of the surface topology on the interaction sign and strength is not trivial. For instance, deep in the ferromagnetic regime, our numerical experiments and analytical results reveal a sharp crossover from a Euclidean transient, consisting of aggregated domains of aligned spins, to an asymptotic logarithmic fractal growth. In contrast, deep into the antiferromagnetic regime the surface roughness is important and is shown analytically to be controlled by vacancies induced by frustrated spins. Finally, in the weak interaction regime, we demonstrate that the non-interacting model is extremal in the sense that the effect of the introduction of interactions is only quadratic in the magnetic coupling strength. In all regimes, we demonstrate the adequacy of a mean-field approximation whenever vacancies are rare. In sum, the logarithmic fractal character is robust with respect to the introduction of spatial correlations in the hierarchical deposition process., Comment: 17 pages, 8 figures

An extended theoretical study of interface potentials in adsorbed colloid-polymer mixtures is performed. To describe the colloid-polymer mixture near a hard wall, a simple Cahn-Nakanishi-Fisher free-energy functional is used. The bulk phase behavior and the substrate-adsorbate interaction are modelled by the free-volume theory for ideal polymers with polymer-to-colloid size ratios q=0.6 and q=1. The interface potentials are constructed with help from a Fisher-Jin crossing constraint. By manipulating the crossing density, a complete interface potential can be obtained from natural, single-crossing, profiles. The line tension in the partial wetting regime and the boundary tension along prewetting are computed from the interface potentials. The line tensions are of either sign, and descending with increasing contact angle. The line tension takes a positive value of 10^-14 - 10^-12 N near a first-order wetting transition, passes through zero and decreases to minus 10^-14 - 10^-12 N away from the first-order transition. The calculations of the boundary tension along prewetting yield values increasing from zero at the prewetting critical point up to the value of the line tension at first-order wetting., Comment: 11 pages, 6 figures

We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation transition using a generating functions theory. The model considers a network with a fixed number of nodes wherein links are introduced using degree-dependent linking probabilities $p_k$. To illustrate the techniques and support our findings using Monte-Carlo simulations, we introduce the exemplary linking rule $p_k$ proportional to $k^{-\alpha}$, with $\alpha$ between -1 and plus infinity. This parameter may be used to interpolate between different regimes. For negative $\alpha$, links are most likely attached to high-degree nodes. On the other hand, in case $\alpha>0$, nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation., Comment: 22 pages, 10 figures

A cyclically operating chemical engine is considered that converts chemical energy into mechanical work. The working fluid is a gas of finite-sized spherical particles interacting through elastic hard collisions. For a generic transport law for particle uptake and release, the efficiency at maximum power $\eta$ takes the form 1/2+c\Delta \mu + O(\Delta \mu^2), with 1/2 a universal constant and $\Delta \mu$ the chemical potential difference between the particle reservoirs. The linear coefficient c is zero for engines featuring a so-called left/right symmetry or particle fluxes that are antisymmetric in the applied chemical potential difference. Remarkably, the leading constant in $\eta$ is non-universal with respect to an exceptional modification of the transport law. For a nonlinear transport model we obtain \eta = 1/(\theta +1), with \theta >0 the power of $\Delta \mu$ in the transport equation

We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group (RG) calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying $2-\alpha_s = \infty$) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with $\beta_s = -1$) of the wetting layer thickness are not modified as long as $\omega < 2$, with $\omega$ the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with $\nu_{\perp} = 1/2$). In contrast, the non-universal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate and strong fluctuation regimes., Comment: 2 figures

The Pippard coherence length $\xi_0$ (the size of a Cooper pair) in an extreme type-I superconductor was determined directly through high-resolution measurement of the nonlocal electrodynamic effect combining low-energy muon spin rotation spectroscopy and polarized neutron reflectometry. The renormalization factor $Z$=m_cp*/2m (m_cp* and m are the mass of the Cooper pair and the electron, respectively) resulting from the electron-phonon interaction, and the temperature dependent London penetration depth $\lambda_L(T)$ were determined as well. A general expression linking $\xi_0$, $Z$ and $\lambda_L(0)$ is introduced and experimentally verified. This expression allows one to determine experimentally the Pippard coherence length in \textit{any} superconductor, independent of whether the electrodynamics is local or nonlocal, conventional or unconventional., Comment: 4 pages, 5 figures, 1 table

An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters.

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E_c. Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model., Comment: 12 pages, 12 figures

Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with probability proportional to (kq)^(-alpha), where alpha is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin-Kasteleyn construction which provides a link between our model and a limit of the Potts model., Comment: 12 pages, 1 figure. To appear in Physica A: Special Issue in honour of Prof. A. N. Berker (2009)

Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a network in which the probability for an edge between nodes $i$ and $j$ to be retained is proportional to $(k_ik_j)^{-\alpha}$ with $k_i$ and $k_j$ the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their properties by analytical and numerical means. The system is examined away from the percolation transition, where the size of the giant cluster is obtained, and close to the transition, where nonuniversal critical exponents are extracted using the generating functions method. The theory is found to agree quite well with simulations. By introducing an extension of the Fortuin-Kasteleyn construction, we find that biased percolation is well described by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous couplings., Comment: 17 pages, 8 figures

We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-\gamma}$. The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$ through $p_{ij}\propto(k_{i}k_{j})^{-\alpha}$. By varying the exponent $\alpha$, we interpolate between random ($\alpha=0$) and systematic failure. For $\alpha >0 $ ($<0$) the most (least) connected nodes are depreciated first. This topological bias introduces a characteristic scale in $P(k)$ of the depreciated network, marking a crossover between two distinct power laws. The critical percolation threshold, at which global connectivity is lost, depends both on $\gamma$ and on $\alpha$. As a consequence, network robustness or fragility can be controlled through fine tuning of the topological bias in the failure process., Comment: Accepted for publication at Phys. Rev. Lett

Polarized neutron reflectometry (PNR) provides evidence that nonlocal electrodynamics governs the magnetic field penetration in an extreme low-k superconductor. The sample is an indium film with a large elastic mean free path (11 mkm) deposited on a silicon oxide wafer. It is shown that PNR can resolve the difference between the reflected neutron spin asymmetries predicted by the local and nonlocal theories of superconductivity. The experimental data support the nonlocal theory, which predicts a nonmonotonic decay of the magnetic field., Comment: 5 pages, 4 figures, LaTex, corrected typos and figures

Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behaviour, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping $\gamma'=(\gamma-\mu)/(1-\mu)$ describes how a shift of the standard exponent $\gamma$ of the degree distribution can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (k_ik_j)^{-\mu}$, where $k_i$ stands for the degree of vertex $i$. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network., Comment: 20 pages, 14 figures

The possibility of surface enhancement of superconductivity is examined experimentally. It is shown that single crystal tin samples with cold-worked surfaces represent a superconductor with a surface-enhanced order parameter (or negative surface extrapolation length b), whose magnitude can be controlled., Comment: 8 pages, 4 figures

The possibility of wetting phase transitions in Bose-Einstein condensed gases is predicted on the basis of Gross-Pitaevskii theory. The surface of a binary mixture of Bose-Einstein condensates can undergo a first-order wetting phase transition upon varying the interparticle interactions, using, e.g., Feshbach resonances. Interesting ultralow-temperature effects shape the wetting phase diagram. The prewetting transition is, contrary to general expectations, not of first order but critical, and the prewetting line does not meet the bulk phase coexistence line tangentially. Experimental verification of these extraordinary results is called for, especially now that it has become possible, using optical methods, to realize a planar "hard wall" boundary for the condensates., Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Lett. in slightly shortened form

Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, $\gamma' = (\gamma - \mu)/(1-\mu)$, describes how a shift of the standard exponent $\gamma$ of the degree distribution $P(q)$ can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (q_iq_j)^{-\mu}$. Replica technique, cavity method and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and non-equilibrium systems, and is illustrated with interdisciplinary applications., Comment: 4 pages, 5 figures

A simulation approach to the stochastic growth of bacterial towers is presented, in which a non-uniform and finite nutrient supply essentially determines the emerging structure through elementary chemotaxis. The method is based on cellular automata and we use simple, microscopic, local rules for bacterial division in nutrient-rich surroundings. Stochastic nutrient diffusion, while not crucial to the dynamics of the total population, is influential in determining the porosity of the bacterial tower and the roughness of its surface. As the bacteria run out of food, we observe an exponentially rapid saturation to a carrying capacity distribution, similar in many respects to that found in a recently proposed phenomenological hierarchical population model, which uses heuristic parameters and macroscopic rules. Complementary to that phenomenological model, the simulation aims at giving more microscopic insight into the possible mechanisms for one of the recently much studied bacterial morphotypes, known as "towering biofilm", observed experimentally using confocal laser microscopy. A simulation suggesting a mechanism for biofilm resistance to antibiotics is also shown.

In this Note a social network model for opinion formation is proposed in which a person connected to $q$ partners pays an {\em attention} $1/q$ to each partner. The mutual attention between two connected persons $i$ and $j$ is taken equal to the geometric mean $1/\sqrt{q_iq_j}$. Opinion is represented as usual by an Ising spin $s=\pm 1$ and mutual attention is given through a two-spin coupling $J_{ij} = J Q/\sqrt{q_iq_j}$, $Q$ being the average connectivity in the network. Connectivity diminishes attention and only persons with low connectivity can pay special attention to each other leading to a durable common (or opposing) opinion. The model is solved in "mean-field" approximation and a critical "temperature" $T_c$ proportional to $JQ$ is found, which is independent of the number of persons $N$, for large $N$., Comment: 5 pages, no figures

Alkanes of medium chain length show an unusual wetting behavior on (salt) water, exhibiting a sequence of two changes in the wetting state. When deposited on the water surface at low temperatures, the liquid alkane forms discrete droplets that are interconnected only by a molecularly thin film. On increase of the temperature, there occurs a sudden jump of the film thickness and, at this first-order transition, a mesoscopically thick layer of liquid alkane is formed. Heating the system further leads to a divergence of the film thickness in a continuous manner. While the long-range forces between substrate and adsorbate are responsible for the critical transition, which occurs at the temperature at which the Hamaker constant changes sign, it is primarily the short-range components of the forces that bring about the first-order transition. We calculate the Hamaker constant of the system and show how, within a modified Cahn theory, accurate predictions of the first-order transition temperatures can be obtained for n-alkanes (pentane and hexane) on water and even on brine. Furthermore, we study the variation of the contact angle as a function of temperature., Comment: 10 pages, 3 figures, contribution to the proceedings of the 15th Symposium on Thermophysical Properties, Boulder, CO (22-27 May 2003)

In recent experiments, a sequence of changes in the wetting state (`wetting transitions') has been observed upon increasing the temperature in systems consisting of pentane on pure water and of hexane on brine. This sequence of two transitions is brought about by an interplay of short-range and long-range interactions between substrate and adsorbate. In this work, we argue that the short-range interaction (contact energy) between hexane and pure water remains unchanged due to the formation of a depletion layer (a thin `layer' of pure water which is completely devoid of ions) at the surface of the electrolyte and that the presence of the salt manifests itself only in a modification of the long-range interaction between substrate and adsorbate. In a five-layer calculation considering brine, water, the first layer of adsorbed hexane molecules, liquid hexane, and vapor, we determine the new long-range interaction of brine with the adsorbate {\em across} the water `layer'. According to the recent theory of the excess surface tension of an electrolyte by Levin and Flores-Mena, this water `layer' is of constant, i.e.\ salt-concentration independent, thickness $\delta$, with $\delta$ being the hydrodynamic radius of the ions in water. Our results are in good agreement with the experimental ones., Comment: 27 pages, 2 tables, 4 figures

A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, $B$, and of death, $D$, determine the carrying capacity $K$. Due to the randomness the population depends strongly on position, $x$, and there is a distribution of carrying capacities, $\Pi (K)$. This distribution has self-similar character owing to the imposed hierarchy. The most probable carrying capacity and its probability are studied as a function of $B$ and $D$. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to random local bactericidal agent (antibiotic spray). A gradual overall temperature change away from optimal growth conditions, for instance, reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state., Comment: 25 pages, 11 (9+2) figures

The Ginzburg-Landau coefficients, and the jump of the specific heat are calculated for a disordered two-band superconductor. We start with the analysis of a more general case arbitrary anisotropy. While the specific heat discontinuity at the critical temperature T_c decreases with increasing disorder, its ratio to the normal state specific heat at T_c increases and slowly converges to the isotropic value. For a strong disorder the deviation from the isotropic value is proportional to the elastic electron scattering time. In the case of a two-band superconductor we apply a simplified model of the interaction independent on momentum within a band. In the framework of this model all thermodynamic values can be found explicitly at any value of the scattering rate. This solution explains the sample dependence of the specific heat discontinuity in MgB_2 and the influence of the disorder on the critical temperature., Comment: New results relate to two-band superconductors, 9 pages, 2 figures

The single-site two-electron exchange amplitude J_sd between the Cu 4s and Cu 3d_{x^2-y^2} states is found to be the pairing mechanism of high-T_c overdoped cuprates. The noninteracting part of the Hamiltonian spans the copper Cu 4s, Cu 3d_{x^2-y^2} and oxygen O 2p_x and O 2p_y states. Within the standard BCS treatment an explicit expression for the momentum dependence of the gap Delta_p is derived and shown to fit the angle-resolved photoemission spectroscopy (ARPES) data. The basic thermodynamic and electrodynamic properties of the model (specific heat C(T), London penetration depth lambda(T)) are analytically derived. These are directly applicable to cuprates without complicating structural accessories (chains, double CuO_2 planes, etc.). We advocate that the pairing mechanism of overdoped and underdoped cuprates is the same, as T_c displays smooth doping dependence. Thus, a long-standing puzzle in physics is possibly solved., Comment: 34 pages, 3 figures, 152 references (updated; more than 250 publications cited), LaTeX2e; Appendix added. This is the final cond-mat version (v4) that takes into account many comments by readers after the paper has been published

High-temperature superconductors are nowadays found in great variety and hold technological promise. It is still an unsolved mystery that the critical temperature T_c of the basic cuprates is so high. The answer might well be hidden in a conventional corner of theoretical physics, overlooked in the recent hunt for exotic explanations of new effects in these materials. A forgotten intra-atomic s-d two-electron exchange in the Cu atom is found to provide a strong (~eV) electron pairing interaction. A Bardeen-Cooper-Schrieffer approach can explain the main experimental observations and predict the correct d_{x^2-y^2} symmetry of the gap., Comment: 4 pages, 3 figures, LaTeX2e

A detailed Linear Combination of Atomic Orbitals (LCAO) tight-binding model is developed for the layered High-Temperature Superconductor cuprates. The band structure of these materials is described using a sigma-band Hamiltonian employing Cu4s, Cu3d_x^2-y^2, O2p_x and O2p_y atomic orbitals. The Fermi level and the shape of the resulting Fermi surface are fitted to recent Angle Resolved Photon Emission Spectroscopy (ARPES) data to realistically determine the dispersion in the conduction band. Electron-electron interactions and, ultimately, Cooper pairing is obtained by introducing a Heitler-London, two-electron exchange between adjacent orbitals within the CuO_2 plane. Finally, using the LCAO wavefunctions determined by the band structure fit, the Bardeen-Cooper-Schrieffer type kernel is derived for interatomic exchange., Comment: 6 pages, LaTeX2e, submitted to Int. J. Mod. Phys. B

An analytical result for the renormalization of the jump of the heat capacity Delta C/C_N by the anisotropy of the order parameter is derived within the framework of the very recent model proposed by Posazhennikova, Dahm and Maki [cond-mat/0204272, submitted to Europhys. Lett.], for both oblate and prolate anisotropy. The graph of Delta C/C_N versus the ratio of the gaps on the equator and the pole of the Fermi surface, Delta_e/\Delta_p, allows a direct determination of the gap anisotropy parameter Delta_e/\Delta_p by fitting data from specific heat measurements Delta C/C_N. Using the experimental value Delta C/C_N=0.82 +/- 10% by Wang, Plackowski, and Junod [Physica C 355 (2001) 179] we find Delta_e/\Delta_p = 4.0., Comment: 3 pages, 1 figure, LaTeX2e, submitted to Europhys. Lett.; analytical result for the relative jump of the specific heat within a two-band model added; references updated and corrected

An analytical result for renormalization of the jump of the heat capacity Delta C/C_N by the anisotropy of the order parameter is derived in the framework of the model proposed by Haas and Maki [Phys. Rev. B 65, 020502(R) (2001)], for both prolate and oblate anisotropy. The graph of Delta C/C_N versus the ratio of the gaps on the equator and the pole, Delta_e/Delta_p, of the Fermi surface allows a direct determination of the gap anisotropy parameter Delta_e/Delta_p using data from specific heat measurements., Comment: 1 page, 1 figure, REVTeX 4, to be submitted to Phys. Rev. B

A mean-field theory is presented which describes the basic observations of recent experiments revealing rich wetting behaviour of n-alkane/methanol mixtures at the liquid-vapour interface. The theory, qualitative and in part heuristic, is based on a microscopic lattice-gas model from which a Cahn-Landau approach is distilled. Besides the physics associated with the short-range components of the intermolecular interactions, effects of the long-range tails of the net van der Waals forces between interfaces are also taken into account. Including weak long-range forces which favour wetting in the theory does not visibly alter the critical wetting transition for the nonane/methanol mixture, in contrast with the generic expectation of first-order wetting for such systems, but in good agreement with experiment. For decane/methanol weak long-range forces bring the transition very close to the prewetting critical point, leading to an adsorption behaviour closely reminiscent of short-range tricritical wetting, observed experimentally for alkane chain length between 9.6 and 10. Finally, for undecane/methanol the transition is clearly of first order. First-order wetting is also seen in the experiment., Comment: 52 pages, 17 figures, to appear in Journal of Statistical Physics. The tex file has been revised after refereeing. The figures are unchanged

In this paper, we report on the sharp peak observed in the third harmonic voltage response generated by a bias sinusoidal current applied to several strips patterned in a YBa2Cu3O7-d thin film and in two La1-xSrxCuO4 thin films, when the temperature is close to the normal-superconductor transition. The lambda-shaped temperature dependence of the third harmonic signal on the current characteristics is studied. Several physical mechanisms of third harmonic generation are examined. PACS Code/Keywords: 74.25.Fy - Third harmonic response, Non-linear voltage response, High-Tc Superconductor., Comment: 14 pages, 10 Figures, submitted to EPJ B (November 2002)

The generation of harmonics of the voltage response is considered when an AC current is applied through a superconducting film above T_c. It is shown that almost at all temperatures the mechanism of the temperature oscillations created by the AC current and the temperature dependence of the resistance dominates over the isothermal nonlinear electric conductivity. Only in a narrow critical region close to T_c the latter is essential for the generation of the harmonics. A detailed investigation of harmonics generation provides an accurate method for measuring the thermal boundary conductance between the film and the insulating substrate. The critical behaviour of the third harmonic will give a new method for the determination of the lifetime of metastable Cooper pairs above T_c. The comparison of the calculated fifth harmonics of the voltage with the experiment is proposed as an important test for the applicability of the employed theoretical models., Comment: 8 pages, LaTeX, submitted to European Journal of Physics B