We report an x-ray reflectivity study of phospholipid membranes deposited on silicon by vesicle fusion. The samples investigated were composed of single phospholipid bilayers as well as two-component lipid bilayer systems with varied charge density. We show that the resolution obtained in the density profile across the bilayer is high enough to distinguish two head-group maxima in the profile if the sample is in the phase coexistence regime. The water layer between the bilayer and silicon is found to depend on the lipid surface charge density.

We study the formation of knots on a macroscopic ball chain, which is shaken on a horizontal plate at 12 times the acceleration of gravity. We find that above a certain critical length, the knotting probability is independent of chain length, while the time to shake out a knot increases rapidly with chain length. The probability of finding a knot after a certain time is the result of the balance of these two processes. In particular, the knotting probability tends to a constant for long chains.

Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long-standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check codes on the binary erasure channel and the binary symmetric channel. In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords and a paramagnetic to glass transition in the space of codes.

We study the thermodynamic properties of spin systems on small-world hypergraphs, obtained by superimposing sparse Poisson random graphs with $p$-spin interactions onto a one-dimensional Ising chain with nearest-neighbor interactions. We use replica-symmetric transfer-matrix techniques to derive a set of fixed-point equations describing the relevant order parameters and free energy, and solve them employing population dynamics. In the special case where the number of connections per site is of the order of the system size, we are able to solve the model analytically. In the more general case where the number of connections is finite, we determine the static and dynamic ferromagnetic-paramagnetic transitions using population dynamics. The results are tested against Monte-Carlo simulations.

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions ${\varphi }_{\lambda }$, and define the value $r_{\lambda }=({\varphi }_{\lambda }\mid {\varphi }_{\lambda })∕⟨{\varphi }_{\lambda }\mid {\varphi }_{\lambda }⟩$ that characterizes the phase rigidity of the eigenfunctions ${\varphi }_{\lambda }$. In the scenario with avoided level crossings, $r_{\lambda }$ varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of $r_{\lambda }$ is an internal property of an open quantum system. In the literature, the phase rigidity $\rho$ of the scattering wave function ${\Psi }_C^E$ is considered. Since ${\Psi }_C^E$ can be represented in the interior of the system by the ${\varphi }_{\lambda }$, the phase rigidity $\rho$ of the ${\Psi }_C^E$ is related to the $r_{\lambda }$ and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity $\rho$ to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant at energies that are determined by the real part of the eigenvalues of the effective Hamiltonian. We illustrate the relation between phase rigidity $\rho$ and transmission numerically for small open cavities.

We study the dynamics of an array of Stuart-Landau oscillators with repulsive coupling. Autonomous network with global repulsive coupling settles on one from a continuum of synchronized regimes characterized by zero mean field. Driving this array by an external oscillatory signal produces a nonzero mean field that follows the driving signal even when the oscillators are not locked to the external signal. At sufficiently large amplitude the external signal synchronizes the oscillators and locks the phases of the array oscillations. Application of this system as a beam-forming element of a phase array antenna is considered. The phase dynamics of the oscillator array synchronization is used to reshape the phases of signals received from the phase array antenna and improve its beam pattern characteristics.

A diagnostic is developed for the nonintrusive study of the azimuthal drift current in the coaxial $\mathbf{E}\times \mathbf{B}$ discharge of a Hall plasma accelerator. The technique of fast current interruption is used to generate a signal on several loop antenna that circle the outer wall of the discharge channel. The signal on the antenna is recorded, and used to determine the spatial distribution of the azimuthal drift at the moment of current interruption. The results of the experiment are compared to estimates derived via prior intrusive measurements, and the intrusive estimates are found to predict the spatial characteristics of the azimuthal drift, but underestimate its total magnitude. The self-induced magnetic field is then calculated and added to the applied magnetic field. The peak total magnetic field is seen to shift $2–5\mathrm{mm}$ towards the anode due to self-induction, and suffer a reduction in magnitude of 10%–15%. The peak in the total magnetic field is then found to more closely coincide with the peak of the measured electric field than the peak of the vacuum magnetic field. It is concluded that the self-induced magnetic field could be important to anomalous electron mobility in the Hall-effect thruster, and simulation efforts should try to include its impact.

A generalized equivalence theorem for polarization theory is formulated and proven. It is shown that anisotropic properties of homogeneous nondepolarizing media can be presented as a combination of four basic mechanisms: linear and circular phase and linear and circular amplitude anisotropy. Expressions for the generalized effect operators of algebraic (or operator) optics are obtained and the inverse problem of crystal optics is solved in terms of physically realizable anisotropy parameters.

Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multiphase fluid systems. However, the underlying second-order analysis of the equation of motion has long been known to be insufficient to consistently derive the fourth-order terms that are necessary to represent an extended interface. These same terms are also responsible for thermodynamic consistency—i.e., to obtain a true equilibrium solution with both a constant chemical potential and a constant pressure. In this article we present an equilibrium analysis of nonideal lattice Boltzmann methods of sufficient order to identify those higher-order terms that lead to a lack of thermodynamic consistency. We then introduce a thermodynamically consistent forcing method.

We present an efficient and highly accurate first-principles calculation method with linear system-size scaling to determine the self-consistent ground-state electron-charge densities of nanostructures suspended between semi-infinite bulks by directly minimizing the energy functional. By making efficient use of the advantages of the real-space finite-difference method, we can impose arbitrary boundary conditions on models and employ spatially localized orbitals. These advantages enable us to calculate the ground-state electron-charge densities in semi-infinite systems. Examples of electronic structure calculations for a one-dimensional case and a conductance calculation for sodium nanowires are presented. The calculated electronic structure of the one-dimensional system agrees well with the exact analytical solution, and the conduction properties of the sodium nanowires are consistent with experimental and other theoretical results. These results imply that our procedure enables us to accurately compute self-consistent electronic structures of semi-infinite systems.

We analyze one thousand independent equilibrium trajectories of a system of 155 Lennard-Jones particles to separate in a model-free approach the role of temperature and the role of the explored potential energy landscape basin depth in the particle dynamics. We show that the diffusion coefficient $D$ can be estimated as a sum over contributions of the sampled basins, establishing a connection between thermodynamics and dynamics in the potential energy landscape framework. We provide evidence that the observed nonlinearity in the relation between local diffusion and basin depth is responsible for the peculiar dynamic behavior observed in supercooled states and provide an interpretation for the presence of dynamic heterogeneities.

We investigate nonequilibrium behavior of driven dissipative systems, using a model we recently presented [Phys. Rev. Lett., 93, 240601 (2004)]. We solve the non-Boltzmann steady state energy distribution and the temporal evolution to it, and find its high energy tail to behave exponentially. We demonstrate that various measures of effective temperatures generally differ. We discuss infinite hierarchies of effective temperatures defined from moments of the nonexponential energy distribution, and relate them to the “configurational temperature,” measured directly from instantaneous particle locations without any kinetic information. We calculate the “granular temperature,” characterizing the average energy in the system, two different “fluctuation temperatures,” scaling fluctuation-dissipation relations, and the “entropic temperature,” defined from differentiating the entropy with respect to energy.

This paper investigates a clustering instability of a freely falling granular jet composed of $100\mathrm{\mu }\mathrm{m}$ glass spheres. The granular flow out of a circular nozzle starts out spatially uniform and then, further downstream, breaks up into well-defined clusters. An optical method is used that measures inhomogeneities in the flow in order to quantify the growth of the clusters. The role of air is investigated in this phenomenon by changing the ambient air pressure down to 1/5000th atm. Clustering is observed down to the lowest pressure and the presence of air leads to larger clusters but does not initiate the cluster formation. The analysis shows that the cluster size is set by fluctuations on the order of the size of the particles at the nozzle.

We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean-field approach which allows one to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean-field approach is relatively robust even in configurations where the single-cluster assumption is not entirely fulfilled and (b) that the eigenvalue-decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue-decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis, which account for nonlinearities in the data, are expected to provide complementary information which allows one to gain deeper insights into the collective dynamics of spatially extended complex systems.

In the intracellular environment, signaling takes place in a nonideal environment that is spatially heterogeneous and that is noisy, with the noise arising from the low copy numbers of the signaling molecules involved. In this paper, we model intracellular signaling pathways as stochastic reaction-diffusion processes and adapt techniques commonly used by physicists to solve for the spatiotemporal evolution of the signaling pathways. We then apply it to study two problems of relevance to the modeling of intracellular signaling pathways. First, we show that, in the limit of small protein diffusion which is typically the case for proteins in the cytosol crowded by other macromolecules, the extent of diffusion control, in the transient regime, on reactions is greater than previous predictions. Second, we show that the presence of scaffold proteins can modify the phosphorylation activity of a mitogen-activated protein kinase cascade, and explain how this activity is modulated by the scaffold protein concentration.

We evaluate the ionic relaxation time of a nematic cell subjected to a potential difference, $V_0$, very large with respect to $V_T=K_{B}T∕q=0.025\mathrm{V}$, where $K_{B}T$ is the thermal energy, and $q$ the electrical charge of the ions, assumed monovalent. The analysis is performed by assuming that the mobilities of the positive and negative ions are the same, and that the ions can be considered pointlike. We show that, for $V_0⪢V_T$, the relaxation time tends to the time of flight of the ions. In our analysis the ionic charges are assumed to form two surface layers responsible for a partial screening of the external field. In this framework, the evolution of the surface-charge density is determined by a simple differential equation related to the conservation of the ions number. According to our calculations, the relaxation time of the surface density of ionic origin, and of the electrical potential close to the electrodes, depends on the applied voltage, in agreement with the experimental observations.

In view of the fact that microtubules exhibit strong anisotropic elastic properties, an orthotropic elastic shell model for microtubules is developed to study buckling behavior of microtubules. The predicted critical pressure is found to agree well with recent unexplained experimental data on pressure-induced buckling of microtubules [Needleman et al., Phys. Rev. Lett. 93, 198104 (2004); Biophys. J. 89, 3410 (2005)] which are lower than that predicted by the isotropic shell model by four orders of magnitude. General buckling behavior of microtubules under axial compression or radial pressure is studied. The results show that the isotropic shell model greatly overestimates the bucking loads of microtubules, except columnlike axially compressed buckling of long microtubules (of length-to-diameter ratio larger than, say, 150). In particular, the present results also offer a plausible explanation for the length dependency of flexibility of microtubules reported in the literature.

The generation of stable buoyant fireballs in a microwave cavity in air at atmospheric pressure without the use of vaporized solids is described. These fireballs have some of the characteristics of ball lightning and resemble those reported by Dikhtyar and Jerby [Phys. Rev. Lett. 96, 045002 (2006)], although of a different color, and do not require the presence of molten or vaporized material. Mechanisms of microwave plasma formation and fluid dynamics can account for the observed behavior of the fireballs, which do not appear to meet the accepted definition of dusty plasmas in this case. Relevance to models of ball lightning and industrial applications are discussed.

In order to probe with high precision the tails of the ground-state energy distribution of disordered spin systems, Körner, Katzgraber, and Hartmann have recently proposed an importance-sampling Monte Carlo Markov chain in the disorder. In this paper, we combine their Monte Carlo procedure in the disorder with exact transfer matrix calculations in each sample to measure the negative tail of ground-state energy distribution $P_d\left(E_0\right)$ for the directed polymer in a random medium of dimension $d=1,2,3$. In $d=1$, we check the validity of the algorithm by a direct comparison with the exact result, namely, the Tracy-Widom distribution. In dimensions $d=2$ and $d=3$, we measure the negative tail up to ten standard deviations, which correspond to probabilities of order $P_d\left(E_0\right)\sim {10}^{-22}$. Our results are in agreement with Zhang’s argument, stating that the negative tail exponent $\eta \left(d\right)$ of the asymptotic behavior $\ln P_d\left(E_0\right)\sim -{\mid E_0\mid }^{\eta \left(d\right)}$ as $E_0\to -\infty$ is directly related to the fluctuation exponent $\theta \left(d\right)$ [which governs the fluctuations $\Delta E_0\left(L\right)\sim L^{\theta \left(d\right)}$ of the ground-state energy $E_0$ for polymers of length $L$] via the simple formula $\eta \left(d\right)=1∕[1-\theta \left(d\right)]$. Throughout the paper, we comment on the similarities and differences with spin glasses.

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold that depends on the distribution of capacities. We then examine the maximal total flux from the root to the leaves. Our methods generalize to simple graphs with loops, e.g., to hierarchical lattices and to complete graphs.