We present theory and experiments for the force-distance curve $F\left(z_0\right)$ of an atomic force microscope (AFM) tip (radius $R$) indenting a supported fluid bilayer (thickness $2d$). For realistic conditions the force is dominated by the area compressibility modulus ${\kappa }_A$ of the bilayer and, to an excellent approximation, given by $F=\pi {\kappa }_{A}R{z}_0^2/{\left(2d-z_0\right)}^2$. The experimental AFM force curves from coexisting liquid ordered and liquid disordered domains in three-component lipid bilayers are well described by our model, which provides ${\kappa }_A$ in agreement with literature values. The liquid ordered phase has a yieldlike response that we model as due to the breaking of hydrogen bonds.

This paper suggests that reaction-diffusion processes, rather than pure topological rules, are responsible for the emergence of heterogeneous structures of complex chemical reaction networks. In such a network, chemical substances react in each node and diffuse between connected nodes. At the same time, each node is able to sense the difference between its own state and the environmental conditions and can rearrange its neighbors via a local rewiring process so as to eliminate the sensed difference. Then, the network, even originally homogeneous, will develop a heterogeneous structure under certain environmental conditions. Such a resultant heterogeneous network may be disassortative, highly clustering, and small world as well. This implies that the reaction-diffusion equilibrium can be statistically controlled by slightly changing the structure of the underlying network. This structure-control mechanism may be especially useful in the situations where some other macroscopic measurements, such as temperature and pressure, are not allowed to be changed through the process.

Rich-club, assortativity and clustering coefficients are frequently used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the assortativity and clustering coefficients of a large network, which reveals that the rich-club connectivity is leveraged throughout the network. Our study suggests that more attention should be paid to the organization pattern of rich nodes, for the structure of a complex system as a whole is determined by the associations between the most influential individuals. Moreover, by manipulating the connectivity pattern in a very small rich-club, it is sufficient to produce a network with desired assortativity or transitivity. Conversely, our findings offer a simple explanation for the observed assortativity and transitivity in many real world networks—such biases can be explained by the connectivities among the richest nodes.

We investigate synchronization issues of a set of mobile agents in plane, where each agent carries an identical chaotic oscillator and interacts with its neighbors through a blinking coupling mechanism. We discuss the effect of blinking pattern on synchronization of the related network. In particular, we show that phase locking of the blinking behavior can dramatically enhance synchronizability of the mobile agent network, while the random blinking pattern works little. Also, we show that by assessing the convergence time, the mobile agent networks with different blinking periods and duty ratios share a common idle duration which is independent of both the blinking period and the corresponding duty ratio.

Classical sum rules arise in a wide variety of physical contexts. Asymptotic expressions have been derived for many of these sum rules in the limit of long orbital period (or large action). Although sum-rule convergence may well be exponentially rapid for chaotic systems in a global phase-space sense with time, individual contributions to the sums may fluctuate with a width which diverges in time. Our interest is in the global convergence of sum rules as well as their local fluctuations. It turns out that a simple version of a lazy baker map gives an ideal system in which classical sum rules, their corrections, and their fluctuations can be worked out analytically. This is worked out in detail for the Hannay-Ozorio sum rule. In this particular case the rate of convergence of the sum rule is found to be governed by the Pollicott-Ruelle resonances, and both local and global boundaries for which the sum rule may converge are given. In addition, the width of the fluctuations is considered and worked out analytically, and it is shown to have an interesting dependence on the location of the region over which the sum rule is applied. It is also found that as the region of application is decreased in size the fluctuations grow. This suggests a way of controlling the length scale of the fluctuations by considering a time dependent phase-space volume, which for the lazy baker map decreases exponentially rapidly with time.

In this work, we present a dielectric function including the three conservation laws (density, momentum and energy) when we take into account electron-electron collisions in a plasma at any degeneracy. This full conserving dielectric function (FCDF) reproduces the random phase approximation (RPA) and Mermin ones, which confirms this outcome. The FCDF is applied to the determination of the proton stopping power. Differences among diverse dielectric functions in the proton stopping calculation are minimal if the plasma electron collision frequency is not high enough. These discrepancies can rise up to 2% between RPA values and the FCDF ones, and to 8% between the Mermin ones and FCDF ones. The similarity between RPA and FCDF results is not surprising, as all conservation laws are also considered in RPA dielectric function. Even for plasmas with low collision frequencies, those discrepancies follow the same behavior as for plasmas with higher frequencies. Then, discrepancies do not depend on the plasma degeneracy but essentially do on the value of the plasma collision frequency.

In this paper, excitation of parasitic waves near cutoff in forward-wave amplifiers is studied in a rather general form. This problem is important for developing high-power sources of coherent, phase controlled short-wavelength electromagnetic radiation because just the waves which can be excited near cutoff have low group velocities. Since the wave coupling to an electron beam is inversely proportional to the group velocity, these waves are the most dangerous parasitic waves preventing stable amplification of desired signal waves. Two effects are analyzed in the paper. The first one is the effect of signal wave parameters on the self-excitation conditions of such parasitic waves. The second effect is the role of the beam geometry on excitation of these parasitic waves in forward-wave amplifiers with spatially extended interaction space, such as sheet-beam devices. It is shown that a large-amplitude signal wave can greatly influence the self-excitation conditions of the parasitic waves which define stability of operation. Therefore the effect described is important for accurate designing of high-power amplifiers of electromagnetic waves.

We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called fixed-node approximation is also proposed. The generality of the method, which also takes advantage of a canonical worm algorithm scheme to measure off-diagonal observables, makes it applicable to a vast variety of quantum systems and eases the study of their ground-state and excited-state properties. As a case study, we investigate the quantum dynamics of the one-dimensional Heisenberg model and we provide accurate estimates of the ground-state energy of the two-dimensional fermionic Hubbard model.

A model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution of velocity increments is calculated explicitly and expressed in terms of generalized hypergeometric functions of the type ${{}_{n}F}_0$, which exhibit power-law tails. The model predictions are found to be in good agreement with experiments on a low temperature gaseous helium jet. It is argued that distributions based on the functions ${{}_{n}F}_0$ might be relevant also for other physical systems with multiscale dynamics.

The mean first passage time of a Brownian particle from an initial unstable state in a metastable system with damping is investigated. The system is analyzed in the low to high damping regime, and the role played by the damping parameter is studied. We observe the noise enhanced stability effect for all the initial unstable states under study and for all values of the damping parameter $\gamma$ investigated. The curves show a behavior of the mean first passage time vs $\gamma$ very close to that observed for an overdamped particle in the presence of colored noise as a function of the correlation time.

We numerically examine the properties of a two-dimensional system of particles which have competing long-range repulsive and short-range attractive interactions as a function of density and temperature. For increasing density, there are well-defined transitions between a low-density clump phase, an intermediate stripe phase, an anticlump phase, and a high-density uniform phase. To characterize the transitions between these phases we propose several measures which take into account the different length scales in the system. For increasing temperature, we find an intermediate phase that is liquidlike on the short length scale of interparticle spacing but solidlike on the larger length scale of the clump, stripe, or anticlump pattern. This intermediate phase persists over the widest temperature range in the stripe phase when the local particle lattice within an individual stripe melts well below the temperature at which the entire stripe structure breaks down, and is characterized by intrastripe diffusion of particles without interstripe diffusion. This is followed at higher temperatures by the onset of interstripe diffusion in an anisotropic diffusion phase and then by breakup of the stripe structure. We identify the transitions between these regimes through diffusion, heat capacity, and energy fluctuation measurements and find that within the intrastripe liquid regime, the excess entropy goes into disordering the particle arrangements within the stripe rather than affecting the stripe structure itself. The clump and anticlump phases also show multiple temperature-induced diffusive regimes which are not as pronounced as those of the stripe phase.

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the 1990s, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.

Thermodynamic properties of a single chain in a confined space have been studied before with the polymer scaling theory and computer simulations. However, a comprehensive understanding of the entropic effects due to the molecular excluded volume and chain connectivity is emerging only recently, especially in the limit of large polymer packing densities as often encountered in biological systems. In this work, we propose a polymer density functional theory (DFT) to study the entropic forces for the confinement of single polymer chains in spherical cavities. At conditions accessible to Monte Carlo simulations, we show that the DFT predictions are in excellent agreement with the simulation results for the distributions of polymer segments as well as the free energy of confinement. The numerical efficiency of the DFT allows us to unify key conclusions from various theoretical analyses and experimental observations.

Structure and function of the adherent cell depend in a crucial way on its microenvironment, including the stiffness of its substrate. It is often asserted that substrate thickness (as opposed to stiffness) plays a negligible role and therefore may be considered semi-infinite. This assertion has been recently challenged, but the characteristic length scale to consider in this regard is poorly understood. We show here that this characteristic length scale is the lateral cell size. As substrate thickness approaches the lateral dimension of the cell, the apparent stiffness of the substrate is amplified to levels much greater than the intrinsic stiffness of the substrate. This change in apparent stiffness is readily sensed by the cell, leading to changes in cell spreading area, stiffness, and contractile forces. In contrast to these responses that occur over the length of the cell, mechanosensing around an isolated point force is influenced greatly by intrinsic substrate stiffness but to a negligible extent by substrate thickness. We conclude that mechanosensing of substrate thickness is dominated in large part by traction forces spread over the lateral dimension of the cell.

The morphology of a typical developing biological transportation network, the vein network of the plasmodium of the myxomycete Physarum polycephalum is analyzed during its free extension. The network forms a classical, regular graph, and has exclusively nodes of degree 3. This contrasts to most real-world transportation networks which show small-world or scale-free properties. The complexity of the vein network arises from the weighting of the lengths, widths, and areas of the vein segments. The lengths and areas follow exponential distributions, while the widths are distributed log-normally. These functional dependencies are robust during the entire evolution of the network, even though the exponents change with time due to the coarsening of the vein network.

In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen from a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant’s fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only. We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value and counting that event as having led to a total spread of the mutation. For advantageous mutations in large populations and regardless of the network’s topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about ${\left[N/\left(r-1\right)\right]}^{1/4}$ mutants, where $N$ is the number of simulation events and $r$ is the ratio of the mutants’ fitness to that of the remainder of the population, leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with $10000$ nodes.

We subjected the time series of quasi-rigid-body vibration pulses (elastic emissions) from laboratory fracture carried out by a piezoelectric accelerometer on concrete and rock specimens under uniaxial compression to statistical analysis. In both cases, we find that the waiting-time distribution can be described by a scaling law extending over several orders of magnitude. This law is indistinguishable from a universal scaling law recently proposed for the waiting-time distributions of acoustic emissions in heterogeneous materials and earthquakes, suggesting its general validity for fracture processes independent of modes and magnitude scales.

Because of a formal equivalence with the partition function of an Ising chain, the semiclassical traces of the quantum baker map can be calculated using the transfer-matrix method. We analyze the transfer matrices associated with the baker map and the symmetry-reflected baker map (the latter happens to be unitary but the former is not). In both cases simple quantum-circuit representations are obtained, which exhibit the typical structure of qubit quantum bakers. In the case of the baker map it is shown that nonunitarity is restricted to a one-qubit operator (close to a Hadamard gate for some parameter values). In a suitable continuum limit we recover the already known infinite-dimensional transfer operator. We devise truncation schemes allowing the calculation of long-time traces in regimes where the direct summation of Gutzwiller’s formula is impossible. Some aspects of the long-time divergence of the semiclassical traces are also discussed.

We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on (i) the localization volume of a mode which defines the number of interacting partner modes, (ii) the overlap integrals which determine the interaction strength, (iii) the average spacing between eigenvalues of interacting modes, which sets a scale for the nonlinearity strength, and (iv) resonance probabilities of interacting modes. Our results are discussed in the light of recent studies on spreading of wave packets in disordered nonlinear systems and are related to the quantum many-body problem in a random chain.

Ferrofluids are suspensions of magnetic nanoparticles which respond to imposed magnetic fields by changing their viscosity without losing their fluidity. Prior work on modeling the behavior of ferrofluids has focused on using phenomenological suspension-scale continuum equations. A disadvantage of this approach is the controversy surrounding the equation describing the rate of change of the ferrofluid magnetization, the so-called magnetization relaxation equation. In this contribution the viscosity of dilute suspensions of spherical magnetic nanoparticles suspended in a Newtonian fluid and under applied shear and constant magnetic fields is studied through rotational Brownian dynamics simulations. Simulation results are compared with the predictions of suspension-scale models based on three magnetization relaxation equations. Excellent agreement is observed between simulation results and the predictions of an equation due to Martsenyuk, Raikher, and Shliomis. Good qualitative agreement is observed with predictions of other equations, although these models fail to accurately predict the magnitude and shear rate dependence of the magnetic-field-dependent effective viscosity. Finally, simulation results over a wide range of conditions are collapsed into master curves using a Mason number defined based on the balance of hydrodynamic and magnetic torques.