The question of the existence of a structural glass transition in two dimensions is studied using mode coupling theory (MCT). We determine the explicit $d$ dependence of the memory functional of mode coupling for one-component systems. Applied to two dimensions we solve the MCT equations numerically for monodisperse hard disks. A dynamic glass transition is found at a critical packing fraction ${\phi }_c^{d=2}\cong 0.697$ which is above ${\phi }_c^{d=3}\cong 0.516$ by about 35%. ${\phi }_c^d$ scales approximately with ${\phi }_{\mathrm{rcp}}^d$, the value for random close packing, at least for $d=2$, 3. Quantities characterizing the local, cooperative “cage motion” do not differ much for $d=2$ and $d=3$, and we, e.g., find the Lindemann criterion for the localization length at the glass transition. The final relaxation obeys the superposition principle, collapsing remarkably well onto a Kohlrausch law. The $d=2$ MCT results are in qualitative agreement with existing results from Monte Carlo and molecular dynamics simulations. The mean-squared displacements measured experimentally for a quasi-two-dimensional binary system of dipolar hard spheres can be described satisfactorily by MCT for monodisperse hard disks over four decades in time provided the experimental control parameter $\Gamma$ (which measures the strength of dipolar interactions) and the packing fraction $\phi$ are properly related to each other.

We study a surface growth model related to the Kardar-Parisi-Zhang equation for nonequilibrium kinetic roughening, but where the thermal noise is replaced by a static columnar disorder $\eta \left(\mathbf{x}\right)$. This model is one of the many representations of the problem of particle diffusion in trapping or amplifying disordered media. We find that probability localization in the latter translates into facet formation in the equivalent surface growth problem. Coarsening of the pattern can therefore be identified with the diffusion of the localization center. The emergent faceted structure gives rise to nontrivial scaling properties, including anomalous surface roughening in excellent agreement with an existing conjecture for kinetic roughening of faceted surfaces. In a wider context, our study sheds light onto the scaling properties in other systems displaying this kind of patterned surface.

In the phase diagram of the protein hen egg-white lysozyme, a region is present in which the lysozyme solution demixes and forms two liquid phases. In situ observations by optical microscopy show that the dense liquid droplets dissolve when crystals grow in this system. During this process the demixed liquid region retracts from the crystal surface. The spatial distribution of the dense phase droplets present special boundary conditions for Fick’s second law for diffusion. In combination with the cylindrical symmetry provided by the kinetically roughened crystals, this system allows for a full numerical analysis. Using experimental data for setting the boundary conditions, a quasi-steady-state solution for the time-dependent concentration profile was shown to be valid. Comparison of kinetically rough growth in a phase separated system and in a nonseparated system shows that the growth kinetics for a three-phase system differs from a two-phase system, in that crystals grow more slowly but the duration of growth is prolonged.

Planar antiferroelectric liquid crystal (AFLC) cells exhibit propagating solitary waves. By measuring the retardation and the apparent tilt angle, we find that the conventional model for the solitary wave propagation in AFLCs is not generally applicable. The model being proposed here shows that the solitary wave propagation both along and normal to the smectic layer plane can be explained by a double well potential energy governing the relative orientations of the $\mathbf{c}$ directors in the adjacent smectic $C$ layers with an energy barrier between the synclinic and the anticlinic states. The quadrupolar term of the interlayer interaction is found to be significantly large in a pure AFLC.

We have studied various ferroelectric liquid crystals to find the average molecular direction of the shortest axis in the perfectly unwound state by using tilted conoscopic measurements. We find that there exist two types of temperature dependencies of the biaxiality. Some materials exhibit increasing biaxiality while others show decreasing biaxiality with increasing temperature. The former shows a temperature-induced sign reversal of biaxiality. Three different physical mechanisms are identified as responsible for the emergence of biaxiality: (i) anisotropic fluctuations of the long molecular axis, (ii) a biased rotation around the long axis, and (iii) the local field effect. By means of a simple theoretical investigation, we conclude that these two types of trends are due mainly to the opposite signs of the biaxial order parameter $C$, which represents the second mechanism: the biased rotation around the long axis. This means that the central phenyl planes of molecules belonging to materials having biaxiality that increases with temperature are oriented on the average parallel to the tilt plane (the shortest index of refraction axis normal to the tilt plane), and, on the contrary, in those of the others molecules are oriented perpendicular to the tilt plane (the shortest index of refraction axis lying in the tilt plane). Thus, the direction of the phenyl ring plane of the liquid crystal molecules determines the different temperature dependencies of the biaxiality. It is also shown that the phenomenon of sign reversal of the biaxiality is due to the competitive contributions of the first and second physical mechanisms.

We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial $C_{\infty v}$ symmetry to biaxial systems exhibiting local $C_{2v}$ symmetry. Our work is motivated by the recently discovered examples of thermotropic biaxial nematic liquid crystals comprising bent-core mesogens, whose molecular structure is characterized by a non-polar-body axis $\left(\mathbf{n}\right)$ as well as a polar axis $\left(\mathbf{p}\right)$ along the bisector of the bent mesogenic core which is coincident with a large, transverse dipole moment. The free energy for this system differs from that of biaxial nematic liquid crystals in that it contains terms violating the $\mathbf{p}\to -\mathbf{p}$ symmetry. We show that, in spite of a general splay instability associated with these parity-odd terms, a uniform polarized biaxial state can be stable in a range of parameters. We then derive the hydrodynamic equations of the system, via the Poisson-bracket formalism, in the polarized state and comment on the structure of the corresponding linear hydrodynamic modes. In our Poisson-bracket derivation, we also compute the flow-alignment parameters along the three symmetry axes in terms of microscopic parameters associated with the molecular geometry of the constituent biaxial mesogens.

A theoretical study is presented of surface waves at a monomolecular surfactant film between an isotropic liquid and a nematic liquid crystal for the case when the surfactant film is in the isotropic two-dimensional fluid phase and induces homeotropic (normal to the interface) orientation of the nematic director. The dispersion relation for the surface waves is obtained, and different surface modes are analyzed with account being taken of the anchoring induced by the surfactant layer, the curvature energy of the interface, and the anisotropy of the viscoelastic coefficients. The dispersion laws for capillary and dilatational surface modes retain structure similar to that in isotropic systems, but involve anisotropic viscosity coefficients. Additional modes are related to relaxation of the nematic director field due to anchoring at the interface. The results can be used to determine different properties of nematic-surfactant-isotropic interfaces from experimental data on surface light scattering.

With the aid of time-resolved dynamic light scattering (DLS) and static light scattering (SLS), we have analyzed the ejection kinetics from the bacterial virus bacteriophage (or phage) $\lambda$, triggered in vitro by its receptor. We have used DLS to investigate the kinetics in such a system. Furthermore, we have shown that both SLS and DLS can be interchangeably used to study the process of phage DNA release. DLS is superior to SLS in that it also allows the change in the light scattering arising from each of the components in the system to be monitored under conditions such that the relaxation times are separable. With help of these two methods we present a model explaining the reason for the observed decrease in the scattering intensity accompanying DNA ejection from phage. We emphasize that ejection from phage capsid occurs through a very long tail (which is nearly three times longer than the capsid diameter), which significantly separates ejected DNA from the scattering volume of the capsid. The scattering intensity recorded during the DNA ejection process is the result of a change in the form factor of the phage particle, i.e., the change in the interference effects between the phage capsid and the DNA confined in the phage particle. When the DNA molecule is completely ejected it remains in the proximity of the phage for some time, thus contributing to the scattering signal as it diffuses away from the phage capsid, into the scattering volume and returns to its unperturbed chain conformation in bulk solution. The free DNA chain does not contribute to the scattered intensity, when measured at a large angle, due to the DNA form factor and the low concentration. Although the final diffusion-controlled step can lead to overestimation of the real ejection time, we can still use both scattering methods to estimate the initial DNA ejection rates, which are mainly dependent on the pressure-driven DNA ejection from the phage, allowing studies of the effects of various parameters affecting the ejection.

We recently introduced a realistic order book model [T. Preis et al., Europhys. Lett. 75, 510 (2006)] which is able to generate the stylized facts of financial markets. We analyze this model in detail, explain the consequences of the use of different groups of traders, and focus on the foundation of a nontrivial Hurst exponent based on the introduction of a market trend. Our order book model supports the theoretical argument that a nontrivial Hurst exponent implies not necessarily long-term correlations. A coupling of the order placement depth to the market trend can produce fat tails, which can be described by a truncated Lévy distribution.

The purpose of the present paper is to describe the effects of electron-electron collisions on the stopping power of plasmas of any degeneracy. Plasma targets are considered fully ionized so electronic stopping is only due to the free electrons. We focus our analysis on plasmas which electronic density is around solid values $n_e\simeq {10}^{23}{\mathrm{cm}}^{-3}$ and which temperature is around $T\simeq 10\mathrm{eV}$; these plasmas are in the limit of weakly coupled plasmas. This type of plasma has not been studied extensively though it is very important for inertial confinement fusion. The electronic stopping is obtained from an exact quantum mechanical evaluation, which takes into account the degeneracy of the target plasma, and later it is compared with common classical and degenerate approximations. Differences are around 30% in some cases which can produce bigger mistakes in further energy deposition and projectile range studies. Then we consider electron-electron collisions in the exact quantum mechanical electronic stopping calculation. Now the maximum stopping occurs at velocities smaller than for the calculations without considering collisions for all kinds of plasmas analyzed. The energy loss enhances for velocities smaller than the velocity at maximum while decreases for higher velocities. Latter effects are magnified with increasing collision frequency. Differences with the same results for the case of not taking into account collisions are around 20% in the analyzed cases.

Thermal position fluctuations of a colloidal particle in an optical trap are measured with microsecond resolution using back-focal-plane interferometry. The mean-square displacement $⟨\Delta x^2\left(t\right)⟩$ and power spectral density are in excellent agreement with the theory for a Brownian particle in a harmonic potential that accounts for hydrodynamic memory effects. The motion of a particle is dominated at short times by memory effects and at longer times by the potential. We identify the time below which the particle’s motion is not influenced by the potential, and find it to be approximately ${\tau }_k∕20$, where ${\tau }_k$ is the relaxation time of the restoring force of the potential. This allows us to exclude the existence of free diffusive motion, $⟨\Delta x^2\left(t\right)⟩\propto t$, even for a sphere with a radius as small as $0.27\mu \mathrm{m}$ in a potential as weak as $1.5\mu \mathrm{N}∕\mathrm{m}$. As the physics of Brownian motion can be used to calibrate an optical trap, we show that neglecting memory effects leads to an underestimation of more than 10% in the detector sensitivity and the trap stiffness for an experiment with a micrometer-sized particle and a sampling frequency above $200\mathrm{kHz}$. Furthermore, these calibration errors increase in a nontrivial fashion with particle size, trap stiffness, and sampling frequency. Finally, we present a method to evaluate calibration errors caused by memory effects for typical optical trapping experiments.

In the present work, we propose a method to determine fluctuation-induced forces in nonequilibrium systems. These forces are the analog of the well-known Casimir forces, which were originally introduced in quantum field theory and later extended to the area of critical phenomena. The procedure starts from the observation that many nonequilibrium systems exhibit fluctuations with macroscopic correlation lengths, and the associated structure factors strongly depend on the wave vectors for long wavelengths; in some cases the correlations become long range, and the structure factors show algebraic divergences in the long-wavelength limit. The introduction of external bodies into such systems in general modifies the spectrum of these fluctuations, changing the value of the renormalized pressure, which becomes inhomogeneous. This inhomogeneous pressure leads to the appearance of a net force between the external bodies. It is shown that the force can be obtained from the knowledge of the structure factor of the homogeneous system. The mechanism is illustrated by means of a simple example: a reaction-diffusion equation, where the correlation function has a characteristic length. The role of this length in the Casimir force is elucidated.

We show that the fluctuation-dissipation relation can be established for a class of stochastic dynamics that lack detailed balance. This class comprises lattice spin models whose time evolution is governed by a master equation with a one-spin-flip transition rate having the up-down symmetry. The relation is obtained by the introduction of a multiplicative perturbation of the transition rate, which reduces to the usual perturbation when detailed balance is fulfilled. As a part of the derivation we set up an equivalent two-spin-flip stochastic dynamics that conserves the magnetization.

We study experimentally the liquid-solid transition in a soft-jammed system and focus on its aging in the solid regime. We investigate the impact of temperature, density, and load changes on the material behavior. We show that all elastic modulus versus time curves fall on a single master curve when rescaled by an appropriate factor function of the density, the temperature, the load, and the time elapsed since preshear. This allows us to distinguish the effect of temperature and density on the mechanical properties and their effect on aging. Since the time evolutions of the elastic modulus under various conditions are similar within a factor, we suggest that the rescaled time reflects the physical age of the material; i.e., it describes the degree of progress of the structural organization relative to a state of reference of the system in the solid regime and constitutes a means for characterizing the effective state of such systems.

An external mechanical torque on colloids immersed in a nematic liquid crystal can induce a Coulomb-like $1∕r$ interaction between them [Lev and Tomchuk, Phys. Rev. E 59, 591 (1999); Lev et al., ibid. 65, 021709 (2002)]. In this paper we show that the director-mediated Coulomb-like interaction of two colloids is determined by the vectors ${\mathbf{\Gamma }}_{\perp }^{\left(1\right)}$ and ${\mathbf{\Gamma }}_{\perp }^{\left(2\right)}$ of the transverse external torques exerted upon these colloids. We derive the $1∕r$ potential in which the scalar product $-({\mathbf{\Gamma }}_{\perp }^{\left(1\right)}\bullet {\mathbf{\Gamma }}_{\perp }^{\left(2\right)})$ of the two torques plays the role of the product of two electrostatic charges. The $1∕r$ interaction is attractive for $({\mathbf{\Gamma }}_{\perp }^{\left(1\right)}\bullet {\mathbf{\Gamma }}_{\perp }^{\left(2\right)})>0$ and repulsive for $({\mathbf{\Gamma }}_{\perp }^{\left(1\right)}\bullet {\mathbf{\Gamma }}_{\perp }^{\left(2\right)})<0$ (“parallel torques” attract whereas “antiparallel torques” repel each other). The vector of transverse torque determines the two-component “elastic charge” (dyad), which is illustrated by the $1∕r^2$ and $1∕r^3$ terms in the elastic energy (the elastic analogs of the monopole-dipole and dipole-dipole interactions). The general status of the pairwise approach to nematic emulsions is considered in terms of the elastic charge density.

We consider a long, semiflexible polymer with persistence length $P$ and contour length $L$ fluctuating in a narrow cylindrical channel of diameter $D$. In the regime $D⪡P⪡L$ the free energy of confinement $\Delta F$ and the length of the channel $R_{\Vert }$ occupied by the polymer are given by Odijk’s relations $\Delta F∕R_{\Vert }=A_{\circ }{k}_{B}T{P}^{-1∕3}{D}^{-2∕3}$ and $R_{\Vert }=L[1-{\alpha }_{\circ }{(D∕P)}^{2∕3}]$, where $A_{\circ }$ and ${\alpha }_{\circ }$ are dimensionless amplitudes. Using a simulation algorithm inspired by the pruned enriched Rosenbluth method, which yields results for very long polymers, we determine $A_{\circ }$ and ${\alpha }_{\circ }$ and the analogous amplitudes for a channel with a rectangular cross section. For a semiflexible polymer confined to the surface of a cylinder, the corresponding amplitudes are derived with an exact analytic approach. The results are relevant for interpreting experiments on biopolymers in microchannels or microfluidic devices.

We investigate DNA stretching during electrophoresis when the mobility abruptly changes. This is a simplified geometry that produces a nonhomogeneous strain rate over the scale of a single molecule. An effective Weissenberg number (Wi) and Deborah number were identified, and the degree of stretching was examined as a function of these two parameters. The system does not undergo a coil-stretch transition. The finite extensibility of the chains only affects the response if the chain is stretched to a significant fraction of the contour length. The wormlike chain shows a characteristic approach to full extension of ${\text{Wi}}^{-1∕2}$.

We investigate the orbital magnetization of DNA molecules in the relaxed circular structure. It is shown that DNA of homogeneous sequence exhibits paramagnetic responses to external magnetic fields and, surprisingly, the magnetism of circular DNA is equivalent to that of linear DNA. This turns out to result from the fact that the electron population is localized largely on one of the strands. More intriguingly, the magnetic susceptibility is observed to depend on the ring topology defined by the linking number. We also consider sequence heterogeneity and find that the magnetization displays characteristic oscillations, the pattern of which depends crucially on the sequence and the base content.

It is shown that many two degree of freedom (2D) nonlinear dynamical systems can be controlled by continuous phase-locking (double autoresonance) between the two canonical angle variables of the system and two independent external oscillating perturbations having slowly varying frequencies. Conditions for stability of the 2D autoresonance and classification of systems with doubly autoresonant solutions in the vicinity of a stable equilibrium are outlined in terms of the Hessian matrix elements of the unperturbed system. The doubly autoresonant states in a generic, driven 2D system can be accessed by starting in equilibrium and simultaneous passage through two linear resonances in the system, provided that the driving amplitudes exceed a threshold scaling as ${\alpha }^{3∕4}$, $\alpha$ being the characteristic chirp rate of the driving frequencies. The formation of nearly periodic trajectories in linearly nondegenerate, 2D driven systems with a single stable equilibrium is suggested as an application. Examples of autoresonant excitation and formation of nearly periodic states in other types of driven systems are presented, including a three-particle Toda chain, a particle in a 2D double-well potential, and a 3D oscillator.

We investigate numerically a traveling wave pattern observed in experimental magnetized Taylor-Couette flow at low magnetic Reynolds number. By accurately modeling viscous and magnetic boundaries in all directions, we reproduce the experimentally measured wave patterns and their amplitudes. Contrary to previous claims, the waves are shown to be transiently amplified disturbances launched by viscous boundary layers, rather than globally unstable magnetorotational modes.