We show that any convex $K$-dimensional system has a level of order $R$ that is proportional to its level of Fisher information $I$. The proportionality constant is $1/8$ the square of the longest chord connecting two surface points of the system. This result follows solely from the requirement that $R$ decrease under small perturbations caused by a coarse graining of the system. The form for $R$ is generally unitless, allowing the order for different phenomena, or different representations (e.g., using time vs frequency) of a given phenomenom, to be compared objectively. Order $R$ is also invariant to uniform magnification of the system. The monotonic contraction properties of $R$ and $I$ define an arrow of time and imply that they are entropies, in addition to their usual status as informations. This also removes the need for data, and therefore an observer, in derivations of nonparticipatory phenomena that utilize $I$. Simple graphical examples of the new order measure show that it measures as well the level of “complexity” in the system. Finally, an application to cell growth during enforced distortion shows that a single hydrocarbon chain can be distorted into a membrane having equal order or complexity. Such membranes are prime constituents of living cells.

In this paper, we discuss how effective environments incorporating periodic measurements can be used to prepare a two-level system (TLS) in almost arbitrary thermal states: Concretely, we study a TLS coupled to a spin environment, the magnetization of which is measured periodically. In ensemble average these measurements cause a relaxation of the TLS into a thermal (diagonal) state. By adjusting the time between the measurements and the detuning of the environmental spins, the creation of very low temperatures as well as inversion becomes possible. Our analytical results derived for large environments are numerically shown to be valid even for quite small environments, down to only a few spins.

A simplified model of a hydrogen-bonding network is proposed in order to clarify the microscopic structure of the cooperative rearranging region (CRR) in Adam-Gibbs theory [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. Our model can be solved analytically, and it successfully explains the reported systematic features of the glass transition of polyhydric alcohols. In this model, hydrogen bonding is formulated based on binding free energy. Assuming a cluster of molecules connected by double hydrogen bonds is a CRR and approximating the hydrogen-bonding network as a Bethe lattice in percolation theory, the temperature dependence of the structural relaxation time can be obtained analytically. Reported data on relaxation times are well described by the obtained equation. By taking the lower limit of the binding free energy with this equation, the Vogel-Fulcher-Tammann equation can be derived. Consequently, the fragility index and glass transition temperature can be expressed as functions of the number of OH groups in a molecule, and this relation agrees well with the reported experimental data.

Using the numerical solution of the time-dependent Ginzburg-Landau equation, we study the entire process of transformation between the lamellar and the hexagonal phases from the early-stage nucleation and growth to the late-stage coarsening regime. The metastable crystalline structure that nucleates first is identified in terms of the mean-field theory under the single-wave-number approximation. This has been borne out by the numerically efficient preparation of single-crystal structure developed via the noise-induced self-organization. We also present results for the scaling of the late-time domain growth, which is quantified by two measures: the structure factor and the orientational correlation function. In particular, the growth exponent is shown to be robust and indifferent to conservation of the order parameter.

Polymer structure modeling is a trend of recent material sciences. Developments of computational science and nanotechnology make it possible to predict properties of complicated molecular structures. Many theoretical and computational methods have succeeded in elucidating the nature of polymer structures. It is not always best to model whole complicated structures depending on computer capabilities. Significant properties of materials may be manifested in simple structural aspects. In the present study, characteristics of a polymer structure are investigated by applying Burnside’s lemma to the modeling procedure. This method is expected to be available to model polymers or molecular crystals in which functional groups play an important role in expressing their functions. Every structure under the symmetry and periodicity is counted completely and the energy distribution caused by the conformations of functional groups can be clarified. The detailed procedure is introduced and the present method is applied to a problem for investigating molecular structures of sulfonated poly(ether ether ketone) (SPEEK). SPEEK is focused on a candidate for proton exchange membranes in polymer electrolyte fuel cells. Sulfonic groups have a significant role in proton exchange membranes to make proton conduction channels. From our analysis, it is found that sulfonic groups tend to be dispersed in SPEEK membranes at their stable conditions. These are unfavorable characteristics for proton exchange membranes due to their difficulty to form desirable water channels inevitable for the high proton conductivity. This is one reason why SPEEK membranes are inferior to Nafion® membranes that express the highest performance as proton exchange membranes. Using the present method, experimental and theoretical results previously reported are confirmed and detailed characteristics are discussed in terms of structural simplicities.

We study experimentally chaos synchronization of nonlinear optoelectronic oscillators with time-delayed mutual coupling and self-feedback. Coupling three oscillators in a chain, we find that the outer two oscillators always synchronize. In contrast, isochronal synchronization of the mediating middle oscillator is found only when self-feedback is added to the middle oscillator. We show how the stability of the isochronal solution of any network, including the case of three coupled oscillators, can be determined by measuring the synchronization threshold of two unidirectionally coupled systems. In addition, we provide a sufficient condition that guarantees global asymptotic stability of the synchronized solution.

We develop generalized time-delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive Floquet exponents, which are particularly well suited for experimental realization. We construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods. In particular, it is shown how periodic orbits can be stabilized with symmetric feedback matrices by introducing an additional latency time in the control loop. Finally, we show using normal form analysis and numerical simulations how our results could be implemented in a laser setup using optoelectronic feedback.

We investigate the interaction of a particle with a finite-size bath represented by a set of independent linear oscillators with frequencies that fall within a finite bandwidth. We discover that when the oscillators have particular frequency distributions, the finite-size bath behaves much as an infinite-size bath exhibiting dissipation properties and thus allowing irreversible energy absorption from a particle immersed in it. We also present a reinterpretation of the Langevin equation using a perturbation approach in which the small parameter represents the inverse of the number of oscillators in the bath, elucidating the relationship between finite-size and infinite-size bath responses.

The phenomenon of Coulombic friction enters the stochastic description of dry friction between two solids and the statistic characterization of vibrating granular media. Here we analyze the corresponding Fokker-Planck equation including both velocity and spatial components, exhibiting a formal connection to a quantum mechanical harmonic oscillator in the presence of a delta potential. Numerical solutions for the resulting spatial displacement statistics show a crossover from exponential to Gaussian displacement statistics. We identify a transient intermediate regime that exhibits multiscaling properties arising from the contribution of Coulombic friction. The possible role of these effects during observations in diffusion experiments is briefly discussed.

We study the dynamics of defect annihilation in flexible crystalline membranes suffering a symmetry-breaking phase transition. The kinetic process leading the system toward equilibrium is described through a Brazovskii-Helfrich-Canham Hamiltonian. In membranes, a negative disclination has a larger energy than a positive disclination. Here we show that this energetic asymmetry does not only affect equilibrium properties, like the Kosterlitz-Thouless transition temperature, but also plays a fundamental role in the dynamic of defects. Both unbinding of dislocations and Carraro-Nelson “antiferromagnetic” interactions between disclinations slow down the dynamics below the Lifshitz-Safran regime observed in flat hexagonal systems.

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the $P$-$V$ diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

We study a contact process with creation at first- and second-neighbor sites and inhibition at first neighbors, in the form of an annihilation rate that increases with the number of occupied first neighbors. Mean-field theory predicts three phases: inactive (absorbing), active symmetric, and active asymmetric, the latter exhibiting distinct sublattice densities on a bipartite lattice. These phases are separated by continuous transitions; the phase diagram is re-entrant. Monte Carlo simulations in two dimensions verify these predictions qualitatively, except for a first-neighbor creation rate of zero. (In the latter case one of the phase transitions is discontinuous.) Our numerical results confirm that the symmetric-asymmetric transition belongs to the Ising universality class, and that the active-absorbing transition belongs to the directed percolation class, as expected from symmetry considerations.

A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally perturbed during a finite time, and then isolated for a sufficiently long time. We show a quantitative explanation that the initial microcanonical state typically reaches a state whose expectation values are well approximated by the average over another microcanonical ensemble.

We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends toward the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.

We examine the jamming transition in a two-dimensional granular polymer system using compressional simulations. The jamming density ${\varphi }_c$ decreases with increasing length of the granular chain due to the formation of loop structures, in excellent agreement with recent experiments. The jamming density can be further reduced in mixtures of granular chains and granular rings, also as observed in experiment. We show that the nature of the jamming in granular polymer systems has pronounced differences from the jamming behavior observed for polydisperse two-dimensional disk systems at point $J$. This result provides further evidence that there is more than one type of jamming transition.

In this paper, the chaotic internal degrees of freedom of a benzene molecule adsorbed on a graphite substrate, their interplay with thermal noise, and their effects on the diffusion and drift are investigated analytically by making use of the presence of two different time scales as well as by molecular-dynamics simulations. The effects of thermal noise are investigated, and it is found that noise does not significantly alter the dynamics of the internal degrees of freedom yet does affect the friction and diffusion of the center of mass. Qualitative and quantitative theoretical predictions for the friction and diffusion of the molecule on the substrate are made and are compared to molecular-dynamics simulations. Contributions to the friction and diffusion from the finite heat bath as well as the slow dynamics of the center of mass are formally identified. It is shown that the torsion in benzene, which dominates the nonlinear coupling, significantly affects the friction of the molecule on the surface. The results compare favorably with recent results from He-neutron spin echo experiments on this system. Based on the analytical and numerical results, some suggestions are made for experimental conditions under which the effects of internal degrees of freedom might be observable.

Receptor-ligand interactions that mediate cellular adhesion are often subjected to forces that regulate their detachment via modulating off-rates. Although the dynamics of detachment is primarily controlled by the physical chemistry of adhesion molecules, cellular features such as cell deformability and microvillus viscoelasticity have been shown to affect the rolling velocity of leukocytes in vitro through experiments and simulation. In this work, we demonstrate via various micromechanical models of two cells adhered by a single (intramolecular) bond that cell deformability and microvillus viscoelasticity modulate transmission of an applied external load to an intramolecular bond, and thus the dynamics of detachment. Specifically, it is demonstrated that the intermolecular bond force is not equivalent to the instantaneous applied force and that the instantaneous bond force decreases with cellular and microvillus compliance. As cellular compliance increases, not only does the time lag between the applied load and the bond force increase, an initial response time is observed during which cell deformation is observed without transfer of force to the bond. It is further demonstrated that following tether formation the instantaneous intramoleular bond force increases linearly at a rate dependent on microvillus viscosity. Monte Carlo simulations with fixed kinetic parameters predict that both cell and microvillus compliance increase the average rupture time, although the average rupture force based on bond length remains nearly unchanged.

In this paper, we investigate the oscillatory dynamics of the tank-treading motion of healthy human erythrocytes in shear flows with capillary number $\text{Ca}=O(1)$ and small to moderate viscosity ratios $0.01⩽⩽1.5$. These conditions correspond to a wide range of surrounding medium viscosities (4–600 m Pa s) and shear flow rates (2–$560\hspace{0.5em}{\text{s}}^{-1}$), and match those used in ektacytometry systems. For a given viscosity ratio, as the flow rate increases, the steady-state erythrocyte length $L$ (in the shear plane) increases logarithmically while its depth $W$ (normal to the shear plane) decreases logarithmically. In addition, the flow rate increase dampens the oscillatory erythrocyte inclination but not its length oscillations (which show relative variations of about $5$–$8\%$). For a given flow rate, as the viscosity ratio increases, the erythrocyte length $L$ contracts while its depth $W$ increases (i.e., the cell becomes less deformed) with a small decrease in the length variations. The average orientation angle of the erythrocyte shows a significant decrease with the viscosity ratio as does the angle oscillation while the oscillation period increases. These trends continue in higher viscosity ratios resulting eventually in the transition from a (weakly oscillatory) tank-treading motion to a tumbling motion. Our computations show that the erythrocyte width $S$, which exists in the shear plane, is practically invariant in time, capillary number, and viscosity ratio, and corresponds to a real cell thickness of about $2.5\hspace{0.5em}\mu \text{m}$. Comparison of our computational results with the predictions of (low degree-of-freedom) theoretical models and experimental findings, suggests that the energy dissipation due to the shape-memory effects is more significant than the energy dissipation due to the membrane viscosity. Our work shows that the oscillatory tank-treading motion can account for more than 50% of the variations found in ektacytometry systems; thus, researchers who wish to study inherent differences between erythrocytes within a population must devise a way of monitoring individual cells over time so that they can remove the oscillation effects.

We model analytically the dynamics of a cytoskeletal filament in a motility assay. The filament is described as rigid rod free to slide in two dimensions. The motor proteins consist of polymeric tails tethered to the plane and modeled as linear springs and motor heads that bind to the filament. As in related models of rigid and soft two-state motors, the binding and unbinding dynamics of the motor heads and the dependence of the transition rates on the load exerted by the motor tails play a crucial role in controlling the filament’s dynamics. Our work shows that the filament effectively behaves as a self-propelled rod at long times, but with non-Markovian noise sources arising from the coupling to the motor binding and unbinding dynamics. The effective propulsion force of the filament and the active renormalization of the various friction and diffusion constants are calculated in terms of microscopic motor and filament parameters. These quantities could be probed by optical force microscopy.

Natural materials such as nacre exhibit a high resistance to crack propagation, inspiring the development of artificial composites imitating the structure of these biological composites. We use a phase field approach to study the role played by the elastic modulus mismatch between stiff and soft layers on crack propagation in such bioinspired composites. Our simulations show that the introduction of a thin layer of a soft phase in a stiff matrix can lead to arrest of a propagating crack and can also lead to crack branching. The crack branching observed in the phase field model is analyzed using a cohesive zone approach. Further, we show that the toughness of such a composite can be substantially higher than that of its constituents.