The heat fluctuation probability distribution function in Brownian transducers operating between two heat reservoirs is studied. We find, both analytically and numerically, that the recently proposed fluctuation theorem for heat exchange [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)] has to be applied carefully when the coupling mechanism between both baths is considered. We also conjecture how to extend such a relation when an external work is present.

We experimentally study the synchronization and the emergence of leader-follower dynamics in two time-delayed mutually coupled fiber ring lasers. We utilize spatiotemporal representations of time series to establish the roles of leader and follower in the synchronized dynamics.

Slider-block models are often used to simulate earthquake dynamics. However, the models’ origins are more conceptual than analytical. This study uses Navier’s equations of an elastic bulk to derive a one-dimensional slider-block model, the Burridge-Knopoff model. This model exhibits a critical phase transition by varying the friction parameter. Accurate analytical estimates are made of event size limits for the small scale, large scale, and intermediate dynamic phases. The absence of large scale quasiperiodic delocalized events is noted for the parameter set investigated here. The time intervals between large scale events are approximately exponentially distributed for the system in its critical state, in agreement with the theory of nonequilibrium critical systems and earthquake dynamics.

Many of the results in the theory of dynamical systems rely on the assumption of hyperbolicity. One of the possible violations of this condition is the presence of unstable dimension variability (UDV), i.e., the existence in a chaotic attractor of sets of unstable periodic orbits, each with a different number of expanding directions. It has been shown that the presence of UDV poses severe limitations to the length of time for which a numerically generated orbit can be assumed to lie close to a true trajectory of such systems (the shadowing time). In this work we propose a method to detect the presence of UDV in real systems from time series measurements. Variations in the number of expanding directions are detected by determining the local topological dimension of the unstable space for points along a trajectory on the attractor. We show for a physical system of coupled electronic oscillators that with this method it is possible to decompose attractors into subsets with different unstable dimension and from this gain insight into the times a typical trajectory spends in each region.

The general periodic boundary condition for the lattice Boltzmann method has been modified to incorporate the pressure difference for fully developed periodic flows. The results demonstrated that, unlike other existing pressure boundary treatments, the proposed procedure/treatment does not generate nonphysical inlet and outlet flow disturbances while preserving the system periodicity. This method is readily applicable to a range of lattice Boltzmann simulations for systems with periodic electric potential and temperature fields.

The effect of asymmetry in the transbilayer lipid distribution on the dynamics of phase separation in fluid vesicles is investigated numerically. This asymmetry is shown to set a spontaneous curvature for the domains that alter the morphology and dynamics considerably. For moderate tension, the domains are capped and the spontaneous curvature leads to anomalously slow dynamics, as compared to the case of symmetric bilayers. In contrast, in the limiting cases of high and low tensions, the dynamics proceeds toward full phase separation.

Recent experiments on liquid water show collective dipole orientation fluctuations dramatically slower than expected (with relaxation time $>50\mathrm{ns}$) [D.P. Shelton, Phys. Rev. B 72, 020201(R) (2005)]. Molecular dynamics simulations of extended simple point charge (SPC/E) water show a large vortexlike structure of the dipole field at ambient conditions surviving over $300\mathrm{ps}$ [J. Higo et al., Proc. Natl. Acad. Sci. U.S.A. 98, 5961 (2001)]. Both results disagree with previous results on water dipoles in similar conditions, for which autocorrelation times are a few picoseconds. Motivated by these recent results, we study the water dipole reorientation using molecular dynamics simulations of the SPC/E model in bulk water for temperatures ranging from ambient $300\mathrm{K}$ down to the deep supercooled region of the phase diagram at $210\mathrm{K}$. First, we calculate the dipole autocorrelation function and find that our simulations are well described by a stretched exponential decay, from which we calculate the orientational autocorrelation time ${\tau }_a$. Second, we define a second characteristic time, namely, the time required for the randomization of molecular dipole orientation, the self-dipole randomization time ${\tau }_r$, which is an upper limit on ${\tau }_a$; we find that ${\tau }_r\approx 5{\tau }_a$. Third, to check if there are correlated domains of dipoles in water which have large relaxation times compared to the individual dipoles, we calculate the randomization time ${\tau }_{\mathrm{box}}$ of the site-dipole field, the net dipole moment formed by a set of molecules belonging to a box of edge $L_{\mathrm{box}}$. We find that the site-dipole randomization time ${\tau }_{\mathrm{box}}\approx 2.5{\tau }_a$ for $L_{\mathrm{box}}\approx 3\mathrm{\AA }$, i.e., it is shorter than the same quantity calculated for the self-dipole. Finally, we find that the orientational correlation length is short even at low $T$.

We perform mean-field density functional theory calculations on a lattice model to study the wetting of a solid substrate decorated with a ring pattern of nanoscale dimensions. We have found three different liquid morphologies on the substrate: a ring morphology where the liquid covers the pattern, a bulge morphology where a droplet is forming on one side of the ring, and a morphology where the liquid forms a cap spanning the nonwetting disk inside the pattern. We investigate the relative stability of these morphologies as a function of the ring size, wall-fluid interaction, and temperature. The results found are in very good agreement with experiments and calculations performed on similar systems at a micrometer length scale. The bulge morphology has also been observed in Monte Carlo simulations of the lattice model. Our results show that (i) morphologies of wetting patterns previously observed on a much larger $\left(\mu \mathrm{m}\right)$ scale can also form on a nm length scale, (ii) whether or not this happens depends crucially on the size of the wettable pattern, and (iii) the wettable ring may only be partially wet by the bulge morphology of the fluid. This morphology is a result of a spontaneously broken symmetry in the system.

We have studied tilted surface layers in the bulk SmA temperature window of one liquid crystal using null transmission ellipsometry. Five distinct nonplanar surface structures were observed. We present analyses of the tilt and azimuthal profiles of the structures and examine the transitions between the structures. The transitions are identified as a double reentrant synclinic-anticlinic-synclinic-anticlinic transition. Meanwhile, the transitions also display reentrant ferroelectric-antiferroelectric-ferroelectric behavior.

Dutcher films consist of a layer of liquid sandwiched between two solid capping layers and can spontaneously self-assemble to form corrugated surfaces. The interplay between the attractive van der Waals forces across the film, and the elastic forces due to the deformation of the capping layers, produces well-defined periodic undulations. We show how computer simulations can capture both the formation of undulations in Dutcher films and the correct periodicity. Furthermore, we simulate Dutcher films which are either compressed or stretched, resulting in the promotion or suppression of undulation growth. In this manner, applied deformations can be shown to guide the self-assembly process in Dutcher films and result in the formation of highly oriented surface corrugations over large distances.

In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF $({\rho }_{\mathrm{ls}}^{\mu }=0.97\pm 0.02)$ group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, $0.65\pm 0.13$; EH, $0.54\pm 0.05$; YH, $0.57\pm 0.05$; $p<0.05$ for both comparisons). Moreover, for the CHF patients we find no circadian changes in ${\rho }_{\mathrm{ls}}^{\mu }$ (day, $0.65\pm 0.13$; night, $0.66\pm 0.12$; n.s.) in contrast to healthy controls (day, $0.54\pm 0.05$; night, $0.61\pm 0.05$; $p=0.002$). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification.

We calculated the changes of the free energy profile of the peptidyl-prolyl torsional angle of the dipeptide valine-proline under pulling forces by simulations. Using a dynamic model built on the equilibrium properties of this system and previously studied dynamic properties of cis-trans isomerization of other dipeptides, we calculated the dynamic viscoelasticity of this degree of freedom. The results show significant differences between how thermal and mechanical forces alter the equilibrium and the dynamics of the isomerization transition. The former does not change the barrier heights but changes the prefactor of the kinetics owing to temperature effects, while the latter changes minima and thus the population. The force that is required to “excite” this degree of freedom is small. Compared to other systems, we found that this degree of freedom becomes already quite rigid at several hertz, which is a much lower value due to the high barrier of the cis-trans isomerization. We also found that the tensile elastic modulus of densely packed omega bonds is at the order of GPa, which is comparable to that of polymer materials. These results give mechanical properties of polyproline elasticity of a local nature and provide guidance for future experimental designs.

Biased diffusion of collagenase on collagen fibrils may represent the first observed adenosine triphosphate-independent extracellular molecular motor. The magnitude of force generated by the enzyme remains unclear. We propose a propulsion mechanism based on a burnt bridges Brownian ratchet model with a varying degree of coupling of the free energy from collagen proteolysis to the enzyme motion. When constrained by experimental observations, our model predicts $0.1\mathrm{pN}$ stall force for individual collagenase molecules. A dimer, surprisingly, can generate a force in the range of $5\mathrm{pN}$, suggesting that the motor can be of biological significance.

Success in measuring transverse sound velocity allowed us to determine, for the first time, all six elastic constants of a protein crystal. An ultrasonic pulse-echo method was used to perform sound velocity measurements on tetragonal hen egg-white (HEW) lysozyme crystals that were partially dehydrated at 42% relative humidity. The measurements were performed using the (110), (101), and (001) crystallographic faces. Thus, all six elastic constants of the dehydrated tetragonal HEW lysozyme crystals were determined: $C_{11}=C_{22}=12.44\mathrm{GPa}$, $C_{12}=7.03\mathrm{GPa}$, $C_{13}=C_{23}=8.36\mathrm{GPa}$, $C_{33}=12.79\mathrm{GPa}$, $C_{44}=C_{55}=2.97\mathrm{GPa}$, and $C_{66}=2.63\mathrm{GPa}$. In addition, for the hydrated crystals, the longitudinal sound velocities along the [110] direction and the direction normal to the (101) face were measured. From these results, all the components of elastic constants in the hydrated crystals were extrapolated.

Synaptic plasticity must be both competitive and stable if ongoing learning of the structure of neural inputs is to occur. In this paper, a wide class of spike-timing-dependent plasticity (STDP) models is identified that have both of these desirable properties in the case in which the input consists of subgroups of synapses that are correlated within the subgroup through the occurrence of simultaneous input spikes. The process of synaptic structure formation is studied, illustrating one particular class of these models. When the learning rate is small, multiple alternative synaptic structures are possible given the same inputs, with the outcome depending on the initial weight configuration. For large learning rates, the synaptic structure does not stabilize, resulting in neurons without consistent response properties. For learning rates in between, a unique and stable synaptic structure typically forms. When this synaptic structure exhibits a bimodal distribution, the neuron will respond selectively to one or more of the subgroups. The robustness with which this selectivity develops during learning is largely determined by the ratio of the subgroup correlation strength to the number of subgroups. The fraction of potentiated subgroups is primarily determined by the balance between potentiation and depression.

Self-similar properties of the ribosome in terms of the mass fractal dimension are investigated. We find that both the 30S subunit and the 16S rRNA have fractal dimensions of 2.58 and 2.82, respectively; while the 50S subunit as well as the 23S rRNA has the mass fractal dimension close to 3, implying a compact three-dimensional macromolecule. This finding supports the dynamic and active role of the 30S subunit in the protein synthesis, in contrast to the pass role of the 50S subunit.

We establish a conceptual relation between the fluctuations of the local density of states (LDOS) and the intensity correlations in speckle patterns resulting from the multiple scattering of waves in random media. We show that among the known types of speckle correlations ($C_1$, $C_2$, $C_3$, and $C_0$) only $C_0$ contributes to LDOS fluctuations in the infinite medium. We propose to exploit the equivalence of LDOS fluctuations and the $C_0$ intensity correlation as a “selection rule” for scattering processes contributing to $C_0$.

Records of the traded value $f_i$ of stocks display fluctuation scaling, a proportionality between the standard deviation ${\sigma }_i$ and the average $⟨f_i⟩$: ${\sigma }_i\propto {⟨f_i⟩}^{\alpha }$, with a strong time scale dependence $\alpha \left(\Delta t\right)$. The nontrivial (i.e., neither 0.5 nor 1) value of $\alpha$ may have different origins and provides information about the microscopic dynamics. We present a set of stylized facts and then show their connection to such behavior. The functional form $\alpha \left(\Delta t\right)$ originates from two aspects of the dynamics: Stocks of larger companies both tend to be traded in larger packages and also display stronger correlations of traded value. The results are integrated into a general framework that can be applied to a wide range of complex systems.

We describe two distinct approaches to obtaining the cloud-point densities and coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation within the grand-canonical ensemble. The first method determines the chemical potential distribution $\mu \left(\sigma \right)$ (with $\sigma$ the polydisperse attribute) under the constraint that the ensemble average of the particle density distribution $\rho \left(\sigma \right)$ match a prescribed parent form. Within the region of phase coexistence (delineated by the cloud curve) this leads to a distribution of the fluctuating overall particle density $n$, $p\left(n\right)$, that necessarily has unequal peak weights in order to satisfy a generalized lever rule. A theoretical analysis shows that as a consequence, finite-size corrections to estimates of coexistence properties are power laws in the system size. The second method assigns $\mu \left(\sigma \right)$ such that an equal-peak-weight criterion is satisfied for $p\left(n\right)$ for all points within the coexistence region. However, since equal volumes of the coexisting phases cannot satisfy the lever rule for the prescribed parent, their relative contributions must be weighted appropriately when determining $\mu \left(\sigma \right)$. We show how to ascertain the requisite weight factor operationally. A theoretical analysis of the second method suggests that it leads to finite-size corrections to estimates of coexistence properties which are exponentially small in the system size. The scaling predictions for both methods are tested via Monte Carlo simulations of a polydisperse lattice-gas model near its cloud curve, the results showing excellent quantitative agreement with the theory.

Motivated by the diversity and complexity of two-dimensional (2D) crystals formed by triangular proteins and protein trimers, we have investigated the structures and phase behavior of hard-disk trimers. In order to mimic specific binding interactions, each trimer possesses an “attractive” disk which can interact with similar disks on other trimers via an attractive square-well potential. At low density and low temperature, the fluid phase mainly consists of tetramers, pentamers, or hexamers. Hexamers provide the structural motif for a high-density, low-temperature periodic solid phase, but we also identify a metastable periodic structure based on a tetramer motif. At high density there is a transition between orientationally ordered and disordered solid phases. The connections between simulated structures and those of 2D protein crystals—as seen in electron microscopy—are briefly discussed.