We consider the fluctuations of a time-integrated particle current around an atypical value in a generic stochastic Markov process involving classical particles with two-site interaction and hard-core repulsion on a finite one-dimensional lattice with open boundaries. We address the question of which interactions one has to impose on such a process to make the atypical value of the current typical. It is known that a corresponding effective stochastic Markov process might exist whose typical current value is equal to the atypical current value in the original process within a time-translational invariant regime. This effective process has, in principle, nonlocal transition rates. Nevertheless, it turns out that under some conditions, the stochastic generator of the effective process has the same dynamical rules as the stochastic generator of the original process. We find these conditions and show that our approach can be generalized to any time-integrated observable.

Brownian dynamics simulation has been employed to study the dynamic behavior of particles in three-dimensional ordered porous media subject to a sinusoidal force field. The media comprises interconnected spherical cavities arranged in a simple cubic lattice. The thermal noise assists the particles to undergo cavity hopping, leading to a displacement behavior analogous to stochastic resonance, when the imposed field is strong enough but not aligned with the aperture lines, and the oscillation frequency is not too high. The periodic mean trajectory depends on the strength, frequency, and orientation of the imposed field. At sufficiently large field strength, the periodic particle displacement can become nonsinusoidal due to the strong hindrance and pinning effect of the cavity wall.

Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of a particle in bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes flat at low frequencies. This detailed understanding of boundary effects on Brownian motion opens a door to developing a 3D microscope using particles as remote sensors.

We investigate the geometrical structure of breaking bursts generated during the creep rupture of heterogeneous materials. Using a fiber bundle model with localized load sharing we show that bursts are compact geometrical objects; however, their external frontiers have a fractal structure which reflects their growth dynamics. The perimeter fractal dimension of bursts proved to have the universal value 1.25 independent of the external load and of the amount of disorder in the system. We conjecture that according to their geometrical features, breaking bursts fall in the universality class of loop-erased self-avoiding random walks with perimeter fractal dimension 5/4 similar to the avalanches of Abelian sand pile models. The fractal dimension of the growing crack front along which bursts occur proved to increase from 1 to 1.25 as bursts gradually cover the entire front.

The nature of the nematic-nematic phase transition in the liquid crystal dimer 1″,9″-bis(4-cyanobiphenyl-4′-yl) nonane (CB9CB) has been investigated using techniques of calorimetry, dynamic dielectric response measurements, and ${}^2\mathrm{H}$ NMR spectroscopy. The experimental results for CB9CB show that, like the shorter homologue CB7CB, the studied material exhibits a normal nematic phase, which on cooling undergoes a transition to the twist-bend nematic phase ($N_{\mathrm{TB}}$), a uniaxial nematic phase, promoted by the average bent molecular shape, in which the director tilts and precesses describing a conical helix. Modulated differential scanning calorimetry has been used to analyze the nature of the $N_{\mathrm{TB}}\text{−}N$ phase transition, which is found to be weakly first order, but close to tricritical. Additionally broadband dielectric spectroscopy and ${}^2\mathrm{H}$ magnetic resonance studies have revealed information on the structural characteristics of the recently discovered twist-bend nematic phase. Analysis of the dynamic dielectric response in both nematic phases has provided an estimate of the conical angle of the heliconical structure for the $N_{\mathrm{TB}}$ phase. Capacitance measurements of the electric-field realignment of the director in initially planar aligned cells have yielded values for the splay and bend elastic constants in the high temperature nematic phase. The bend elastic constant is small and decreases with decreasing temperature as the twist-bend phase is approached. This behavior is expected theoretically and has been observed in materials that form the twist-bend nematic phase. ${}^2\mathrm{H}$ NMR measurements characterize the chiral helical twist identified in the twist-bend nematic phase and also allow the determination of the temperature dependence of the conical angle and the orientational order parameter with respect to the director.

The extension of DNA confined to nanochannels has been studied intensively and in detail. However, quantitative comparisons between experiments and model calculations are difficult because most theoretical predictions involve undetermined prefactors, and because the model parameters (contour length, Kuhn length, effective width) are difficult to compute reliably, leading to substantial uncertainties. Here we use a recent asymptotically exact theory for the DNA extension in the “extended de Gennes regime” that allows us to compare experimental results with theory. For this purpose, we performed experiments measuring the mean DNA extension and its standard deviation while varying the channel geometry, dye intercalation ratio, and ionic strength of the buffer. The experimental results agree very well with theory at high ionic strengths, indicating that the model parameters are reliable. At low ionic strengths, the agreement is less good. We discuss possible reasons. In principle, our approach allows us to measure the Kuhn length and the effective width of a single DNA molecule and more generally of semiflexible polymers in solution.

We present an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 min) large price fluctuations are connected to the failure of the subtle mechanism of compensation between the flows of market and limit orders: in other words, the missed revelation of the latent order book breaks the dynamical equilibrium between the flows, triggering the large price jumps. On smaller time scales (30 s), instead, the static depletion of the limit order book is an indicator of an intrinsic fragility of the system, which is related to a strongly nonlinear enhancement of the response. In order to quantify this phenomenon we introduce a measure of the liquidity imbalance present in the book and we show that it is correlated to both the sign and the magnitude of the next price movement. These findings provide a quantitative definition of the effective liquidity, which proves to be strongly dependent on the considered time scales.

We show that accounting for internal character among interacting heterogeneous entities generates rich transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different critical points arising for different character-dependent grouping mechanisms. These critical points move in opposite directions as the population's diversity decreases. Our analytical theory may help explain why a particular class of universality is so common in the real world, despite the fundamental differences in the underlying entities. It also correctly predicts the nonmonotonic temporal variation in connectivity observed recently in one such system.

The fragilities of over 150 different network-forming glass melts are shown to conform to a common dependence on just one parameter: the connectivity of the weakest network structure present in the associated glass solid. This includes both nonoxide network-forming chalcogenide melts as well as a variety of alkali oxide glasses, and spans a broad range of connectivity, ϕ, from polymeric structures $(\varphi =2)$ to overconstrained random networks with connectivities well in excess of the rigidity threshold $({\varphi }_C=2.4)$. A theoretical framework for the origin of this universal pattern is offered within the context of entropic models of the glass transition.

Modularity is a key organizing principle in real-world large-scale complex networks. The relatively sparse interactions between modules are critical to the functionality of the system and are often the first to fail. We model such failures as site percolation targeting interconnected nodes, those connecting between modules. We find, using percolation theory and simulations, that they lead to a “tipping point” between two distinct regimes. In one regime, removal of interconnected nodes fragments the modules internally and causes the system to collapse. In contrast, in the other regime, while only attacking a small fraction of nodes, the modules remain but become disconnected, breaking the entire system. We show that networks with broader degree distribution might be highly vulnerable to such attacks since only few nodes are needed to interconnect the modules, consequently putting the entire system at high risk. Our model has the potential to shed light on many real-world phenomena, and we briefly consider its implications on recent advances in the understanding of several neurocognitive processes and diseases.

Identifying nonlinear structures in a time series, acquired from real-world systems, is essential to characterize the dynamics of the system under study. A single time series alone might be available in most experimental situations. In addition to this, conventional techniques such as power spectral analysis might not be sufficient to characterize a time series if it is acquired from a complex system such as a thermoacoustic system. In this study, we analyze the unsteady pressure signal acquired from a turbulent combustor with bluff-body and swirler as flame holding devices. The fractal features in the unsteady pressure signal are identified using the singularity spectrum. Further, we employ surrogate methods, with translational error and permutation entropy as discriminating statistics, to test for determinism visible in the observed time series. In addition to this, permutation spectrum test could prove to be a robust technique to characterize the dynamical nature of the pressure time series acquired from experiments. Further, measures such as correlation dimension and correlation entropy are adopted to qualitatively detect noise contamination in the pressure measurements acquired during the state of combustion noise. These ensemble of measures is necessary to identify the features of a time series acquired from a system as complex as a turbulent combustor. Using these measures, we show that the pressure fluctuations during combustion noise has the features of a high-dimensional chaotic data contaminated with white and colored noise.

We investigate the transport properties of a particle subjected to a deterministic inertial rocking system, under a constant bias, for which the phase of the symmetric spatial potential used is time modulated. We show that this modulated phase, assisted by a periodic driving force, can lead to the occurrence of the so-called absolute negative mobility (ANM), the phenomenon in which the particle surprisingly moves against the bias. Furthermore, we discover that ANM predominantly originates from chaotic-periodic transitions. While a detailed mechanism of ANM remains unclear, we show that one can manipulate the control parameters, i.e., the amplitude and the frequency of the phase, in order to enforce the motion of the particle in a given direction. Finally, for this experimentally realizable system, we devise a two-parameter current plot which may be a good guide for controlling ANM.

Liquid flow dynamics through the armchair $(6,6)–(160,160)$ carbon nanotubes (CNTs) is elucidated by molecular dynamics simulations. The liquid is modeled by nonpolar argon atoms to understand the fundamental flow physics. The velocity profiles and slip lengths are discussed considering the radial distributions of the fluid density by the presently proposed finite difference-based velocity fitting method. It is found that as the CNT diameter $D$ increases, the slip length and the flow rate enhancement show three-step transitional profiles in the region of $D\le 2.3$ nm. The slip length and the flow rate stepwise increase at the first transition while they drop at the second and third transitions. The first transition corresponds to the structural change from the single-file chain to single-ring structures of the molecule cluster. The second and third transitions take place when the ring structure starts to develop another inner layer.

We study aqueous, freestanding, thin films stabilized by a surfactant with respect to mixing and dynamical systems properties. With this special setup, a two-dimensional fluid can be realized experimentally. The physics of the system involves a complex interplay of thermal convection and interface and gravitational forces. Methodologically, we characterize the system using two classical dynamical systems properties: Lyapunov exponents and entropies. Our experimental setup produces convection with two stable eddies by applying a temperature gradient in one spot that yields weakly turbulent mixing. From dynamical systems theory, one expects a relation of entropies, Lyapunov exponents, a prediction with little experimental support. We can confirm the corresponding statements experimentally, on different scales using different methods. On the small scale the motion and deformation of fluid filaments of equal size (color imaging velocimetry) are used to compute Lyapunov exponents. On the large scale, entropy is computed by tracking the left-right motion of the center fluid jet at the separatrix between the two convection rolls. We thus combine here dynamical systems methods with a concrete application of mixing in a nanoscale freestanding thin film.

Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equations as in density-functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large nonmetallic materials and metals at high temperatures.

A small quantum absorption refrigerator, consisting of three qubits, is discussed in the transient regime. We discuss time scales for coherent dynamics, damping, and approach to the steady state, and we study cooling and entanglement. We observe that cooling can be enhanced in the transient regime, in the sense that lower temperatures can be achieved compared to the steady-state regime. This is a consequence of coherent dynamics but can occur even when this dynamics is strongly damped by the dissipative thermal environment, and we note that precise control over couplings or timing is not needed to achieve enhanced cooling. We also show that the amount of entanglement present in the refrigerator can be much larger in the transient regime compared to the steady state. These results are of relevance to future implementations of quantum thermal machines.

The absorbing phase transition of the modified conserved lattice gas (m-CLG) model was investigated in one dimension. The m-CLG model was modified from the conserved lattice gas (CLG) model in such a way that each active particle hops to one of the nearest-neighbor and next-nearest-neighbor empty sites. The order parameter exponent, the dynamic exponent, and the correlation length exponent were estimated from the power-law behavior and finite-size scaling of the active particle densities. The exponents were found to differ considerably from those of the ordinary CLG model and were also distinct from those of the Manna model, suggesting that next-nearest-neighbor hopping is a relevant factor that alters the critical behavior in the one-dimensional CLG model.

The modeling of bubbles initiated by laser-irradiated nanoparticles is of interest for many applications. There is at present no comprehensive physical picture for all the stages of the process. We present an alternative approach with a key assumption: the vapor bubble evolves adjacent to the nanoparticle. To take into account the irreversible evolution, the statistical rate theory was used, thus avoiding the introduction of extra ad hoc parameters. Model results agree well with published data and our measurements. The only free parameter, the thermal boundary conductance, can be obtained by adjusting the model to the experimental data.

When the surface of a nominally flat binary material is bombarded with a broad, normally incident ion beam, disordered hexagonal arrays of nanodots can form. Shipman and Bradley have derived equations of motion that govern the coupled dynamics of the height and composition of such a surface [Shipman and Bradley, Phys. Rev. B 84, 085420 (2011)]. We investigate the influence of initial conditions on the hexagonal order yielded by integration of those equations of motion. The initial conditions studied are hexagonal and sinusoidal templates, straight scratches, and nominally flat surfaces. Our simulations indicate that both kinds of templates lead to marked improvements in the hexagonal order if the initial wavelength is approximately equal to or double the linearly selected wavelength. Scratches enhance the hexagonal order in their vicinity if their width is close to or less than the linearly selected wavelength. Our results suggest that prepatterning a binary material can dramatically increase the hexagonal order achieved at large ion fluences.

Resonance properties of a stack consisting of a cholesteric liquid crystal and isotropic medium layers are investigated. Bragg's conditions for photonic band gaps are presented for the considered system. It is shown that a significant control of the system zone structure is possible in the case of a proper selection of the sublayer parameters. It is also shown that an effect of complete suppression of absorption is not usually observed in the case of anisotropic absorption in cholesteric liquid crystal sublayers. The possibility to achieve this effect in the considered system, imposing certain conditions on the thickness and the refraction index of the isotropic medium sublayers, is shown. Also, it is shown that in such conditions a large increase of the maximum of photonic density of states happens at the appropriate zone borders.