By conditioning a stochastic process on the value of an observable, one obtains a new stochastic process with different properties. We apply this idea in the context of active matter and condition interacting self-propelled particles on their individual motility. Using the effective process formalism from dynamical large deviations theory, we derive the interactions that actuate the imposed mobility against jamming interactions in two toy models—the totally asymmetric exclusion process and run-and-tumble particles, in the case of two or three particles. We provide a framework which takes into account the energy-consumption required for self-propulsion and address the question of how energy-efficient the emergent interactions are. Upon conditioning, run-and-tumble particles develop an alignment interaction and achieve a higher gain in efficiency than TASEP particles. A point of diminishing returns in efficiency is reached beyond a certain level of conditioning. With recourse to a general formula for the change in energy efficiency upon conditioning, we conclude that the most significant gains occur when there are large fluctuations in mobility to exploit. From a detailed comparison of the emergent effective interaction in a two- versus a three-body scenario, we discover evidence of a screening effect which suggests that conditioning can produce topological rather than metric interactions.

Gene regulation in a cellular environment is a stochastic phenomenon leading to a large variability in mRNAs and protein numbers that are often produced in bursts. The regulation leading to varied protein dynamics can be ascribed to transcriptional or post-transcriptional mechanisms. In transcriptional regulation, the gene dynamically switches between an active and an inactive state, while in the post-transcriptional regulation small RNAs tune the activity of mRNAs. In either scenario, it is possible to calculate the time-dependent probability distribution of proteins and address the interesting question pertaining to their first passage time statistics. The coefficient of variation of first passage time can be considered to be an indicator of efficiency in controlling regulatory pathways and we show that post-transcriptional regulation performs better than simple transcriptional regulation for comparable protein yields.

We study the clustering of a model cyanobacterium Synechocystis into microcolonies. The bacteria are allowed to diffuse onto surfaces of different hardness and interact with the others by aggregation and detachment. We find that soft surfaces give rise to more microcolonies than hard ones. This effect is related to the amount of heterogeneity of bacteria's dynamics as given by the proportion of motile cells. A kinetic model that emphasizes specific interactions between cells, complemented by extensive numerical simulations considering various amounts of motility, describes the experimental results adequately. The high proportion of motile cells enhances dispersion rather than aggregation.

Positron annihilation lifetime spectroscopy has been used to study 4-hexyl-4′-isothiocyanatobiphenyl. Changes of the orthopositronium lifetime parameters with temperature have been observed for the supercooled smectic-$E$ phase. The measurements confirm that positronium is created and annihilates in a layer of a lower electron density containing alkyl chains of molecules. The two-state bond-lattice model of glass transition explains the thermal activation of the centers where orthopositronium is created and annihilates when the glass of the smectic-$E$ phase softens. However, the subsequent cold crystallization of the softened regions also influences the orthopositronium lifetime and intensity, which complicates the picture seen by positrons. The measurements during isothermal crystallization suggest that it progresses in two stages. The first stage can be described by the Avrami equation with the Avrami exponent close to unity, which indicates low-dimensional crystallization. Similarly to liquid $n$ alkanes, the application of pressure is equivalent to temperature lowering with the similar equivalence relationship between pressure and temperature, which seems to confirm the structure of the smectic-$E$ phase with sublayers containing alkyl chains in a molten state. The dependence of the orthopositronium lifetime on pressure for the smectic-$E$ phase may be described by the bubble model where the positronium bubble is approximated with a finite square potential well with the depth of $U=1.45\mathrm{eV}$.

In this paper, the effect of two-frequency modulation of boundary temperatures on the onset of natural convection in a layer of fluid (with Prandtl number $<12.5$) between two vertical parallel planes is considered. The ratio of the two forcing frequencies and the mixing angle for the amplitude of modulation provide an efficient way of controlling the underlying instability. At the onset of instability, the fluid layer executes harmonic and subharmonic oscillations. The transition between harmonic and subharmonic responses is found to occur through an intermediate bicritical state. In addition to bicritical states, the instability is found to exhibit an almost tricritical state for a particular combination of the modulation parameters. The onset of the instability depends upon the modulation parameters and Prandtl number of the fluid.

We measured the effective diffusion coefficient in regions of microfluidic networks of controlled geometry using the fluorescence recovery after photobleaching (FRAP) technique. The geometry of the networks was based on Voronoi tessellations, and had varying characteristic length scale and porosity. For a fixed network, FRAP experiments were performed in regions of increasing size. Our results indicate that the boundary of the bleached region, and in particular the cumulative area of the channels that connect the bleached region to the rest of the network, are important in the measured value of the effective diffusion coefficient. We found that the statistical geometrical variations between different regions of the network decrease with the size of the bleached region as a power law, meaning that the statistical error of effective medium approximations decrease with the size of the studied medium with no characteristic length scale.

A theoretically highly efficient mechanism, operating at high laser intensities and powers, is identified for spectral transferring huge laser energies to shorter ultraviolet and x-ray wavelengths. With megajoule laser energies currently available at near-optical wavelengths, this transfer would, in theory, enable megajoule x-ray lasers, a huge advance over the millijoules x-ray pulses produced now. In fact, enabling even kilojoule x-ray lasers would still be a fantastic advance, and a more likely achievable one, considering practical experimental inefficiencies.

Droplet freezing not only is of fundamental interest but also plays an important role in numerous natural and industrial processes. However, it is challenging to numerically simulate the droplet freezing process due to its involving a complex three-phase system with dynamic phase change and heat transfer. Here we propose an axisymmetric lattice Boltzmann (LB) model to simulate the freezing process of a sessile water droplet with consideration of droplet volume expansion. Combined with the multiphase flow LB model and the enthalpy thermal LB model, our proposed approach is applied to simulate the sessile water droplet freezing on both hydrophilic and hydrophobic surfaces at a fixed subcooled temperature. Through comparison with the experimental counterpart, the comparison results show that our axisymmetric LB model can satisfactorily describe such sessile droplet freezing processes. Moreover, we use both LB simulations and analytical models to study the effects of contact angle and volume expansion on the freezing time and the cone shape formed on the top of frozen droplets. The analytical models are obtained based on heat transfer and geometric analyses. Additionally, we show analytically and numerically that the freezing front-to-interface angle keeps nearly constant (smaller than 90°).

We apply extensive Monte Carlo simulations to study the probability distribution $P\left(m\right)$ of the order parameter $m$ for the simple cubic Ising model with periodic boundary condition at the transition point. Sampling is performed with the Wolff cluster flipping algorithm, and histogram reweighting together with finite-size scaling analyses are then used to extract a precise functional form for the probability distribution of the magnetization, $P\left(m\right)$, in the thermodynamic limit. This form should serve as a benchmark for other models in the three-dimensional Ising universality class.

Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in the statistical properties of observables due to reversals can be represented by a change in the probability measure. We consider operators on the space of probability measures that induce changes in the statistical properties of a process, and we formulate entropy production in terms of these change-of-probability-measure (CPM) operators. This mathematical underpinning of the origin of entropy production allows us to achieve an organization of various forms of fluctuation relations: All entropy production has a nonnegative mean value, admit the integral fluctuation theorem, and satisfy a rather general fluctuation relation. Other results such as the transient fluctuation theorem and detailed fluctuation theorems then are derived from the general fluctuation relation with more constraints on the operator of entropy production. We use a discrete-time, discrete-state-space Markov process to draw the contradistinction among three reversals of a process: time reversal, protocol reversal, and the dual process. The properties of their corresponding CPM operators are examined, and the domains of validity of various fluctuation relations for entropy production in physics and chemistry are revealed. We also show that our CPM operator formalism can help us rather easily extend other fluctuation relations for excess work and heat, discuss the martingale properties of entropy production, and derive the stochastic integral formulas for entropy production in constant-noise diffusion process with Girsanov theorem. Our formalism provides a general and concise way to study the properties of entropy-related quantities in stochastic thermodynamics and information theory.

While phase reduction is a well-established technique for the analysis of perturbed limit cycle oscillators, practical application requires perturbations to be sufficiently weak thereby limiting its utility in many situations. Here, a general strategy is developed for constructing a set of phase-amplitude reduced equations that is valid to arbitrary orders of accuracy in the amplitude coordinates. This reduction framework can be used to investigate the behavior of oscillatory dynamical systems far beyond the weakly perturbed paradigm. Additionally, a patchwork phase-amplitude reduction method is suggested that is useful when exceedingly large magnitude perturbations are considered. This patchwork method incorporates the high-accuracy phase-amplitude reductions of multiple nearby periodic orbits that result from modifications to nominal parameters. The proposed method of high-accuracy phase-amplitude reduction can be readily implemented numerically and examples are provided where reductions are computed up to fourteenth order accuracy.

Here, we propose a class of scale-free networks $G(t;m)$ with intriguing properties, which cannot be simultaneously held by all the theoretical models with power-law degree distribution in the existing literature, including the following: (i) average degrees $\langle k\rangle$ of all the generated networks are no longer constant in the limit of large graph size, implying that they are not sparse but dense; (ii) power-law parameters $\gamma$ of these networks are precisely calculated equal to 2; and (iii) their diameters $D$ are all invariant in the growth process of models. While our models have deterministic structure with clustering coefficients equivalent to zero, we might be able to obtain various candidates with nonzero clustering coefficients based on original networks using reasonable approaches, for instance, randomly adding new edges under the premise of keeping the three important properties above unchanged. In addition, we study the trapping problem on networks $G(t;m)$ and then obtain a closed-form solution to mean hitting time ${\langle \mathcal{H}\rangle }_t$. As opposed to other previous models, our results show an unexpected phenomenon that the analytic value for ${\langle \mathcal{H}\rangle }_t$ is approximately close to the logarithm of the vertex number of networks $G(t;m)$. From the theoretical point of view, these networked models considered here can be thought of as counterexamples for most of the published models obeying power-law distribution in current study.

Simulations are widely used to study nucleation in first order phase transitions due to the fact that they have access to the relevant length and time scales. However, simulations face the problem that nucleation is an activated process. Therefore, rare event simulation techniques are needed to promote the formation of the critical nucleus. The Seeding method, where the simulations are started with the nucleus already formed, has proven quite useful in efficiently providing estimates of the nucleation rate for a wide range of orders of magnitude. So far, Seeding has been employed in the $NPT$ ensemble, where the nucleus either grows or redissolves. Thus, several trajectories have to be run in order to find the thermodynamic conditions that make the seeded nucleus critical. Moreover, the nucleus lifetime is short and the statistics for obtaining its properties is consequently poor. To deal with these shortcomings we extend the Seeding method to the $NVT$ ensemble. We focus on the problem of bubble nucleation in a metastable Lennard Jones fluid. We show that, in the $NVT$ ensemble, it is possible to equilibrate and stabilise critical bubbles for a long time. The nucleation rate inferred from $NVT$-Seeding is fully consistent with that coming from $NPT$-Seeding. The former is quite suitable to obtain the nucleation rate along isotherms, whereas the latter is preferable if the dependence of the rate with temperature at constant pressure is required. Care should be taken with finite size effects when using $NVT$-Seeding. Further work is required to extend $NVT$ seeding to other sorts of phase transitions.

The twist-bend nematic phase $\left(N_{\mathrm{TB}}\right)$ is characterized by a conically twisting director and by a dramatic softening of the bend elastic constant before the transition to the $N_{\mathrm{TB}}$ phase. In the recently found splay nematic phase ($N_S$) the splay elastic constant tends to zero, resulting in a splay modulation perpendicular to the director. We model both phases with a single Q-tensor free energy including a term that breaks the degeneracy between the splay and bend elastic constant, and a flexoelectric term coupling the divergence of the Q-tensor with polarization. The $N_{\mathrm{TB}}$ or $N_S$ phase is obtained by a change of sign of one elastic parameter. Measured elastic constants show that the $N-N_{\mathrm{TB}}$ transition is mainly driven by the increase of the nematic order, while the $N_S$ transition is due to flexoelectric coupling.

We show that when linear azimuthal perturbations on the surfaces of a fluid shell are regrouped according to ${\alpha }^m$, they can be divided into Bell model terms, coupling terms, and the newly identified thin-shell correction terms, where $\alpha$ is the ratio of $R_{\text{out}}$ to $R_{\text{in}}$, and $m$ is the mode number of a given unstable mode on the surfaces. It is also revealed that ${\alpha }^m$ is a convenient index variable of coupling effects, with which we show that the evolution of instability is composed of three stages, i.e., strongly coupled stage, transition stage, and uncoupled stage. Roughly, when ${\alpha }^m<6$, the fluid shell is in the strongly coupled stage, where both coupling effects and the newly identified thin-shell corrections play important roles. Strong feed through is expected to be observed. The uncoupled stage is reached at ${\alpha }^m\sim 36$, where Bell's model of independent surface holds. In between is the transition stage, where mode competitions on the two surfaces are expected to be observed. These results afford an intuitive picture which is easy to use in guiding the design of experiments. They may also help to quickly grasp major features of instability experiments of this kind.

We experimentally investigate the cooperative excitations in the transition from a self-excited three-dimensional ordered plane wave to a defect-mediated turbulence (DMT) state with multiple unstable defect filaments in a dusty plasma system. It is found that, with increasing effective driving, a single acoustic vortex (AV) with positive or negative helicity winding around a long straight defect filament with small wiggling in the $2+1\mathrm{D}$ (dimensional) space-time space starts to emerge along the center axis of the small dust cluster. The sequential ruptures of the crest surfaces from the cluster boundary followed by their reconnection with adjacent ruptured crest surfaces, or repelling one of the pairwise generated defects out of the boundary, are the key for the single AV generation. Further increasing driving makes the single defect filament exhibit helical excursion in the $2+1\mathrm{D}$ space. The system eventually enters the state with a few short-lived AVs and the DMT state with multiple AVs. The gradual increasing defect filament fluctuations and defect number in the transition to the DMT more strongly distort the nearby waveforms, which leads to the transition from the emergence of distinct sideband peaks to the broadened peaks in the power spectra of temporal dust density fluctuation. For the system with a larger cluster size, the single AV states are skipped in the transition to the DMT state.

The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrödinger equation in one and three dimensions for a one-body soft Coulomb potential in a laser field. The accuracy is tested comparing the solution to finite difference grid calculations using several examples. The approach is not limited to one particle systems and the example presented for two electrons demonstrates the potential to tackle larger systems using correlated basis functions.

We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain $z=2.0245\left(15\right)$ for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our estimate of $z$ is fully consistent with recent field theoretic results.

In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called “friction.” To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the Otto efficiency, and the power of the Lindbladian engine can be nonzero in the short-time limit. Based on additional numerical calculations of these outcomes, we discuss possible origins of such differences between two engines and reveal them. Our results imply that, even with an equilibrium bath, a nonequilibrium working fluid brings on the higher performance than what an equilibrium working fluid does.