The Fluctuation-Dissipation Theorem (FDT) is a powerful tool to estimate the thermal noise of physical systems in equilibrium. In general, however, thermal equilibrium is an approximation or cannot be assumed at all. A more general formulation of the FDT is then needed to describe the behavior of the fluctuations. In our experiment we study a microcantilever brought out of equilibrium by a strong heat flux generated by the absorption of the light of a laser. While the base is kept at cryogenic temperatures, the tip is heated up to the melting point, thus creating the highest temperature difference the system can sustain. We independently estimate the temperature profile of the cantilever and its mechanical fluctuations as well as its dissipation. We then demonstrate how the thermal fluctuations of all the observed degrees of freedom, though increasing with the heat flux, are much lower than what is expected from the average temperature of the system. We interpret these results using a minimal extension of the FDT: this dearth of thermal noise arises from a dissipation shared between clamping losses and distributed damping.

Plants have a special structure, torus-margo (TM) pit, which comprises a thickened torus at the center encircled by a highly porous margo. It is regarded as a key evolutionary structure to enable stable water transport, minimizing the air spread in the vessels. However, its valve-like dynamics to regulate two-phase flows still remains unclear even at a single pit level. Here, we study the air spreading dynamics using a bioinspired model of this soft pit valve. We divide it into the initial onset and the consecutive air-spreads, and propose the criteria of TM structures as the valve-like function. To delay the onset of air spread, the margo region should be thin and deformable enough to seal the pit aperture with the torus before the air penetration. Even after the onset, the membranes whose maximum pore size is smaller than its thickness can avoid continuous air-spread. The criteria also fit properly into botanical data on the morphologies of TM pits, implying that their valve-like behaviors may alleviate the tradeoff between hydraulic safety and efficiency at the single pit level. Our study would help to understand of the mechanistic pit-level strategy and also can provide insight into fluidic systems to control interfacial phenomena.

The colocalization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. We employ the active-Brownian-particle model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step. Our analysis allows for an optional (but not necessary) orientation-dependent propulsion speed, as often employed in force-free particle steering. The results agree well with measurement data for a thermophoretic microswimmer presented in the companion paper [Söker et al., Phys. Rev. Lett. 126, 228001 (2021)], and they can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind our formal results is robustly captured and elucidated by a schematic two-species “run-and-tumble” model.

We show that the Bose-glass phase of a one-dimensional disordered Bose fluid exhibits a chaotic behavior, i.e., an extreme sensitivity to external parameters. Using bosonization, the replica formalism and the nonperturbative functional renormalization group, we find that the ground state is unstable to any modification of the disorder configuration (“disorder” chaos) or variation of the Luttinger parameter (“quantum” chaos, analog to the “temperature” chaos in classical disordered systems). This result is obtained by considering two copies of the system, with slightly different disorder configurations or Luttinger parameters, and showing that intercopy statistical correlations are suppressed at length scales larger than an overlap length ${\xi }_{\mathrm{ov}}\sim {\left|\epsilon \right|}^{-1/\alpha }$ ($\left|\epsilon \right|\ll 1$ is a measure of the difference between the disorder distributions or Luttinger parameters of the two copies). The chaos exponent $\alpha$ can be obtained by computing ${\xi }_{\mathrm{ov}}$ or by studying the instability of the Bose-glass fixed point for the two-copy system when $\epsilon \ne 0$. The renormalized, functional, intercopy disorder correlator departs from its fixed-point value—characterized by “cuspy” singularities—via a chaos boundary layer, in the same way as it approaches the Bose-glass fixed point when $\epsilon =0$ through a quantum boundary layer. Performing a linear analysis of perturbations about the Bose-glass fixed point, we find $\alpha =1$.

Elastic materials with holes and inclusions are important in a large variety of contexts ranging from construction material to biological membranes. More recently, they have also been exploited in mechanical metamaterials, where the geometry of highly deformable structures is responsible for their unusual properties, such as negative Poisson's ratio, mechanical cloaking, and tunable phononic band gaps. Understanding how such structures deform in response to applied external loads is thus crucial for designing novel mechanical metamaterials. Here we present a method for predicting the linear response of infinite 2D solid structures with circular holes and inclusions by employing analogies with electrostatics. Just like an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects, external stress induces elastic multipoles inside holes and inclusions. Stresses generated by these induced elastic multipoles then lead to interactions between holes and inclusions, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands the induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external stress field and also between them. The results of our method show good agreement with both linear finite element simulations and experiments.

We present a method for predicting the linear response deformation of finite and semi-infinite 2D solid structures with circular holes and inclusions by employing the analogies with image charges and induction in electrostatics. Charges in electrostatics induce image charges near conductive boundaries and an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects. Similarly, charges in elasticity induce image charges near boundaries and external stress induces polarization (quadrupoles and other multipoles) inside holes and inclusions. Stresses generated by these induced elastic multipoles as well as stresses generated by their images near boundaries then lead to interactions between holes and inclusions and with their images, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external field, between them, and with their images. The results of our method for linear deformation of circular holes and inclusions near straight and curved boundaries show good agreement with both linear finite element simulations and experiments.

Effective prophylactic vaccines usually induce the immune system to generate potent antibodies that can bind to an antigen and thus prevent it from infecting host cells. B cells produce antibodies by a Darwinian evolutionary process called affinity maturation (AM). During AM, the B cell population evolves in response to the antigen to produce antibodies that bind specifically and strongly to the antigen. Highly mutable pathogens pose a major challenge to the development of effective vaccines because antibodies that are effective against one strain of the virus may not protect against a mutant strain. Antibodies that can protect against diverse strains of a mutable pathogen have high “breadth” and are called broadly neutralizing antibodies (bnAbs). In spite of extensive studies, an effective vaccination strategy that can generate bnAbs in humans does not exist for any highly mutable pathogen. Here we study a minimal model to explore the mechanisms underlying how the selection forces imposed by antigens can be optimally chosen to guide AM to maximize the evolution of bnAbs. For logistical reasons, only a finite number of antigens can be administered in a finite number of vaccinations; that is, guiding the nonequilibrium dynamics of AM to produce bnAbs must be accomplished nonadiabatically. The time-varying Kullback-Leibler divergence (KLD) between the existing B cell population distribution and the fitness landscape imposed by antigens is a quantitative metric of the thermodynamic force acting on B cells. If this force is too small, adaptation is minimal. If the force is too large, contrary to expectations, adaptation is not faster; rather, the B cell population is extinguished for reasons that we describe. We define the conditions necessary for the force to be set optimally such that the flux of B cells from low to high breadth states is maximized. Even in this case we show why the dynamics of AM prevent perfect adaptation. If two shots of vaccination are allowed, the optimal protocol is characterized by a relatively low optimal KLD during the first shot that appropriately increases the diversity of the B cell population so that the surviving B cells have a high chance of evolving into bnAbs upon subsequently increasing the KLD during the second shot. Phylogenetic tree analysis further reveals the evolutionary pathways that lead to bnAbs. The connections between the mechanisms revealed by our analyses and recent simulation studies of bnAb evolution, the problem of generalist versus specialist evolution, and learning theory are discussed.

We study the Soret effect in binary dimer-monomer mixtures using nonequilibrium molecular dynamics simulations and investigate the pure contribution of the internal degree of freedom of flexible molecules to the Soret effect. We observe that the thermal diffusion factor tends to decrease and change its sign as the molecules become softer. We propose two possible mechanisms for our observations: change of the molecule structures with the temperature, causing bulkier molecules to migrate to the hotter region, and asymmetry of the restitution between rigid and flexible molecules, due to which flexible molecules show larger restitution when placed at the hotter region.

Synchronization is often observed in the swimming of flagellated cells, either for multiple appendages on the same organism or between the flagella of nearby cells. Beating cilia are also seen to synchronize their dynamics. In 1951, Taylor showed that the observed in-phase beating of the flagella of coswimming spermatozoa was consistent with minimization of the energy dissipated in the surrounding fluid. Here we revisit Taylor's hypothesis for three models of flagella and cilia: (1) Taylor's waving sheets with both longitudinal and transverse modes, as relevant for flexible flagella, (2) spheres orbiting above a no-slip surface to model interacting flexible cilia, and (3) whirling rods above a no-slip surface to address the interaction of nodal cilia. By calculating the flow fields explicitly, we show that the rate of working of the model flagella or cilia is minimized in our three models for (1) a phase difference depending on the separation of the sheets and precise waving kinematics, (2) in-phase or opposite-phase motion depending on the relative position and orientation of the spheres, and (3) in-phase whirling of the rods. These results will be useful in future models probing the dynamics of synchronization in these setups.

We investigate the local time $T_{\text{loc}}$ statistics for a run and tumble particle (RTP) in one dimension, which is the quintessential model for the motion of bacteria. In random walk literature, the RTP dynamics is studied as the persistent Brownian motion. We consider the inhomogeneous version of this model where the inhomogeneity is introduced by considering the position-dependent rate of the form $R\left(x\right)=\gamma \frac{{\left|x\right|}^{\alpha }}{l^{\alpha }}$ with $\alpha \ge 0$. For $\alpha =0$, we derive the probability distribution of $T_{\text{loc}}$ exactly, which is expressed as a series of $\delta$ functions in which the coefficients can be interpreted as the probability of multiple revisits of the RTP to the origin starting from the origin. For general $\alpha$, we show that the typical fluctuations of $T_{\text{loc}}$ scale with time as $T_{\text{loc}}\sim t^{\frac{1+\alpha }{2+\alpha }}$ for large $t$ and their probability distribution possesses a scaling behavior described by a scaling function which we have computed analytically. Second, we study the statistics of $T_{\text{loc}}$ until the RTP makes a first passage to $x=M(>0)$. In this case, we also show that the probability distribution can be expressed as a series sum of $\delta$ functions for all values of $\alpha (\ge 0)$ with coefficients originating from appropriate exit problems. All our analytical findings are supported with numerical simulations.

We use a convolutional neural network (CNN) and two logistic regression models to predict the probability of nucleation in the two-dimensional Ising model. The three methods successfully predict the probability for the nearest-neighbor Ising model for which classical nucleation is observed. The CNN outperforms the logistic regression models near the spinodal of the long-range Ising model, but the accuracy of its predictions decreases as the quenches approach the spinodal. An occlusion analysis suggests that this decrease is due to the vanishing difference between the density of the nucleating droplet and the background. Our results are consistent with the general conclusion that predictability decreases near a critical point.

Weakly compressible particle-based discretization methods, utilized for the solution of the subsonic Navier-Stokes equation, are gaining increasing popularity in the fluid dynamics community. One of the most popular among these methods is the weakly compressible smoothed particle hydrodynamics. Since the dynamics of a single numerical particle is determined by fluid dynamic transport equations, the particle per definition should represent a homogeneous fluid element. However, it can be easily argued that a single particle behaves only pseudo-Lagrangian as it is affected by volume partition errors and can hardly adapt its shape to the actual fluid flow. Therefore, we will assume that the kernel support provides a better representative of an actual fluid element. By means of nonequilibrium molecular dynamics (NEMD) analysis, we derive isothermal transport equations for a kernel-based fluid element. The main discovery of the NEMD analysis is a molecular stress tensor, which may serve to explain current problems encountered in applications of weakly compressible particle-based discretization methods.

Several recent experiments, including our own experiments in the fission yeast, Schizosaccharomyces pombe, have characterized the motions of gene loci within living nuclei by measuring the locus position over time, then proceeding to obtain the statistical properties of this motion. To address the question of whether a population of such single-particle tracks, obtained from many different cells, corresponds to a single mode of diffusion, we derive theoretical equations describing the probability distribution of the displacement covariance, assuming the displacement itself is a zero-mean multivariate Gaussian random variable. We also determine the corresponding theoretical means, variances, and third central moments. Bolstering the theory is good agreement between its predictions and the results obtained for various simulated and measured data sets, including simulated particle trajectories undergoing simple and anomalous diffusion, and the measured trajectories of an optically trapped bead in water, and in a viscoelastic polymer solution. We also show that, for sufficiently long tracks, each covariance distribution in all of these examples is well-described by a skew-normal distribution with mean, variance, and skewness given by the theory. However, for the experimentally measured motion of a gene locus in S. pombe, we find that the first two covariance distributions are wider than predicted, although the third and subsequent covariance distributions are well-described by theory. This observation suggests that the origin of the theory-experiment discrepancy in this case is associated with localization noise, which influences only the first two covariances. Thus, we hypothesized that the discrepancy is caused by locus-to-locus heterogeneity in the localization noise, of independent measurements of the same tagged site. Indeed, simulations implementing heterogeneous localization noise revealed that the excess covariance widths can be largely recreated on the basis of heterogeneous noise. Thus, we conclude that the motion of gene loci in fission yeast is consistent with a single mode of diffusion.

Dislocation pileups directly impact the material properties of crystalline solids through the arrangement and collective motion of interacting dislocations. We study the statistical mechanics of these ordered defect structures embedded in two-dimensional crystals, where the dislocations themselves form one-dimensional lattices. In particular, pileups exemplify a new class of inhomogeneous crystals characterized by spatially varying lattice spacings. By analytically formulating key statistical quantities and comparing our theory to numerical experiments using an intriguing mapping of dislocation positions onto the eigenvalues of recently studied random matrix ensembles, we uncover two types of one-dimensional phase transitions in dislocation pileups: A thermal depinning transition out of long-range translational order from the pinned-defect phase, due to a periodic Peierls potential, to a floating-defect state, and finally the melting out of a quasi-long-range ordered floating-defect solid phase to a defect liquid. We also find the set of transition temperatures at which these transitions can be directly observed through the one-dimensional structure factor, where the delta function Bragg peaks, at the pinned-defect to floating-defect transition, broaden into algebraically diverging Bragg peaks, which then sequentially disappear as one approaches the two-dimensional melting transition of the host crystal. We calculate a set of temperature-dependent critical exponents for the structure factor and radial distribution function, and obtain their exact forms for both uniform and inhomogeneous pileups using random matrix theory.

Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic geometry of a thin elastic shell. However, morphogenesis often involves large bending deformations that are outside the formal range of validity of these shell theories. Here, by asymptotic expansion of three-dimensional incompressible morphoelasticity in the limit of a thin shell, we derive a shell theory for large intrinsic bending deformations and emphasize the resulting geometric material anisotropy and the elastic role of cell constriction. Taking the invagination of the green alga Volvox as a model developmental event, we show how results for this theory differ from those for a classical shell theory that is not formally valid for these large bending deformations and reveal how these geometric effects stabilize invagination.

Many sensory pathways in the brain include sparsely active populations of neurons downstream from the input stimuli. The biological purpose of this expanded structure is unclear, but it may be beneficial due to the increased expressive power of the network. In this work, we show that certain ways of expanding a neural network can improve its generalization performance even when the expanded structure is pruned after the learning period. To study this setting, we use a teacher-student framework where a perceptron teacher network generates labels corrupted with small amounts of noise. We then train a student network structurally matched to the teacher. In this scenario, the student can achieve optimal accuracy if given the teacher's synaptic weights. We find that sparse expansion of the input layer of a student perceptron network both increases its capacity and improves the generalization performance of the network when learning a noisy rule from a teacher perceptron when the expansion is pruned after learning. We find similar behavior when the expanded units are stochastic and uncorrelated with the input and analyze this network in the mean-field limit. By solving the mean-field equations, we show that the generalization error of the stochastic expanded student network continues to drop as the size of the network increases. This improvement in generalization performance occurs despite the increased complexity of the student network relative to the teacher it is trying to learn. We show that this effect is closely related to the addition of slack variables in artificial neural networks and suggest possible implications for artificial and biological neural networks.

The time evolution of an occupation number is studied for a fermionic or bosonic oscillator linearly fully coupled to several fermionic and bosonic heat baths. The influence of the characteristics of thermal reservoirs of different statistics on the nonstationary population probability is analyzed at large times. Applications of the absence of equilibrium in such systems for creating a dynamic (nonstationary) memory storage are discussed.

We study a class of stochastic processes of the type $\frac{d^{n}x}{d{t}^n}=v_0\sigma \left(t\right)$ where $n>0$ is a positive integer and $\sigma \left(t\right)=\pm 1$ represents an active telegraphic noise that flips from one state to the other with a constant rate $\gamma$. For $n=1$, it reduces to the standard run-and-tumble process for active particles in one dimension. This process can be analytically continued to any $n>0,$ including noninteger values. We compute exactly the mean-squared displacement at time $t$ for all $n>0$ and show that at late times while it grows as $\sim t^{2n-1}$ for $n>1/2$, it approaches a constant for $n<1/2$. In the marginal case $n=1/2$, it grows very slowly with time as $\sim lnt$. Thus, the process undergoes a localization transition at $n=1/2$. We also show that the position distribution $p_n(x,t)$ remains time-dependent even at late times for $n\ge 1/2$, but approaches a stationary time-independent form for $n<1/2$. The tails of the position distribution at late times exhibit a large deviation form, $p_n(x,t)\sim exp\left[-\gamma t{\mathrm{\Phi }}_n\left(\frac{x}{x^{*}\left(t\right)}\right)\right]$, where $x^{*}\left(t\right)=v_0{t}^n/\mathrm{\Gamma }(n+1)$. We compute the rate function ${\mathrm{\Phi }}_n\left(z\right)$ analytically for all $n>0$ and also numerically using importance sampling methods, finding excellent agreement between them. For three special values $n=1$, $n=2,$ and $n=1/2$ we compute the exact cumulant-generating function of the position distribution at all times $t$.

Understanding the drift motion and dynamical locking of crystalline clusters on patterned substrates is important for the diffusion and manipulation of nano- and microscale objects on surfaces. In a previous work, we studied the orientational and directional locking of colloidal two-dimensional clusters with triangular structure driven across a triangular substrate lattice. Here we show with experiments and simulations that such locking features arise for clusters with arbitrary lattice structure sliding across arbitrary regular substrates. Similar to triangular-triangular contacts, orientational and directional locking are strongly correlated via the real- and reciprocal-space Moiré patterns of the contacting surfaces. Due to the different symmetries of the surfaces in contact, however, the relation between the locking orientation and the locking direction becomes more complicated compared to interfaces composed of identical lattice symmetries. We provide a generalized formalism which describes the relation between the locking orientation and locking direction with arbitrary lattice symmetries.

Single-stranded RNA viruses efficiently encapsulate their genome into a protein shell called the capsid. Electrostatic interactions between the positive charges in the capsid protein's N-terminal tail and the negatively charged genome have been postulated as the main driving force for virus assembly. Recent experimental results indicate that the N-terminal tail with the same number of charges and same lengths packages different amounts of RNA, which reveals that electrostatics alone cannot explain all the observed outcomes of the RNA self-assembly experiments. Using a mean-field theory, we show that the combined effect of genome configurational entropy and electrostatics can explain to some extent the amount of packaged RNA with mutant proteins where the location and number of charges on the tails are altered. Understanding the factors contributing to the virus assembly could promote the attempt to block viral infections or to build capsids for gene therapy applications.