Rate dependent response of nanoscale structures having a multiwell energy landscape.

A stochastic and rate-dependent response originating from thermal fluctuations over a highly nonconvex energy landscape is a prevailing aspect of the mechanical behavior of nanoscale structures. The overdamped dynamics of a bistable chain subjected to thermal fluctuations is prototypical of such behavior. Based on this approach, we find a new nondimensional quantity, similar in its mathematical structure to Boltzmann's factor, which captures the intricate competition between rate, temperature, and energy barriers underlying the system dynamics. In turn, we obtain simple universal laws for predicting statistical properties of the mechanical response.

A new method for the calculation of functional and path integrals.

This paper addresses a disconnect between the pivotal role of functional (path) integrals in modern theories, such as quantum mechanics and statistical thermodynamics, and the currently limited ability to perform the actual calculation. We present a new method for calculating functional integrals, based on a finite-element formulation, which solves all limitations of existing methods. This approach is far more robust, versatile, and powerful than the prevailing methods, thus allowing for more sophisticated computations and the study of problems that could not previously be tackled. Importantly, existing procedures, element libraries and shape functions, which have been developed throughout the years in the context of engineering analysis and partial differential equations, may be directly employed for this purpose.

Multistable Metafluid based Energy Harvesting and Storage.

The thermodynamic properties of fluids play a crucial role in many engineering applications, particularly in the context of energy. Fluids with multistable thermodynamic properties may offer new paths for harvesting and storing energy via transitions between equilibria states. Such artificial multistable fluids can be created using the approach employed in metamaterials, which controls macro-properties through micro-structure composition. In this work, the dynamics of such "metafluids" is examined for a configuration of calorically-perfect compressible gas contained within multistable elastic capsules flowing in a fluid-filled tube. The velocity-, pressure-, and temperature-fields of multistable compressible metafluids is studied by both analytically and experimentally, focusing on transitions between different equilibria. The dynamics of a single capsule is first examine, which may move or change equilibrium state, due to fluidic forces. The interaction and motion of multiple capsules within a fluid-filled tube is then studied. It shows that such a system can be used to harvest energy from external temperature variations in either time or space. Thus, fluidic multistability allows specific quanta of energy to be captured and stored indefinitely as well as transported as a fluid, via tubes, at standard atmospheric conditions without the need for thermal isolation.

A metafluid with multistable density and internal energy states.

Investigating and tailoring the thermodynamic properties of different fluids is crucial to many fields. For example, the efficiency, operation range, and environmental safety of applications in energy and refrigeration cycles are highly affected by the properties of the respective available fluids. Here, we suggest combining gas, liquid and multistable elastic capsules to create an artificial fluid with a multitude of stable states. We study, theoretically and experimentally, the suspension's internal energy, equilibrium pressure-density relations, and their stability for both adiabatic and isothermal processes. We show that the elastic multistability of the capsules endows the fluid with multistable thermodynamic properties, including the ability of capturing and storing energy at standard atmospheric conditions, not found in naturally available fluids.

Towards multi-scale modeling of muscle fibers with sarcomere non-uniformities.

A theoretical framework for studying the collective behavior of a large ensemble of half sarcomeres in a myofibril is presented. The approach is based on transforming the large system of discrete elements (half-sarcomeres) into a continuum for which macro-behavior is dictated by micro-properties. Specifically, we consider statistical properties of the ensemble rather than solving for each degree of freedom. This enables a reasonable computational effort and provides important insights. We demonstrate that such a multi-scale approach is indispensable for studying quantitatively the role of sarcomere non-uniformities in muscle mechanics. Specifically, we illustrate that adopting a model with a non-physiological number of sarcomeres can lead to a non-realistic behavior and therefore to erroneous interpretation. Further, we demonstrate that the new modeling approach provides a suitable platform for addressing controversial phenomena, such as residual enhanced tension, creep, length redistribution, and damage due to eccentric contraction.

Solitary waves in a nonintegrable chain with double-well potentials.

We study solitary waves in a one-dimensional lattice of identical masses that are connected in series by nonlinear springs. The potential of each spring is nonconvex, where two disjoint convex regions, phase I and phase II, are separated by a concave, spinodal region. Consequently, the force-strain relation of the spring is nonmonotonous, which gives rise to a bistable behavior. Based on analytical treatment, with some approximations, combined with extensive numerical simulations, we are able to reveal important insights. For example, we find that the solitary-wave solution is indifferent to the energy barrier that separates the two energy wells associated with phase I and phase II, and that the shape of the wave can be described by means of merely two scalar properties of the potential of the springs, namely, the ratio of stiffness in phase II and phase I, and the ratio between the Maxwell's force and corresponding transition strain. The latter ratio provides a useful measure for the significance of the spinodal region. Linear stability of the solitary-wave solution is studied analytically using the Vakhitov-Kolokolov criterion applied to the approximate solutions obtained in the first part. These results are validated by numerical simulations. We find that the solitary-wave solution is stable provided that its velocity is higher than some critical value. It is shown that, practically, the solitary waves are stable for almost the entire range of possible wave velocities. This is also manifested in the interaction between two solitary waves or between a solitary wave and a wall (rigid boundary). Such interaction results in a minor change of height and shape of the solitary wave along with the formation of a trail of small undulations that follow the wave, as expected in a nonintegrable system. Even after a significant number of interactions the changes in the wave height and shape are minor, suggesting that the bistable chain may be a useful platform for delivering information over long distances, even concurrently with additional information (other solitary waves) passing through the chain.

Curvature-Induced Spatial Ordering of Composition in Lipid Membranes.

Phase segregation of membranal components, such as proteins, lipids, and cholesterols, leads to the formation of aggregates or domains that are rich in specific constituents. This process is important in the interaction of the cell with its surroundings and in determining the cell's behavior and fate. Motivated by published experiments on curvature-modulated phase separation in lipid membranes, we formulate a mathematical model aiming at studying the spatial ordering of composition in a two-component biomembrane that is subjected to a prescribed (imposed) geometry. Based on this model, we identified key nondimensional quantities that govern the biomembrane response and performed numerical simulations to quantitatively explore their influence. We reproduce published experimental observations and extend them to surfaces with geometric features (imposed geometry) and lipid phases beyond those used in the experiments. In addition, we demonstrate the possibility for curvature-modulated phase separation above the critical temperature and propose a systematic procedure to determine which mechanism, the difference in bending stiffness or difference in spontaneous curvatures of the two phases, dominates the coupling between shape and composition.

Contraction induced muscle injury: towards personalized training and recovery programs.

Skeletal muscles can be injured by their own contractions. Such contraction-induced injury, often accompanied by delayed onset of muscle soreness, is a leading cause of the loss of mobility in the rapidly increasing population of elderly people. Unlike other types of muscle injuries which hurt almost exclusively those who are subjected to intensive exercise such as professional athletes and soldiers in training, contraction induced injury is a phenomenon which may be experienced by people of all ages while performing a variety of daily-life activities. Subjects that experience contraction induced injury report on soreness that usually increases in intensity in the first 24 h after the activity, peaks from 24 to 72 h, and then subsides and disappears in a few days. Despite their clinical importance and wide influence, there are almost no studies, clinical, experimental or computational, that quantitatively relate between the extent of contraction induced injury and activity factors, such as number of repetitions, their frequency and magnitude. The lack of such quantitative information is even more emphasized by the fact that contraction induced injury can be used, if moderate and controlled, to improve muscle performance in the long term. Thus, if properly understood and carefully implemented, contraction induced injury can be used for the purpose of personalized training and recovery programs. In this paper, we review experimental, clinical, and theoretical works, attempting towards drawing a more quantitative description of contraction induced injury and related phenomena.

A theoretical study of biological membrane response to temperature gradients at the single-cell level.

Recent experimental studies provide evidence for the existence of a spatially non-uniform temperature field in living cells and in particular in their plasma membrane. These findings have led to the development of a new and exciting field: thermal biology at the single-cell level. Here, we examine theoretically a specific aspect of this field, i.e. how temperature gradients at the single-cell level affect the phase behaviour and geometry of heterogeneous membranes. We address this issue by using the Onsager reciprocal relations combined with a simple model for a binary lipid mixture. We demonstrate that even small temperature variations along the membrane may introduce intriguing phenomena, such as phase separation above the critical temperature and unusual shape response. These results also suggest that the shape of a membrane can be manipulated by dynamically controlling the temperature field in its vicinity. The effects of intramembranous temperature gradients have never been studied experimentally. Thus, the predictions of the current contribution are of a somewhat speculative nature. Experimental verification of these results could mark the beginning of a new line of research in the field of biological membranes. We report our findings with the hope of inspiring others to perform such experiments.

Closing the loop: lamellipodia dynamics from the perspective of front propagation.

We develop a simple physical model that captures the large-scale lamellipodia dynamics in crawling cells and explains the observed spectrum of fish keratocytes behavior. The main ingredients in this description are the geometrical evolution of the lamellipodium leading edge, the dynamic remodeling of the actin network, and the interconnection between them. We deviate from existing theoretical works and consider the lamellipodium leading edge as a propagating front. The agreement of our model with experimental works suggests that the large-scale morphological and migration features exhibited by keratocyte cells are a direct consequence of the closed feedback loop between the shape of the leading edge and the density of the actin network.

Fibrin polymerization in blood coagulation-a statistical model.

A theoretical model for the growth of fibrin clots is derived. The model is based on a statistical description of the polymerization process underlying the formation of the fibrin polymeric network. The model provides insights regarding the role of various factors, such as thrombin concentration, plasmin concentration, and the local shear rate in the coagulation process. In particular, the effect of these factors on the mechanical properties of the clot is studied. Numerical results are in very good agreement with quantitative and qualitative experimental observations. Importantly, no fitting parameters are used, and all model parameters, such as fibrin persistence length and monomer size, are in accordance with experimental reports.