Nonequilibrium Interactions Research Articles

Generation of acoustic-Brownian noise in nuclear magnetic resonance under non-equilibrium thermal fluctuations

We present an analytical study on generation of acoustic-Brownian noise in nuclear magnetic resonance (NMR) induced as a result of thermal fluctuations of the magnetic moments under non-equilibrium thermal interactions which has not been explored independent of Nyquist–Johnson noise until now. The mechanism of physical coupling between non-equilibrium thermal fluctuations and magnetic moments is illustrated using Lighthill’s formulation on suspension dynamics. We discover that unlike Nyquist–Johnson noise which has a uniform spectral density across a range of frequencies, the spectral dependence of acoustic-Brownian noise decreases with an increase in frequency and resembles Brownian noise associated with a particle in a potential well. The results have applications in the field of image enhancement algorithm as well as noise reduction instrumentation in NMR systems.

Linear Response Theory and Entropic Fluctuations in Repeated Interaction Quantum Systems

We study Linear Response Theory and Entropic Fluctuations of finite dimensional non-equilibrium repeated interaction systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different values, we prove analogs of the Green-Kubo fluctuation-dissipation formula and Onsager reciprocity relations on energy flux observables. Then we prove a Large Deviation Principle, or Fluctuation Theorem, and a Central Limit Theorem on the full counting statistics of entropy fluxes. We consider two types of non-equilibrium RIS: either the temperatures of the probes are deterministic and arrive in a cyclic way, or the temperatures of the probes are described by a sequence of i.i.d. random variables with uniform distribution over a finite set.

Different transport behaviors and mechanisms of perfluorooctanoate (PFOA) and perfluorooctane sulfonate (PFOS) in saturated porous media

Perfluorooctanoate (PFOA) and perfluorooctane sulfonate (PFOS) in soil aroused increasing concern, however there is little information about their transport in porous media, which is urgently needed to better control their environmental risks. In this study, saturated sand columns (considering the coupled effect of solution cation type and pH) and a two-site nonequilibrium transport model (TSM) were used to investigate the transport behaviors and mechanisms of PFOA and PFOS. Breakthrough data and the TSM parameters showed PFOA had higher mobility than PFOS, and divalent cation could inhibit their transport by increasing the nonequilibrium interactions between them and the sand. pH had little influence on PFOA migration when there was only monovalent cation in the solution since PFOA had limited affinity with the sand, however, polyvalent cation could provide additional adsorption sites for it through cation bridging and enhance the effect of pH. Differently, decreasing pH inhibited the transport of PFOS more significantly, and the effect was stronger than that of changing cation type. That proved mechanisms like hydrogen-bonding which were sensitive to solution pH played an important role in PFOS migration. These results provide important scientific basis to the remediation strategy and the migration prediction model development of PFOA and PFOS.

Dynamical analysis and anti-oscillation-based adaptive control of the FO arch MEMS with optimality

This paper mainly investigates dynamical analysis and anti-oscillation-based adaptive control issues of the fractional-order (FO) arch microelectromechanical system (MEMS) with optimality. With the aid of phase diagram and Lyapunov exponent, the dynamical analysis reveals that chaotic oscillation originated in non-equilibrium interaction of potential energy can deteriorate the performance of the FO arch MEMS under different FOs and excitation amplitudes. During the design process, a recurrent non-singleton type-2 fuzzy neural network with a transformation is employed to approximate uncertain function and the Nussbaum function is used to tackle the problem of unknown control direction from actuation characteristic in the field of Caputo fractional derivative. Meanwhile, a tracking differentiator based on the hyperbolic sine function is designed to solve the repeated differentiation of virtual control because of complicated FO calculation. Then, an anti-oscillation-based adaptive control scheme fused with the Nussbaum function, neural network, tracking differentiator and optimal control is developed in the framework of backstepping by means of continuous frequency distributed model. The asymptotic stability of the proposed solution is proved based on the Lyapunov stability criterion. Finally, simulation results validate the feasibility of the presented scheme under multi-step methods of numerical solution.

Visualizing Interactions Between Liquid Propane and Heavy Oil

AbstractIn this study, we use a custom-designed visual cell to investigate nonequilibrium interactions between liquid propane (C3(l)) and a heavy oil sample (7.2 deg API) at varying experimental conditions. We inject C3(l) into the visual cell containing the heavy oil sample (pressure-buildup process) and allow the injected C3(l) to interact with the oil sample (soaking process). We measure visual-cell pressure and visualize the C3/heavy oil interactions during the pressure-buildup and soaking processes. Nonequilibrium interactions occurring at the interfaces of C3(l)/heavy oil and C3(l)/C3(g) are recorded with respect to time. The results show that the complete mixing of heavy oil with C3(l) occurs in two stages. First, upward extracting flows of oil components from bulk heavy oil phase toward C3(l) phase form a distinguished layer (L1) during the soaking process. The extracted oil components become denser over time and move downward (draining flows) toward the C3(l)/heavy oil interface due to gravity. The gradual color change of L1 from colorless (color of pure C3(l)) to black suggests the mixing of oil components with C3(l). After L1 appears to be uniform, a second layer (L2) is formed above L1 in the bulk C3(l) phase. Extracting and draining flows become active once again, leading to the mixing of oil components from L1 into L2. At final conditions, heavy oil and C3(l) appear to be mixed and form a single uniform phase.

Nonlocal hydrodynamic modeling high-rate shear processes in condensed matter

Problem of mathematical modeling high-rate processes in condensed medium is considered by using new nonlocal hydrodynamic approach based on the results of non-equilibrium statistical mechanics and cybernetical physics. Interrelationships between the spatiotemporal correlations in the integral thermodynamic relationships between forces and fluxes and the system internal structure made it possible to describe the self-organization of new dynamic structures in the open system. The temporal structure evolution is described by methods of the control theory of adaptive systems. The proposed approach to the structure evolution allows a new insight into the system state stability. The proposed approach is used to describe high-rate shear flow in the Couette formulation. Explicit approximate solutions to the problem show that steady pure shear flow far from equilibrium looses its stability due to dynamic structure evolution. Near the boundaries there appear layers where continuum mechanics becomes invalid and non-equilibrium interfacial interaction with the walls forms vortex structures. In transient modes a meta-stable state can occur where the system evolution can change its direction due to any weak impact.

Exact Phoretic Interaction of Two Chemically Active Particles.

We study the nonequilibrium interaction of two isotropic chemically active particles taking into account the exact near-field chemical interactions as well as hydrodynamic interactions. We identify regions in the parameter space wherein the dynamical system describing the two particles can have a fixed point-a phenomenon that cannot be captured under the far-field approximation. We find that, due to near-field effects, the particles may reach a stable equilibrium at a nonzero gap size or make a complex that can dissociate in the presence of sufficiently strong noise. We explicitly show that the near-field effects originate from a self-generated neighbor-reflected chemical gradient, similar to interactions of a self-propelling phoretic particle and a flat substrate.

Dynamically and thermally nonequilibrium fluctuation-electromagnetic interactions: Recent results and trends

Our recent theoretical developments related to the nonrelativistic and relativistic fluctuation-electromagnetic interactions of bodies with different temperatures moving translationally and (or) rotationally relative to each other are briefly summarized. Three basic geometrical configurations and physical systems are discussed: “a small particle and a thick plate” (i); “a small particle in a radiative vacuum background” (ii) and “two thick plates in relative motion” (iii) — classical Casimir-Lifshitz configuration with allowance for relative motion and different temperatures of plates. For configuration 3, it is shown that the theory of friction and heat exchange by Levin-Polevoi-Rytov proves to be quite adequate contrary to the settled point of view of many authors.

Non-equilibrium interaction between catalytic colloids: boundary conditions and penetration depth.

Spherical colloids that catalyze the interconversion reaction A⇋B between solute molecules A and B whose concentration at infinity is maintained away from equilibrium effectively interact due to the non-uniform fields of solute concentrations. We show that this long range 1/r interaction is suppressed via a mechanism that is superficially reminiscent but qualitatively very different from electrostatic screening: catalytic activity drives the concentrations of solute molecules towards their equilibrium values and reduces the chemical imbalance that drives the interaction between the colloids. The imposed non-equilibrium boundary conditions give rise to a variety of geometry-dependent scenarios; while long-range interactions are suppressed (except for a finite penetration depth) in the bulk of the colloid solution in 3D, they can persist in quasi-2D geometry in which the colloids but not the solutes are confined to a surface, resulting in the formation of clusters or Wigner crystals, depending on the sign of the interaction between colloids.

Convective flows along the bodies of animals

The production of high-quality livestock products is associated with the creation of optimal microclimate parameters in the premises for animals. Animals are a source of heat, and the convective flows formed along the body and the associated temperature mass-transfer fields, as well as the stresses arising under conditions of non-equilibrium interaction with the external environment, are of practical interest. In solving the stated problem of heat and mass transfer, we adopted an approximately convective flow consisting only of a vortex layer of free turbulence and considered the momentum equations of the lifting forces arising from heating and the amount of excess heat in the jet. It was assumed that the heat transfer per unit area of the warm surface is constant in height and length of the cylinder. As a result of a theoretical study of heat and mass transfer, the dependences of speed, excess temperatures, and convective flow were established. Analysis of the obtained dependences made it possible to conclude that the speed along the body increases with increasing mass of animals. This creates the prerequisites for using the heat generated by them to maintain the necessary temperature parameters of the air in the room. It is concluded that it is necessary to use only the upflows to provide animals with the necessary amount of oxygen. The resulting convective flow along the body of animals of different masses varies with a constant increase in the growth of animals. The upflows formed around the body of the animal are strong enough and lead to the rise of significant masses of air. Taking into account the physiology of cattle, it was concluded that the prepared air should be supplied to the heads of animals, as up to 30% of heat and carbon dioxide is released during exhalation, and animals’ bodies should be flooded with air in piggery.

Dependence of non-equilibrium Casimir forces on material optical properties toward chaotic motion during device actuation.

The sensitivity of nonequilibrium Casimir forces on material optical properties can have strong impact on the actuation of devices. For this purpose, we considered nonequilibrium Casimir interactions between good and poor conductors, for example, gold (Au) and highly doped silicon carbide (SiC), respectively. Indeed, for autonomous conservative systems, the bifurcation and phase portrait analysis have shown that the nonequilibrium Casimir forces can have significant impact on the stable and unstable operating regimes depending on the material optical properties. At a few micrometer separations, for systems with high conductivity materials, an increasing temperature difference between the actuating components can enhance the stable operation range due to the reduction of the Casimir force, while for the poor conductive materials, the opposite takes place. For periodically driven dissipative systems, the Melnikov function and Poincare portrait analysis have shown that for poor conductive systems, the nonequilibrium Casimir forces lead to an increased possibility for chaotic behavior and stiction with an increasing temperature difference between the actuating components. However, for good conducting systems, the thermal contribution to Casimir forces reduces the possibility for chaotic behavior with increasing temperature, as comparison with systems without thermal fluctuations shows. Nevertheless, the positive benefit of good conductors toward increased actuation stability and reduced the chaotic behavior under nonequilibrium conditions can be easily compromised by any voltage application. Therefore, thermal, nonequilibrium Casimir forces can influence the actuation of devices toward unstable and chaotic behavior in strong correlation with their optical properties, and associated conduction state, as well as applied electrostatic potentials.

Active Phase Separation in Mixtures of Chemically Interacting Particles.

We theoretically study mixtures of chemically interacting particles, which produce or consume a chemical to which they are attracted or repelled, in the most general case of many coexisting species. We find a new class of active phase separation phenomena in which the nonequilibrium chemical interactions between particles, which break action-reaction symmetry, can lead to separation into phases with distinct density and stoichiometry. Because of the generic nature of our minimal model, our results shed light on the underlying fundamental principles behind nonequilibrium self-organization of cells and bacteria, catalytic enzymes, or phoretic colloids.

Efficient calculation of heterogeneous non-equilibrium statistics in coupled firing-rate models

Understanding nervous system function requires careful study of transient (non-equilibrium) neural response to rapidly changing, noisy input from the outside world. Such neural response results from dynamic interactions among multiple, heterogeneous brain regions. Realistic modeling of these large networks requires enormous computational resources, especially when high-dimensional parameter spaces are considered. By assuming quasi-steady-state activity, one can neglect the complex temporal dynamics; however, in many cases the quasi-steady-state assumption fails. Here, we develop a new reduction method for a general heterogeneous firing-rate model receiving background correlated noisy inputs that accurately handles highly non-equilibrium statistics and interactions of heterogeneous cells. Our method involves solving an efficient set of nonlinear ODEs, rather than time-consuming Monte Carlo simulations or high-dimensional PDEs, and it captures the entire set of first and second order statistics while allowing significant heterogeneity in all model parameters.

Revealing circadian mechanisms of integration and resilience by visualizing clock proteins working in real time

The circadian clock proteins KaiA, KaiB, and KaiC reconstitute a remarkable circa-24 h oscillation of KaiC phosphorylation that persists for many days in vitro. Here we use high-speed atomic force microscopy (HS-AFM) to visualize in real time and quantify the dynamic interactions of KaiA with KaiC on sub-second timescales. KaiA transiently interacts with KaiC, thereby stimulating KaiC autokinase activity. As KaiC becomes progressively more phosphorylated, KaiA’s affinity for KaiC weakens, revealing a feedback of KaiC phosphostatus back onto the KaiA-binding events. These non-equilibrium interactions integrate high-frequency binding and unbinding events, thereby refining the period of the longer term oscillations. Moreover, this differential affinity phenomenon broadens the range of Kai protein stoichiometries that allow rhythmicity, explaining how the oscillation is resilient in an in vivo milieu that includes noise. Therefore, robustness of rhythmicity on a 24-h scale is explainable by molecular events occurring on a scale of sub-seconds.

Nonequilibrium atom-surface interaction with lossy multilayer structures

The impact of lossy multi-layer structures on nonequilibrium atom-surface interactions is discussed. Specifically, the focus lies on a fully non-Markovian and nonequilibrium description of quantum friction, the fluctuation-induced drag force acting on an atom moving at constant velocity and height above the multi-layer structures. Compared to unstructured bulk material, the drag force for multi-layer systems is considerably enhanced and exhibits different regimes in its velocity and distance dependences. These features are linked to the appearance of coupled interface polaritons within the superlattice structures. Our results are not only useful for an experimental investigation of quantum friction but also highlight a way to tailor the interaction by simply modifying the structural composition of the multi-layer systems.

Study of Thermomechanical Properties of an Al‐Zn‐Based Composite Reinforced with Dodecaboride Particles

The effect of the addition of AlB12 particles to gravity cast Al‐Zn alloys was studied and related to the composite deformation at high temperature. The characterization techniques of choice were thermomechanical analysis (TMA), Brinell hardness (HB), and optical microscopy. After homogenization treatment, Al‐5 wt.% Zn and Al‐10 wt.% Zn with 0, 2.08, 4.16 wt.% B samples were quenched in ice water and tested using a thermomechanical analyzer at different temperatures. It was found that after TMA treatment, Brinell hardness of the composites increased for higher concentrations of zinc and AlB12 particles, as expected. Such increment was not, however, uniform for all samples at higher temperature levels, suggesting a nonequilibrium interaction between reinforcing particles and zinc. This was further corroborated by TMA experiments, which revealed that for samples with Al‐10 wt.% Zn, high temperature deformation augmented as more AlB12 particles were present. After high temperature treatment, precipitation of zinc‐rich allotriomorphs was observed by the optical microscopy performed on the samples near or on the aluminum grain boundaries, which discarded the potential effect of fine precipitation due to aging.

Non-equilibrium pair interactions in colloidal dispersions

We study non-equilibrium pair interactions between microscopic particles moving through a model shear-thinning fluid. Prior efforts to model pair interactions in non-Newtonian fluids have largely focused on constitutive models derived from polymer-chain kinetic theories focusing on conformational degrees of freedom, but neglecting the details of microstructural evolution beyond a single polymer length scale. To elucidate the role of strong structural distortion in mediating pair interactions in Brownian suspensions, we formulate and solve a Smoluchowski equation describing the detailed evolution of the particle configuration between and around a pair of microscopic probes driven at fixed velocity by an external force through a colloidal dispersion. To facilitate analysis, we choose a model system of Brownian hard spheres that do not interact hydrodynamically; while simple, this ‘freely draining’ model permits insight into connections between microstructure and rheology. The flow induces a non-equilibrium particle density gradient that gives rise to both viscous drag and an interactive force between the probes. The drag force acts to slow the centre-of-mass velocity of the pair, while the interactive force arising from osmotic pressure gradients can lead to attraction or repulsion, as well as deterministic reorientation of the probes relative to the external force. The degree to which the microstructure is distorted, and the shape of that distortion, depend on the arrangement of the probes relative to one another and their orientation to the driving force. It also depends on the magnitude of probe velocity relative to the Brownian velocity of the suspension. When only thermal fluctuations set probe velocity, the equilibrium depletion attraction is recovered. For weak forcing, long-ranged interactions mediated via the bath-particle flux give rise to entropic forces on the probes. The linear response is a viscous drag that slows forward motion; only the weakly nonlinear response can produce relative motion–attraction, repulsion or reorientation of the probes. We derive entropic coupling tensors, similar in ethos to pair hydrodynamic tensors, to describe this behaviour. The structural symmetry that permits this analogy is lost when forcing becomes strong, revealing instabilities in system behaviour. Far from equilibrium, the interactive force depends explicitly on the initial probe separation, orientation and strength of forcing; widely spaced probes interact through the distorted microstructure, whereas the behaviour of closely spaced probes is largely set by excluded-volume effects. In this regime, a pair of closely spaced probes sedimenting side-by-side tend to attract and reorient to permit alignment of their line-of-centres with the flow, while widely spaced probes fall without reorienting. Our results show qualitative agreement with experimental observations and provide a potential connection to the observed column instability in shear-thinning fluids.

Nonequilibrium interactions between ideal polymers and a repulsive surface.

We use Newtonian and overdamped Langevin dynamics to study long flexible polymers dragged by an external force at a constant velocity v. The work W performed by that force depends on the initial state of the polymer and the details of the process. The Jarzynski equality can be used to relate the nonequilibrium work distribution P(W) obtained from repeated experiments to the equilibrium free energy difference ΔF between the initial and final states. We use the power law dependence of the geometrical and dynamical characteristics of the polymer on the number of monomers N to suggest the existence of a critical velocity v_{c}(N), such that for v<v_{c} the reconstruction of ΔF is an easy task, while for v significantly exceeding v_{c} it becomes practically impossible. We demonstrate the existence of such v_{c} analytically for an ideal polymer in free space and numerically for a polymer which is being dragged away from a repulsive wall. Our results suggest that the distribution of the dissipated work W_{d}=W-ΔF in properly scaled variables approaches a limiting shape for large N.

Ensemble-averaged Rabi oscillations in a ferromagnetic CoFeB film

Rabi oscillations describe the process whereby electromagnetic radiation interacts coherently with spin states in a non-equilibrium interaction. To date, Rabi oscillations have not been studied in one of the most common spin ensembles in nature: spins in ferromagnets. Here, using a combination of femtosecond laser pulses and microwave excitations, we report the classical analogue of Rabi oscillations in ensemble-averaged spins of a ferromagnet. The microwave stimuli are shown to extend the coherence-time resulting in resonant spin amplification. The results we present in a dense magnetic system are qualitatively similar to those reported previously in semiconductors which have five orders of magnitude fewer spins and which require resonant optical excitations to spin-polarize the ensemble. Our study is a step towards connecting concepts used in quantum processing with spin-transport effects in ferromagnets. For example, coherent control may become possible without the complications of driving an electromagnetic field but rather by using spin-polarized currents.

Collectivity in diffusion of colloidal particles: from effective interactions to spatially correlated noise

The collectivity in the simultaneous diffusion of many particles, i.e. the interdependence of stochastic forces affecting different particles in the same solution, is a largely overlooked phenomenon with no well-established theory. Recently, we have proposed a novel type of thermodynamically consistent Langevin dynamics driven by spatially correlated noise (SCN) that can contribute to the understanding of this problem. This model draws a link between the theory of effective interactions in binary colloidal mixtures and the properties of SCN. In the current article, we review this model from the perspective of collective diffusion and generalize it to the case of multiple (N > 2) particles. Since our theory of SCN-driven Langevin dynamics has certain issues that could not be resolved within this framework, in this article we also provide another approach to the problem of collectivity. We discuss the multi-particle Mori–Zwanzig model, which is fully microscopically consistent. Indeed, we show that this model supplies a lot of information, complementary to the SCN-based approach, e.g. it predicts the deterministic dynamics of the relative distance between the particles, it provides an approximation for non-equilibrium effective interactions and predicts the collective sub-diffusion of tracers in the group. These results provide the short-range, inertial limit of the earlier model and agree with its predictions under some general conditions. In this article we also review the origin of SCN and its consequences for a variety of physical systems, with emphasis on the colloids.