Macroscopic State Research Articles

Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres

The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic equation, recently derived for this system. As a consequence of the confinement, the pressure tensor and the heat flux contain, in addition to the terms associated to the motion of the particles, collisional transfer contributions, similar to those that appear beyond the dilute limit. The complexity of these terms, and of the kinetic equation itself, compromise the potential of the equation to describe the rich phenomenology observed in this kind of systems. For this reason, a simpler model equation based on the Boltzmann equation is proposed. The model is formulated to keep the main properties of the underlying equation, and it is expected to provide relevant information in more general states than the original equation. As an illustration, the solution describing a macroscopic state with uniform temperature, but a density gradient perpendicular to the plates is considered. This is the equilibrium state for an elastic system, and the inhomogeneous cooling state for the case of inelastic hard spheres. The results are in good agreement with previous results obtained directly from the Boltzmann equation.

Ductile failure as a constitutive instability in porous plastic solids

A criterion for ductile rupture is derived using Rice’s theory for macroscopic strain localization, and a constitutive relation for porous plastic solids that accounts for inhomogeneous yielding at the mesoscale. At the microscopic scale, it is assumed that failure occurs by void coalescence along a band of voids. An approximate, parameter-free closed form expression for the failure criterion is derived as a function of a single scalar damage variable –the porosity– and the macroscopic stress state, characterized by the stress triaxiality and Lode parameters. For practical applications, an uncoupled approach is developed whereby the failure criterion is supplemented with a damage-free plasticity model and a loading path dependent damage evolution law. The predictive capabilities of the approach are illustrated by comparisons with finite element cell model studies. In particular, the influence of strain hardening is investigated in some detail.

Statistical properties of cold bosons in a ring trap

A study of an interacting system of bosons in a ring trap at a finite temperature is presented. We consider a gas with contact and long-range dipolar interactions within a framework of the classical fields approximation. For a repulsive gas we have obtained coherence length, population of the ground state and its fluctuations as a function of temperature. In the case of an attractive gas we study local density fluctuations. Additionally, we exactly calculate the partition function for the ideal gas in the canonical ensemble and derive several other macroscopic state functions.

Evolution of fabric in spherical granular assemblies under the influence of various loading conditions through DEM

Fabric of a granular assembly represents the topology of the contact network. This paper investigates the evolution of contact anisotropy (fabric) and average coordination number for a granular assembly subjected to uniaxial compression through the Discrete Element Method (DEM). A monosize three-dimensional random close-packed granular assembly with periodic boundary conditions under uniaxial compression is considered in this work. The fabric evolution is studied by post-processing the output data of the DEM simulation. The influence of cyclic loading, strain rate, and Young’s modulus on the evolution of contact anisotropy and average coordination number is presented. The Young’s modulus of the particle shows a significant influence on the particle contact creation during compression of the granular assembly with high strain rate. Effect of inertia on the contact anisotropy is observed to be significant during the compression of granular assemblies with different Young’s modulus under high strain rate. The paper concludes with a semi-empirical model to predict the evolution of contact anisotropy as a function of the macroscopic stress state of the assembly during quasi-static uniaxial compaction. The model also introduces two microscopic non-dimensional parameters that are independent of friction between the particles and can be used to relate the macroscopic stresses with the contact anisotropy.

By-passing fluctuation theorems

Fluctuation theorems impose constraints on possible work extraction probabilities in thermodynamical processes. These constraints are stronger than the usual second law, which is concerned only with average values. Here, we show that such constraints, expressed in the form of the Jarzysnki equality, can be by-passed if one allows for the use of catalysts---additional degrees of freedom that may become correlated with the system from which work is extracted, but whose reduced state remains unchanged so that they can be re-used. This violation can be achieved both for small systems but also for macroscopic many-body systems, and leads to positive work extraction per particle with finite probability from macroscopic states in equilibrium. In addition to studying such violations for a single system, we also discuss the scenario in which many parties use the same catalyst to induce local transitions. We show that there exist catalytic processes that lead to highly correlated work distributions, expected to have implications for stochastic and quantum thermodynamics.

Domain wall melting in spin-1 XXZ chains

In this letter we study the non-equilibrium spin dynamics in the non-integrable spin-1 XXZ chain, emerging after joining two macroscopic pure states with different magnetizations. Employing the so-called time-dependent variational principle (TDVP) we simulate the dynamics of the total magnetization in the right (left) half of the system up to times that are normally inaccessible by standard tDMRG methods. We identify three distinct phases depending on the anisotropy of the chain, corresponding to diffusive, marginally super-diffusive and insulating. We observe a transient ballistic behaviour with a crossover time that diverges as the isotropic point is approached. We conclude that on intermediate-large time scales the dynamics is well described by the integrable Landau-Lifschitz classical differential equation.

Single-Cell Entropy to Quantify the Cellular Order Parameter from Single-Cell RNA-Seq Data

The cell is the basic functional and biological unit of life, and a complex system that contains a huge number of molecular components. How can we quantify the macroscopic state of a cell from the microscopic information of these molecular components? This is a fundamental question to increase the understanding of the human body. The recent maturation of single-cell RNA sequencing (scRNA-seq) technologies has allowed researchers to gain information on the transcriptomes of individual cells. Although considerable progress has been made in terms of cell-type clustering over the past few years, there is no strong consensus about how to define a cell state from scRNA-seq data. Here, we present single-cell entropy (scEntropy) as an order parameter for cellular transcriptome profiles from scRNA-seq data. scEntropy is a straightforward parameter with which to define the intrinsic transcriptional state of a cell that can provide a quantity to measure the developmental process and to distinguish different cell types. The proposed scEntropy followed by Gaussian mixture model (scEGMM) provides a coherent method of cell-type classification that is simple, includes no parameters or clustering and is comparable to existing machine learning-based methods in benchmarking studies. The results of cell-type classification based on scEGMM are robust and easy to biologically interpret.

Entangling Macroscopic Light States by Delocalized Photon Addition.

We present a scheme, based on the delocalized heralded addition of a single photon, to entangle two or more distinct field modes, each containing arbitrary light states. A high degree of entanglement can in principle endure light states of macroscopic intensities and is expected to be particularly robust against losses. We experimentally establish and measure significant entanglement between two identical weak laser pulses containing up to 60 photons each.

Linear Aging Behavior at Short Timescales in Nanoscale Contacts.

Nanoscale silica-silica contacts were recently found to exhibit logarithmic aging for times ranging from 0.1 to 100s, consistent with the macroscopic rate and state friction laws and several other aging processes. Nanoscale aging in this system is attributed to progressive formation of interfacial siloxane bonds between surface silanol groups. However, understanding or even data for contact behavior for aging times <0.1 s, before the onset of logarithmic aging, is limited. Using a combination of atomic force microscopy experiments and kinetic MonteCarlo simulations, we find that aging is nearly linear with aging time at short timescales between ∼ 5 and 90ms. We demonstrate that aging at these timescales requires the existence of a particular range of reaction energy barriers for interfacial bonding. Specifically, linear aging behavior consistent with experiments requires a narrow peak close to the upper bound of this range of barriers. These new insights into the reaction kinetics of interfacial bonding in nanoscale aging advance the development of physically based rate and state friction laws for nanoscale contacts.

Cooling the mechanical resonator by Gaussian pulses

The optomechanical system has been widely used torealize the quantum ground state cooling of mechanical resonator, which is the way to create macroscopic quantum state. How to get the better cooling effect is evidently the central point. However, it has been demonstrated that there is a cooling limit if using only one single continuous-wave pump to drive the mechanical resonator, i.e., the cooling rate cannot be decreased by increasing the drive intensity or the mechanical frequency, so that the new dynamics should be developed. Here we present an approach to cool the mechanical resonator by the Gaussian pulses. For the pulsed optomechanical system, the common steady-state expansion approach is not available, since no steady state can be found in most cases. We use the new linearized approach to get the effective Hamiltonian and the dynamical evolution of the optomechanical system, with which the thermal phonon number of the mechanical resonator can be achieved directly. After investigating how the pulse profile, drive intensity and pulse duration affect the evolution of thermal phonon number in details, we show that the mechanical resonator can be well cooled down to the ground state by a single pulse, and can be well preserved by the multiple pulses, with the appreciated drive intensity, duration. Moreover, the character of drive intensity increasing and decreasing of the pulse profile, enables one to delay the squeezing effect which results in the heating of the mechanical resonator. As a result, the cooling limit of single continuous-wave driven optomechanical system can be broken by the pulsed optomechanical system. Even the half of the cooling limit of the continuous optomechanical system can be achieved by the short and strong Gaussian pulses, which is the main advantage of the ground state cooling by pulse drives.

Observation of exciton polariton condensation in a perovskite lattice at room temperature

Bose-Einstein condensation in strongly correlated lattices provides the possibility to coherently generate macroscopic quantum states, which have attracted tremendous attention as ideal platforms for quantum simulation. Ultracold atoms in optical lattices are one of such promising systems, where their realizations of different phases of matter exhibit promising applications in condensed matter physics, chemistry, and cosmology. Nevertheless, this is only accessible with ultralow temperatures in the nano to micro Kelvin scale set by the typical inverse mass of an atom. Alternative systems such as lattices of trapped ions and superconducting circuit arrays also rely on ultracold temperatures. Exciton polaritons with extremely light effective mass, are regarded as promising alternatives to realize Bose-Einstein condensation in lattices at higher temperatures. Along with the condensation, an efficient exciton polariton quantum simulator would require a strong lattice with robust trapping at each lattice site as well as strong inter-site coupling to allow coherent quantum motion of polaritons within the lattice. However, exciton polaritons in a strong lattice have only been shown to condense at liquid helium temperatures. Here, we report the observation of exciton polariton condensation in a one-dimensional strong lead halide perovskite lattice at room temperature. Modulated by deep periodic potentials, the strong lead halide perovskite lattice exhibits a large forbidden bandgap opening up to 13.3 meV and a lattice band up to 8.5 meV wide, which are at least 10 times larger than previous systems. Above a critical density, we observe exciton polariton condensation into py orbital states with long-range spatial coherence at room temperature. Our result opens the route to the implementation of polariton condensates in quantum simulators at room temperature.

Revealing photonic Lorentz force as the microscopic origin of topological photonic states

Abstract Charged particles like electrons moving in a magnetic field encounter Lorentz force, which governs the formation of electronic topological edge states in quantum Hall effect systems. Here we show that photons transporting in magneto-optical materials and structures also encounter a physical effect called photonic Lorentz force via the indirect interaction with the magneto-optical medium assisted effective magnetic field. This effect can induce half-cycle spiral motion of light at the surface of a homogeneous metallic magneto-optical medium and inhomogeneous magneto-optical photonic crystals, and it governs the intriguing one-way transport properties of robustness and immunity against defects, disorders, and obstacles. Thus, photonic Lorentz force serves as the fundamental microscopic origin of macroscopic photonic topological states, much the same as classical Lorentz force does to electronic topological states.

Феномен нелінійного мислення у науці

In the article, the author’s attention is focused on modern scientific interpretations of the phenomenon of non-determinism. The author also focused on generalizing the results of the study by scientists of nonlinear processes of self-organization of complex systems. The main objective of this article is to study the phenomenon of the so-called “non-linear thinking” in science. Of particular interest was the philosophical assessment of the very subject of this thinking. The author tried to reveal the essence in the interpretation of statistical laws. He also sought to prove that these patterns represent a more fundamental aspect of reality than dynamic laws. The choice of the topic of the article, the application of its theoretical and methodological approaches are determined by the very subject of thought and the nature of the tasks set. The following methods of cognition were used in the article: general philosophical, special general scientific theoretical methods. The author followed the principle of objectivity, applied causal analysis. So it turned out that many dynamical systems - physical, chemical, biological - fall under nonlinear dynamic equations. Here they are entirely predictable. However, they become unpredictable if they appear at the macro level. After all, individual systems are considered “normal” and function in accordance with deterministic laws only up to a certain time. This is the period between situations of bifurcation. Here their “behavior” can be fully predicted. However, in their own development, they can come to certain extreme changes. To further overcome them, two options for the state of quality appear. Each of them can happen first. This happens when the object passes through the so-called critical points. It is impossible to predict which variant will achieve ontological legitimation. For some time, the object experiences microfluctuations between the two physical alternatives. But with an increase in the value of the key parameter of one of the alternatives, further complication of the state occurs. This process is a sequential bifurcation, like the alternation of two existing states. It is characterized by periods of instability. In this case, it is impossible to predict the state of development of the object. Even more effective is the study of the phenomenon of non-determinism in relation to space-time models of the behavior of systems. By means of scientific research, it was reliably established that at the points of bifurcation of such an environment, successive microchanges reach large values. Their scale is sometimes compared to the system itself. Here the system changes due to fluctuations, up to the appearance of a new quality. In modern cosmological concepts, the results of the study of nonequilibrium systems are fully used. Mainly in the field of verification of the new hypothesis of cosmogenesis. Scientists hypothesize that the universe was in extremely nonequilibrium states in the first moments of Planck's time. If it were otherwise, then the Universe at the dawn of its own formation would be in a state of equilibrium. Then, according to the law of action of the masses, a quantitative equality of matter and antimatter would arise. Therefore, in opposition of matter and antimatter, equal amounts of them would annihilate each other. A deep understanding of the significance of the new style of scientific thinking is closely related to a radical revision of the idea of self-organization of matter in nature. This ability to change was previously studied only within the limits of macroscopic statistical equilibrium states. This is a new style of scientific thinking and the resulting new picture of the world. They are related to the study of nonlinear and unbalanced open systems. All this demonstrates a non-trivial understanding of matter itself and its ability to self-organize. Matter takes on new forms of existence. Their appearance is due to their own internal forces and the properties of matter itself. Here, worldview generalizations of such discoveries are important. After all, they allow you to more clearly see the world, which is self-organizing as a whole and at different levels of its existence. The generalized results of studying the topic give grounds for the following conclusion. The subject of the new style of scientific thinking is the nonlinear processes of selforganization of matter. This style of thinking, as well as the discoveries of non-linear natural science, make it possible to understand the nature of the surrounding world in a new way. Namely - the ability of a substance to self-organize as a whole and at various levels of its own being. This is due to the internal forces and properties of this world

A density functional theory based thermodynamic model of hydrogen coverage on the W(110) surface

Tungsten will be used as a plasma facing material in the next generation of fusion reactors. To aid in understanding atomic scale H–W interactions, we investigated hydrogen coverage on the tungsten (110) surface via periodic density functional theory, providing the most stable configurations that hydrogen forms on the surface at coverage ratios of interval 0.25, step-wise, up to a full mono-layer of hydrogen. We then calculate the Gibbs free energy for the stable configurations in the presence of hydrogen gas at specified temperature and pressure. It follows that the configuration, and corresponding coverage ratio, which yields the lowest Gibbs free energy is used to estimate the macroscopic surface state. Our findings based on the model compare well to low energy electron diffraction measurements, primarily the presence of well-ordered phases with coverage ratios 0.5, 0.75, and 1.0, respectively, and that no ordered phases are expected as temperature increases and surface depletion occurs.

Area Occupancy-Based Adaptive Density Estimation for Mixed Road Traffic

Managing congestion in mixed traffic conditions, characterized by heterogeneous and lane-less traffic, is a challenging task. Traditionally density, defined as the number of vehicles in a road stretch, is used to quantify congestion. However, direct measurement of density is difficult and hence is usually estimated from other variables. In this paper, a relationship is derived between traffic density and area occupancy, a variable that can incorporate heterogeneity and lane-less movement. Using the derived density-area occupancy relation, a non-continuum macroscopic single state linear time varying model was developed. Estimation of density was done by using the Kalman filtering technique and corroborated with simulated density. The need for dynamic estimation is motivated by evaluating the performance of two static estimation schemes in the presence of uncertainties. Performance was tested for different traffic scenarios such as congestion and non-recurrent traffic incidents. Further, to improve the estimation accuracy in scenarios involving transitions in traffic conditions, an adaptive estimator was developed. It was found that the adaptive estimator provided the best estimation accuracy.

Synchronization in coupled oscillators with multiplex interactions

The study of synchronizations in coupled oscillators is very important for understanding the occurrence of self-organized behaviors in complex systems. In the traditional Kuramoto model that has been extensively applied to the study of synchronous dynamics of coupled oscillators, the interaction function among oscillators is pairwise. The multiplex interaction mechanism that describes triple or multiple coupling functions has been a research focus in recent years. When the multiplex coupling dominates the interactions among oscillators, the phase oscillator systems can exhibit the typical abrupt desynchronization transitions. In this paper, we extensively investigate the synchronous dynamics of the Kuramoto model with mean-field triple couplings. We find that the abrupt desynchronization transition is irreversible, i.e. the system may experience a discontinuous transition from coherent state to incoherent state as the coupling strength deceases adiabatically, while the reversed transition cannot occur by adiabatically increasing the coupling. Moreover, the coherent state strongly depends on initial conditions. The dynamical mechanism of this irreversibility is theoretically studied by using the self-consistency approach. The neutral stability of ordered state is also explained through analyzing the linear-stability of the incoherent state. Further studies indicate that the system may experience a cascade of desynchronized standing-wave transitions when the width of the distribution function of natural frequencies of oscillators is changed. At the critical coupling, the motion of coupled oscillators in high-dimensional phase space becomes unstable through the saddle-node bifurcation and collapses into a stable low-dimensional invariant torus, which corresponds to the standing-wave state. The above conclusions and analyses are further extended to the case of multi-peak natural-frequency distributions. The results in this work reveal various collective synchronous states and the mechanism of the transitions among these macroscopic states brought by multiplex coupling. This also conduces to the in-depth understanding of transitions among collective states in other complex systems.

Macroscopic basic characteristics of a road network under the influence of traffic generation and attraction source agglomeration

The macroscopic fundamental diagram (MFD), which can describe the macroscopic state of a regional network intuitively, describes a unimodal, statistical and reproducible relationship between accumulation and the trip completion flow of a region. Existing researches have proved that using MFD characteristics can ‘metering’ the boundary flow and relieve the traffic congestion problem effectively. As the foundation of traffic control, existing studies on the characteristic of MFD have proved that external origin to destination demand does not influence the MFD distribution. However, the traffic generation and attraction sources in the regional road networkwill changes the distribution of traffic density of the road network, thus affecting the characteristic of MFD. However, to date, no related analysis explored the influence of the traffic generation and attraction sourcesin the regional road network. To solve this problem, according to the spatial and temporal distribution of traffic generation and attraction sources in the regional road network, this paper puts forward an aggregation degree index analysis model of traffic generation and attraction sources, based on the dynamic parameters of traffic generation and attraction sources, and section traffic impedance. Taking a square-format road network as the target, nine groups of schemes for different traffic generation and attraction sources are designed. Two conclusions can be drawn after comparing the MFD curve of the road network under different aggregation degree index of traffic generation and attraction sources: (1) when the traffic flow of the road network is in the state of free flow or critical flow, the aggregation effect of traffic generation and attraction sources has no effect on MFD distribution; (2) when the traffic flow of the road network is in the congestion flow state, the aggregation effect of traffic generation and attraction sources influences MFD distribution. Moreover, under the same road network flow conditions, the aggregation degree of traffic generation and attraction sources is lower in the road network (the distribution of traffic generation and attraction volume is more balanced), the trip completion flow of road network will be higher. Otherwise, the aggregation degree of traffic generation and attraction sources is higher in the road network (the distribution of traffic generation and attraction volume is more unbalanced), the trip completion flow of road network will be lower.

Thermodynamics of Moving Bodies or a New Approach to Emergent Gravity

Recent theoretical developments propose that gravity is emergent phenomenon. In line with this, in this paper, we show that gravitational and inertial properties of matter can be sufficiently explained by thermodynamics for a system consisting of material systems immersed in the quantum vacuum energy reservoir without reference to the microscopic constituencies of the quantum vacuum. The study focuses on the transfer of energy and matter in the interaction of material system with its vacuum surroundings and the relation of those to the system's macroscopic state variables and mechanical behavior of the system associated with forces acting on it. This analysis suggests that vacuum energy density about material systems is diminished and quantum vacuum energy density field takes on specific gradient there. Hence, gravity appears as effect of the change in the energy density of medium related with presence of another material object modifying vacuum surroundings and causing spontaneous motion of the system to minimize its energy driven by the second law. Whereas, inertia is explained to be an emergent thermodynamic effect of the change in the vacuum energy field about objects associated with the alteration of energy of systems itself due to the transfer of energy between systems to its surroundings. When those energy transfer operations do not comply with the second law of thermodynamic in terms of direction and rate of the energy flow, there will be generated resistance to the imposed changes known as inertial force. In such representation the equivalence principle finds unique definition revealing its origin.

Efficiency of a Micro-Macro Acceleration Method for Scale-Separated Stochastic Differential Equations

We discuss through multiple numerical examples the accuracy and efficiency of a micro-macro acceleration method for stiff stochastic differential equations (SDEs) with a time-scale separation between the fast microscopic dynamics and the evolution of some slow macroscopic state variables. The algorithm interleaves a short simulation of the stiff SDE with extrapolation of the macroscopic state variables over a longer time interval. After extrapolation, we obtain the reconstructed microscopic state via a matching procedure: we compute the probability distribution that is consistent with the extrapolated state variables, while minimally altering the microscopic distribution that was available just before the extrapolation. In this work, we numerically study the accuracy and efficiency of micro-macro acceleration as a function of the extrapolation time step and as a function of the chosen macroscopic state variables. Additionally, we compare the effect of different hierarchies of macroscopic state variables. We illustrate that the method can take significantly larger time steps than the inner microscopic integrator, while simultaneously being more accurate than approximate macroscopic models.

Heralded Generation of Macroscopic Superposition States in a Spinor Bose-Einstein Condensate.

Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.