Lattice Model Research Articles

Molecular heat transport across a time-periodic temperature gradient.

The time-periodic modulation of a temperature gradient can alter the heat transport properties of a physical system. Oscillating thermal gradients give rise to behaviors such as modified thermal conductivity and controllable time-delayed energy storage that are not present in a system with static temperatures. Here, we examine how the heat transport properties of a molecular lattice model are affected by an oscillating temperature gradient. We use analytical analysis and molecular dynamics simulations to investigate the vibrational heat flow in a molecular lattice system consisting of a chain of particles connected to two heat baths at different temperatures, where the temperature difference between baths is oscillating in time. We derive expressions for heat currents in this system using a stochastic energetics framework and a nonequilibrium Green's function approach that is modified to treat the nonstationary average energy fluxes. We find that emergent energy storage, energy release, and thermal conductance mechanisms induced by the temperature oscillations can be controlled by varying the frequency, waveform, and amplitude of the oscillating gradient. The developed theoretical approach provides a general framework to describe how vibrational heat transmission through a molecular lattice is affected by temperature gradient oscillations.

Fluid dynamics and leukocyte transit in the lymphatic system

Abstract The lymphatic system plays a vital role in maintaining fluid balance in living tissue and serves as a pathway for the transport of antigen, immune cells and metastatic cancer cells. Here, we investigate how the movement of cells through a contracting lymphatic vessel differs from steady flow using a lattice Boltzmann-based computational model. Our model consists of cells carried by flow in a 2D vessel with regularly spaced, bi-leaflet valves that ensure net downstream flow as the vessel walls contract autonomously in response to calcium and nitric oxide levels regulated by stretch and shear stress levels. The orientation of the vessel with respect to gravity, which may oppose or assist fluid flow, significantly modulates cellular motion due to its effect on the contraction dynamics of the vessel, even when the cells themselves are neutrally buoyant. Additionally, our model shows that cells are carried along with the flow, but when the vessel is actively contracting, they move faster than the average fluid velocity. We also find that the fluid forces cause significant deformation of the compliant cells, especially in the vicinity of the valves. Our study highlights the importance of considering the complex, transient flows near the valves in understanding cellular motion in lymphatic vessels.

Migdal–Eliashberg superconductivity in a Kondo lattice

We apply the Migdal–Eliashberg theory of superconductivity to heavy-fermion and mixed valence materials. Specifically, we extend the Anderson lattice model to a case when there exists a strong coupling between itinerant electrons and lattice vibrations. Using the saddle-point approximation, we derive a set of coupled nonlinear equations which describe competition between the crossover to a heavy-fermion or mixed-valence regimes and conventional superconductivity. We find that superconductivity at strong coupling emerges on par with the development of the many-body coherence in a Kondo lattice. Superconductivity is gradually suppressed with the onset of the Kondo screening and for strong electron-phonon coupling the Kondo screening exhibits a characteristic re-entrant behavior. Even though for both weak and strong coupling limits the suppression of superconductivity is weaker in the mixed-valence regime compared to the local moment one, superconducting critical temperature still remains nonzero. In the weak coupling limit the onset of the many body coherence develops gradually, in the strong coupling limit it emerges abruptly in the mixed valence regime while in the local moment regime the f-electrons remain effectively decoupled from the conduction electrons. Possibility of experimental realization of these effects in Ce-based compounds is also discussed.

Complexity of fermionic states

How much information does a fermionic state contain? To address this fundamental question, we define the complexity of a particle-conserving many-fermion state as the entropy of its Fock space probability distribution, minimized over all Fock representations. The complexity characterizes the minimum computational and physical resources required to represent the state and store the information obtained from it by measurements. Alternatively, the complexity can be regarded as a Fock space entanglement measure describing the intrinsic many-particle entanglement in the state. We establish a universal lower bound for the complexity in terms of the single-particle correlation matrix eigenvalues and formulate a finite-size complexity scaling hypothesis. Remarkably, numerical studies on interacting lattice models suggest a general model-independent complexity hierarchy: ground states are exponentially less complex than average excited states, which, in turn, are exponentially less complex than generic states in the Fock space. Our work has fundamental implications on how much information is encoded in fermionic states. Published by the American Physical Society 2024

Two-dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method

Two-dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method

Reduced stress propagation leads to increased mechanical failure resistance in auxetic materials

Materials with a negative Poisson ratio have the counterintuitive property of expanding laterally when they are stretched longitudinally. They are accordingly termed auxetic, from the Greek auxesis meaning to increase. Experimental studies have demonstrated auxetic materials to have superior material properties, compared with conventional ones. These include synclastic curvature, increased acoustic absorption, increased resilience to material fatigue, and increased resistance to mechanical failure. Until now, the latter observations have remained poorly understood theoretically. With this motivation, the contributions of this work are twofold. First, we elucidate analytically the way in which stress propagates spatially across a material following a localized plastic failure event, finding a significantly reduced stress propagation in auxetic materials compared with conventional ones. In this way, a plastic failure event occurring in one part of a material has a reduced tendency to trigger knock-on plastic events in neighboring regions. Second, via the numerical simulation of a lattice elastoplastic model, we demonstrate a key consequence of this reduced stress propagation to be an increased resistance to mechanical failure. This is seen not only via an increase in the externally measured yield strain, but also via a decreased tendency for plastic damage to percolate internally across a sample in catastrophic system-spanning clusters.

Swelling Behaviors of Natural Rubber/Solvent Systems Based on the Extended Modified Double Lattice Model

AbstractSwelling experiments are conducted on nonfiller natural rubber using four solvents (toluene, cyclohexane, tetrahydrofuran (THF), and methylethylketone (MEK)) over temperatures from 10 to 70 °C. Toluene, cyclohexane, and THF, classified as effective solvents, show swelling ratios between 3 and 7, influenced by the crosslink density of the rubber. MEK, however, has a lower ratio of 1.5 to 2. Temperature has a minor impact on swelling compared to the crosslink density. The study evaluates the Extended Modified Double Lattice (EMDL) model for its mixing contribution in polymer network swelling, aiming to improve the Flory–Hüggins (FH) model. The superiority of EMDL above FH is in the boundary condition at the unvulcanized state, the former aligning its interaction energy with values from solvent activities in primary linear polymer/solvent solutions, unlike the FH model. The EMDL model also accounts for oriented interactions in polar solvents through a secondary lattice, linking specific interaction energy with solvent dipole moments. The study observes a nonlinear correlation between crosslinking density and sulfur amount, proposing a nonrandom mixing at lower sulfur concentrations. This model shows strong alignment with experimental data, suggesting that replacing the FH model's mixing contribution with the EMDL model could improve results with minimal additional complexity.

Lattice numerical modeling of the effects of synthetic gas flow rate and pre-existing cleat dimensions on the crack propagation and cavity growth in UCG process

Lattice numerical modeling of the effects of synthetic gas flow rate and pre-existing cleat dimensions on the crack propagation and cavity growth in UCG process

Phase diagram of a square lattice model of XY spins with direction-dependent interactions

Phase diagram of a square lattice model of XY spins with direction-dependent interactions

Modeling from the first principles of the electronic properties of compositions of REE as precursors of high-temperature superconductors

Modeling of the first principles of the electronic properties of complex oxides of rare earth elements (BaY2O4, BaGd2O4, BaLu2O4) as precursors of high-temperature superconductors has been performed. The VASP software package was used as a modeling environment, in particular the method of coupled plane waves (PAW method), which allows us to obtain fairly accurate results for calculating the electron density and band structure. From the analysis of the obtained band energy structure, it follows that the studied REE oxides have a band gap width Eg = 3.29–3.84 eV, which is characteristic for dielectric materials. The studied compounds based on these rare earth elements selected from the yttrium (Y, La, Gd–Lu) and cerium (Ce–Eu) groups are characterized by an increase in Fermi energy and a decrease in the band gap as the atomic number (39, 64, 71) of the element in the periodic table increases. A method for modeling the quantum layers of the studied materials by simulating the restriction of the crystal structure along one of the coordinate axes is proposed. This representation approximates the model of the crystal lattice of REE oxides to the situation of analyzing a quantum layer whose thickness is equal to the size of the crystal cell along the specified axis. The rupture of atomic bonds in a crystal is simulated by increasing the distance between atomic layers along this axis to values at which the value of free energy is stabilized. In the quantum layer of rare earth element oxide (with its thickness close to 1 nm), a wider range of energy values is formed in which electrons are distributed than is observed in the continuous version, and the expansion of the electron distribution area extends to the energy levels of the band gap. This is explained by the fact that the geometric discretization of nanoscale structures determines the discreteness of the quantum-dimensional energy spectrum.

Evaluation of the effect of oxygen incorporation on the thermo–chemical–mechanical properties of the proton-conducting oxide BaZr0.8Yb0.2O3-δ

This study aims to evaluate the effects of multiple defect species produced by water and oxygen incorporation on the lattice parameters of BaZr0.8Yb0.2O3-δ (BZYb20) and model its chemical expansion considering these effects. In this study, the lattice constant of BZYb20 was investigated under oxygen partial pressure (pO2 = 1–10−3 bar), water vapor partial pressure (pH2O = 0.0023 bar and dry) and over a wide range of temperatures (473–1173 K) using two approaches: model calculations and high-temperature X-ray diffraction (HT-XRD). HT-XRD measurements revealed that the lattice expansion of BZYb20 changed within 700–900 K in a humidified atmosphere. In a nonhumidified atmosphere, this temperature range shifts lower. High-temperature gravimetric measurements of oxygen incorporation showed that the change in oxygen vacancy concentration was sufficiently small, and the effect of oxygen incorporation on the lattice constant was negligible. High-temperature gravimetric measurements of water incorporation yielded thermodynamic parameters for the hydration reaction. Based on these results, the HT-XRD results were reproduced by fitting a lattice constant model that neglects the effects of oxygen. Therefore, the effect of oxygen incorporation on chemical expansion can be ignored, and the chemical expansion can be estimated using the model developed in this study.

Topological oscillated edge states in trimer lattices

We investigate a 1D trimer optical lattice model. Two kinds of topological oscillating optical transmission phenomena at edges are shown. The exact and the approximate solutions of the system’s edge states are obtained with and without the inversion symmetry for this system respectively. Based on the solutions, the existence and the periods of the oscillations can be controlled arbitrarily. Moreover, in a system without inversion symmetry, controlling the incident beam can eliminate both types of oscillations, resulting in a more stable edge state compared to the one with inversion symmetry. This prompts us to reconsider topological systems under symmetry protection.

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

Three-dimensional numerical modeling of the temporal evolution of backward erosion piping

Backward erosion piping (BEP) is a complex degradation mechanism in geotechnical flood protection infrastructure (GFPI) that is still relatively less understood, particularly when considering its time-dependent features. This manuscript presents a novel dual random lattice modeling approach for three-dimensional simulation of BEP, with a focus on its evolution over time. The key novelty of this presented framework is twofold: (1) we propose and incorporate a novel constitutive relationship for computation of time-dependent soil erosion based on the theory of rate processes, and (2) we devise an algorithm for calculation of coupled degradation of the dual lattices for accurate computation of 3-D hydraulic gradients. The constitutive relationship was developed from fundamental granular physics, and brings the potential to provide deeper fundamental physical understanding of the phenomenon. The capabilities of the modeling framework are investigated by comparison with available laboratory experiments which illustrates good agreement in the spatial advancement of piping erosion, pipe progression speeds, as well as the evolution of local gradients. To the best knowledge of the authors, the presented model is the first to be able to capture all of the aforementioned features when simulating BEP.

Clustering-enhanced Lattice discrete particle modeling for quasi-brittle fracture and fragmentation analysis

Clustering-enhanced Lattice discrete particle modeling for quasi-brittle fracture and fragmentation analysis

Non-Poissonian bursts in the arrival of phenotypic variation can strongly affect the dynamics of adaptation.

Modelling the rate at which adaptive phenotypes appear in a population is a key to predicting evolutionary processes. Given random mutations, should this rate be modelled by a simple Poisson process, or is a more complex dynamics needed? Here we use analytic calculations and simulations of evolving populations on explicit genotype-phenotype maps to show that the introduction of novel phenotypes can be 'bursty' or overdispersed. In other words, a novel phenotype either appears multiple times in quick succession, or not at all for many generations. These bursts are fundamentally caused by statistical fluctuations and other structure in the map from genotypes to phenotypes. Their strength depends on population parameters, being highest for 'monomorphic' populations with low mutation rates. They can also be enhanced by additional inhomogeneities in the mapping from genotypes to phenotypes. We mainly investigate the effect of bursts using the well-studied genotype-phenotype map for RNA secondary structure, but find similar behaviour in a lattice protein model and in Richard Dawkins's biomorphs model of morphological development. Bursts can profoundly affect adaptive dynamics. Most notably, they imply that fitness differences play a smaller role in determining which phenotype fixes than would be the case for a Poisson process without bursts.

A new curved road lattice model integrating the multiple prediction effect under V2X environment

In order to explore the driver's multiple prediction effects of flux changes (MPEFC) on traffic flow on a curved road, parameters of the weighted flow gradient of multiple lattices ahead are introduced to characterize the MPEFC effect on a curved road. On this basis, combined with the characteristics of a curved road, a lattice model considering the drive's MPEFC effects is proposed under the V2X environment. The stability criterion is obtained. Through the reduced perturbation method, the density wave equation and its solution used to describe the propagation law of traffic congestion near the critical point are derived. The results show that the stability of traffic flow on a curved road increases along with the increase in radian, and that considering the MPEFC effects simultaneously has a significant stabilizing effect for traffic flow on a curved road. It is also discovered that under the V2X environment, the traffic flow is optimally stabilized by considering the information of just two lattices ahead.

Dynamical behaviors of an impulsive stochastic neural field lattice model

This paper is concerned with the asymptotic behaviors of the solutions of an impulsive stochastic neural field lattice model driven by nonlinear noise. We first show the existence and uniqueness of weak pullback mean random attractors for the impulsive stochastic systems. Then by the properties of Markov processes, the existence of evolution system of measures for the impulsive stochastic systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.

Topological defects and boundary states in four-dimensional topological insulator

We show the connection between the second Chern number and topological defects, in a (4+1)-dimensional time-reversal invariant Dirac lattice model. It is discovered that two types of topological defects, the five-dimensional (5D) and four-dimensional (4D) point defects arise from the singular points of wave functions together with the geometric meaning of the second Chern number. We demonstrated that the 5D point defects appear at the band crossing positions with a topological transition, leading to a jump of the second Chern number. The 4D point defects exist in an insulating bulk, whose topological charges can give the evaluations of the second Chern number of energy bands. Finally, we discussed the possible structures of the boundary states in the light of the realization way of the 4D model. Our theory provides not only a new perspective to grasp the second Chern number, but also a simple approach to derive its values without calculating any integrals.

Dynamics of a Random Hopfield Neural Lattice Model with Adaptive Synapses and Delayed Hebbian Learning

Dynamics of a Random Hopfield Neural Lattice Model with Adaptive Synapses and Delayed Hebbian Learning