Lattice Model Research Articles

Copper(II) salts and complexes of 2-amino-5-nitropyridine*

Four new copper compounds of 2-amino-5-nitropyridine/pyridinium (5NAP/5NAPH) have been prepared and characterized: (5NAPH)2[CuBr4], 2; (d2-5NAPD)2[CuBr4], 2a; (5NAP)2CuCl2, 3; (5NAP)2CuBr2, 4. Compounds 2 and 2a are isomorphous and crystallize in the triclinic space group P-1. Packing is stabilized by hydrogen/deuterium bonds. Short Br…Br contacts provide potential magnetic superexchange pathways, but only very weak antiferromagnetic exchange is observed (J/kB∼-2 K). Compounds 3 and 4 are also isomorphous and crystallize in the monoclinic space group P21/c. The molecules are linked into chains by bihalide bridges, and the chains linked into rectangular/square layers by short X…X. contacts. Variable temperature magnetic data were best fit by the S = ½ antiferromagnetic rectangular model for 3 (C = 0.429(1) emu-K/mol-Oe, J/kB = −9.38(6) K, J’/kB = −5.91(4) K). Variable temperature magnetic susceptibility data for 4 were best fit by the two-dimensional antiferromagnetic square lattice model (C = 0.43(1) emu-K/mol-Oe, J/kB = −36.5(2) K).

An improved coupled map lattice model and its application in image encryption

An improved coupled map lattice model and its application in image encryption

Pylattica: a package for prototyping lattice models in chemistry and materials science

pylattica: a package for prototyping lattice models in chemistry and materials science

Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions.

We show that numerical linked cluster expansions (NLCEs) based on sufficiently large building blocks allow one to obtain accurate low-temperature results for the thermodynamic properties of spin lattice models with continuous disorder distributions. Specifically, we show that such results can be obtained computing the disorder averages in the NLCE clusters before calculating their weights. We provide a proof of concept using three different NLCEs based on L, square, and rectangle building blocks. We consider both classical (Ising) and quantum (Heisenberg) spin-1/2 models and show that convergence can be achieved down to temperatures that are up to two orders of magnitude lower than the relevant energy scale in the model. Additionally, we provide evidence that in one dimension one can obtain accurate results for observables such as the energy down to their ground-state values.

Iwahori‐metaplectic duality

AbstractWe construct a family of solvable lattice models whose partition functions include ‐adic Whittaker functions for general linear groups from two very different sources: from Iwahori‐fixed vectors and from metaplectic covers. Interpolating between them by Drinfeld twisting, we uncover unexpected relationships between Iwahori and metaplectic Whittaker functions. This leads to new Demazure operator recurrence relations for spherical metaplectic Whittaker functions. In prior work of the authors it was shown that the row transfer matrices of certain lattice models for spherical metaplectic Whittaker functions could be represented as ‘half‐vertex operators’ operating on the ‐Fock space of Kashiwara, Miwa and Stern. In this paper the same is shown for all the members of this more general family of lattice models including the one representing Iwahori Whittaker functions.

Relating fragile-to-strong transition to fragile glass via lattice model simulations.

Glass formers are, in general, classified as strong or fragile depending on whether their relaxation rates follow Arrhenius or super-Arrhenius temperature dependence. There are, however, notable exceptions, such as water, which exhibit a fragile-to-strong (FTS) transition and behave as fragile and strong, respectively, at high and low temperatures. In this work, the FTS transition is studied using a distinguishable-particle lattice model previously demonstrated to be capable of simulating both strong and fragile glasses [C.-S. Lee, M. Lulli, L.-H. Zhang, H.-Y. Deng, and C.-H. Lam, Phys. Rev. Lett. 125, 265703 (2020)0031-900710.1103/PhysRevLett.125.265703]. Starting with a bimodal pair-interaction distribution appropriate for fragile glasses, we show that by narrowing down the energy dispersion in the low-energy component of the distribution, a FTS transition is observed. The transition occurs at a temperature at which the stretching exponent of the relaxation is minimized, in agreement with previous molecular dynamics simulations.

Subsystem eigenstate thermalization hypothesis for translation invariant systems.

The eigenstate thermalization hypothesis for translation invariant quantum spin systems has been proved recently by using random matrices. In this paper, we study the subsystem version of the eigenstate thermalization hypothesis for translation invariant quantum systems without referring to random matrices. We first find a relation between the quantum variance and the Belavkin-Staszewski relative entropy. Then, by showing the small upper bounds on the quantum variance and the Belavkin-Staszewski relative entropy, we prove the subsystem eigenstate thermalization hypothesis for translation invariant quantum systems with an algebraic speed of convergence in an elementary way. The proof holds for most of the translation invariant quantum lattice models with exponential or algebraic decays of correlations.

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.

Elastic properties prediction of two- and three-dimensional multi-material lattices

Advances in multi-material additive manufacturing have opened unprecedented new opportunities for the design and manufacture of lightweight multifunctional structures. The ability to create complex topologies, at a relatively fine resolution, in addition to controlling the material composition on a voxel basis have significantly expanded the design space. To explore this large design space efficiently, accurate and cost-effective modeling tools are essential. In this paper, mechanics-based models for predicting the elastic properties of multi-material 2D and 3D lattice structures are developed or extended. The outcomes are compared with the predictions obtained from finite element models and experimental data. The results reveal that the adapted analytical models demonstrate good accuracy in predicting the elastic modulus of multi-material lattices for relative densities up to approximately 25 % while have considerably less computational cost compared to finite element using solid elements (providing the most accurate results in comparison with experiment). Careful consideration of the accuracy of the predictions is necessary for the use of these models for lattices with high relative density values. Besides, several homogenization-based models were studied to investigate their applicability to multi-material lattice structures when the assumption of scale-separation is considered valid. The capability of these models in predicting the whole elasticity tensor and the potential of multi-material lattices in manipulating the anisotropy are demonstrated. Finally, the introduced prediction frameworks are compared in order to provide an overview of their respective advantages and disadvantages in the case of multi-material lattice structures.

Fluid dynamics and leukocyte transit in the lymphatic system.

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. In this study, 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.

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.

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.

Examination of the role of mutualism in immune evasion.

Though the earliest stages of oncogenesis, post initiation, are not well understood, it is generally appreciated that a successful transition from a collection of dysregulated cells to an aggressive tumour requires complex ecological interactions between cancer cells and their environment. One key component of tumorigenesis is immune evasion. To investigate the interplay amongst the ecological behaviour of mutualism and immune evasion, we used a computational simulation framework. Sensitivity analyses of the growth of a virtual tumour implemented as a 2D-hexagonal lattice model suggests tumour survival depends on the interplay between growth rates, mutualism and immune evasion. In 60% of simulations, cancer clones with low growth rates, but exhibiting mutualism were able to evade the immune system and continue progressing suggesting that tumours with equivalent growth rates and no mutualism are more likely to be eliminated than tumours with mutualism. Tumours with faster growth rates showed a lower dependence upon mutualism for progression. Geostatistical analysis showed decreased spatial heterogeneity over time for polyclonal tumours with a high division rate. Overall, these results suggest that in slow growing tumours, mutualism is critical for early tumorigenesis.