Lattice Model Research Articles

Quantum simulation of a honeycomb lattice model by high-order moiré pattern

Quantum simulation of a honeycomb lattice model by high-order moiré pattern

Random matrix model of Kolmogorov-Zakharov turbulence.

We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite-size system with many degrees of freedom. For the case of a direct cascade, the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border, a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border, the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade, the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic, showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.

ЕЛЕКТРОФІЗИЧНІ ПРОЦЕСИ У КОМПОЗИТНИХ НАПІВПРОВІДНИХ ЕКРАНАХ ТА ЇХНІЙ ВПЛИВ НА ДІЕЛЕКТРИЧНІ ПАРАМЕТРИ СИЛОВИХ ВИСОКОВОЛЬТНИХ КАБЕЛІВ

The methodology for modelling the percolation process in semiconductor shields of power high-voltage cables is proposed. The semiconductor screen is represented by a two-dimensional lattice model with a polymer matrix filled with conductive carbon black particles. Model matrix's of the composite, depending on the probability of filling and the concentration of the conductive filler, agree with micrographs of the distribution of soot in the polyethylene matrix of the semiconducting screen of the power cable. Taking into account the stochastic of the percolation process, the concentration range of the conductive filler, which determines the flow threshold in the presented model, was determined. Disturbances are observed on the experimental time dependence of the absorption current of the power cable, which is indirect evidence of the accumulation of surface charges at the interface between the semiconductor screen and high-voltage polymer insulation. The time dependences of the electric capacity and the tangent of the dielectric loss angle at a frequency of 120 Hz confirm the stochastic nature of the process of accumulation of surface charges. This process causes a time-delayed interphase polarization in power high-voltage cables. References 36, figure 5.

On different approaches to integrable lattice models

Interaction-round the face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e. the models the Boltzmann weights of which satisfy the quantum Yang–Baxter equation, are of particular interest. In this paper, we investigate trigonometric Boltzmann weights of integrable IRF models. By using an ansatz proposed by one of the authors in some previous works, the Boltzmann weights of the restricted IRF models based on the affine Lie algebras su(2)k and su(3)k are computed for fundamental and adjoint representations for some fixed levels k. New solutions for the Boltzmann weights are obtained. We also study the vertex-IRF correspondence in the context of an unrestricted IRF model based on su(3)k (for general k) and discuss how it can be used to find Boltzmann weights in terms of the quantum R^ matrix when the adjoint representation defines the admissibility conditions.

Lattice Model Results for Pattern Formation in a Mixture with Competing Interactions.

A monolayer consisting of two types of particles, with energetically favored alternating stripes of the two components, is studied by Monte Carlo simulations and within a mesoscopic theory. We consider a triangular lattice model and assume short-range attraction and long-range repulsion between particles of the same kind, as well as short-range repulsion and long-range attraction for the cross-interaction. The structural evolution of the model upon increasing temperature is studied for equal chemical potentials of the two species. We determine the structure factor, the chemical potential-density isotherms, the specific heat, and the compressibility, and show how these thermodynamic functions are associated with the spontaneous formation of stripes with varying degrees of order.

Universal properties of branched copolymers in dilute solutions

We analyze the universal conformational properties of complex copolymer macromolecules, based on two topologies: the rosette structure containing fc linear branches and fr closed loops grafted to the central core, and the symmetric pom-pom structure, consisting of a backbone linear chain terminated by two branching points with functionalities f. We assume that the constituent strands (branches) of these structures can be of two different chemical species a and b. Depending on the solvent conditions, the inter- or intrachain interactions of some links may vanish, which corresponds to Θ-state of the corresponding polymer species. Applying both the analytical approach within the frames of direct polymer renormalization and numerical simulations based on the lattice model of polymer, we evaluated the set of parameters characterizing the size properties of constituent parts of two complex topologies and estimated quantitatively the impact of interactions between constituent parts on these size characteristics.

Collagen Lattice Model, Populated with Heterogeneous Cancer-Associated Fibroblasts, Facilitates Advanced Reconstruction of Pancreatic Cancer Microenvironment.

Pancreatic ductal adenocarcinoma (PDAC) is a solid-tumor malignancy. To enhance the treatment landscape of PDAC, a 3D model optimized for rigorous drug screening is essential. Within the PDAC tumor microenvironment, a dense stroma comprising a large extracellular matrix and cancer-associated fibroblasts (CAFs) is well-known for its vital role in modulating tumor growth, cellular heterogeneity, bidirectional paracrine signaling, and chemoresistance. In this study, we employed a fibroblast-populated collagen lattice (FPCL) modeling approach that has the ability to replicate fibroblast contractility in the collagenous matrix to build dense stroma. This FPCL model allows CAF differentiation by facilitating multifaceted cell-cell interactions between cancer cells and CAFs, with the differentiation further influenced by mechanical forces and hypoxia carried within the 3D structure. Our FPCL models displayed hallmark features, including ductal gland structures and differentiated CAFs with spindle shapes. Through morphological explorations alongside in-depth transcriptomic and metabolomic profiling, we identified substantial molecular shifts from the nascent to mature model stages and potential metabolic biomarkers, such as proline. The initial pharmacological assays highlighted the effectiveness of our FPCL model in screening for improved therapeutic strategies. In conclusion, our PDAC modeling platform mirrors complex tumor microenvironmental dynamics and offers an unparalleled perspective for therapeutic exploration.

Experimental investigation and numerical modeling of effect of specimen size on microwave-induced fracturing of diorite

The effect of specimen size on microwave-induced fracturing of rocks has not been well understood. In this study, the experimental tests using open-ended microwave and numerical simulations coupling COMSOL Multiphysics and four-dimensional lattice spring model (4D-LSM) were carried out to investigate the evolution process of microwave-induced cracks, and to elucidate the mechanisms responsible for size-dependent microwave-induced fracturing. The experiments show that with the increase of the specimen dimension, the number of microwave-induced cracks is almost constant, and the total crack length first increases and then decreases, while the maximum crack width and maximum crack depth decrease gradually. A comparison of the experimental and numerical temperature characteristics as well as cracking characteristics indicates that the models established in this study are reasonable in the simulation of the rock fracturing behaviours. The numerical results show that the crack initiation time increases logarithmically with the increase of the specimen dimension. For the small-sized specimens, the microwave-induced cracks started from the outer boundary of the specimen and propagated toward to specimen center and into the depth. For the medium-sized and large-sized specimens, the microwave-induced cracks initiated near the outer boundary of the antenna aperture, and then propagated toward to the center of the specimen and the outer boundary of the specimen. The main reason for the size-dependent of fracturing behavior is that the local fracture energy will dramatically decrease when the crack is approaching the specimen boundary.

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.

Membrane Catalyzed Formation of Nucleotide Clusters and Their Role in the Origins of Life: Insights from Molecular Simulations and Lattice Modeling.

One of the mysteries in studying the molecular "Origin of Life" is the emergence of RNA and RNA-based life forms, where nonenzymatic polymerization of nucleotides is a crucial hypothesis in formation of large RNA chains. The nonenzymatic polymerization can be mediated by various environmental settings, such as cycles of hydration and dehydration, temperature variations, and proximity to a variety of organizing matrices, such as clay, salt, fatty acids, lipid membrane, and mineral surface. In this work, we explore the influence of different phases of the lipid membrane toward nucleotide organization and polymerization in a simulated prebiotic setting. Our molecular simulations quantify the localization propensity of a mononucleotide, uridine monophosphate (UMP), in distinct membrane settings. We perform all-atom molecular dynamics (MD) simulations to estimate the role of the monophasic and biphasic membranes in modifying the behavior of UMPs localization and their clustering mechanism. Based on the interaction energy of mononucleotides with the membrane and their diffusion profile from our MD calculations, we developed a lattice-based model to explore the thermodynamic limits of the observations made from the MD simulations. The mathematical model substantiates our hypothesis that the lipid layers can act as unique substrates for "catalyzing" polymerization of mononucleotides due to the inherent spatiotemporal heterogeneity and phase change behavior.

Deformation features of high-pressure rotary pile reinforced strata by discrete lattice spring modeling (DLSM)

Deformation features of high-pressure rotary pile reinforced strata by discrete lattice spring modeling (DLSM)

Force-induced desorption of copolymeric comb polymers

We investigate a lattice model of comb copolymers that can adsorb at a surface and that are subject to a force causing desorption. The teeth (the comb’s side chains) and the backbone of the comb are chemically distinct and can interact differently with the surface. That is, the strength of the surface interaction can be different for the monomers in the teeth and in the backbone. We consider several cases including (i) the uniform case where the number of teeth is fixed and the lengths of the branches in the backbone and the lengths of the teeth are all identical, (ii) the case where the teeth are short compared to the branches in the backbone, (iii) the situation where the teeth are long compared to the backbone, and (iv) the case where the number of teeth approaches infinity. We obtain expressions for the free energies in the thermodynamic limit in terms of those for self-avoiding walks and discuss the nature of the phase diagrams of the model.

Size effect on compressive strength of foamed concrete: Experimental and numerical studies

This study investigates the size effect on the compressive strength of foamed concrete at the mesoscale level combining X-ray computed tomography (X-CT) and a discrete lattice model. Image segmentation techniques and X-CT were employed to obtain virtual specimens comprising hydrated cement paste and air voids. The lineal-path function and pore size distribution was used to characterise the air void structure. A two-dimensional lattice fracture model of foamed concrete considering different wet densities was established. The model was verified experimentally at a wet density of 700 kg/m3 and then used to predict the strengths of specimens with wet densities of 600 and 800 kg/m3. Square and rectangular specimens (slenderness ratio = 2) with widths of 10, 20, 40, 70.7, and 100 mm were investigated. Results show that the air void structure significantly influences the observed size effect on the compressive strength in the investigated size range. A random forest regressor was used to predict the compressive strength of the foamed concrete; the regressor yielded satisfactory results. Finally, existing analytical size effect models were used to fit the simulated strength. Although good fitting was achieved, special attention should be given to the applicable range and physical meaning of fitted empirical parameters.

Shape-interaction dualism: unraveling complex phase behavior in triangular particle monolayers

This paper examines the effect of finite attractive and repulsive interactions on the self-assembly of triangular-shaped particles on a triangular lattice. The ground state analysis of the lattice model has revealed an infinite sequence of ordered structures, a phenomenon referred to as the ‘devil’s staircase’ of phase transitions. The model has been studied at finite temperatures using both the transfer-matrix and tensor renormalization group methods. The concurrent use of these two methods lends credibility to the obtained results. It has been demonstrated that the initial ordered structures of the ‘devil’s staircase’ persist at non-zero temperatures. Further increase of the attraction between particles or a decrease of the temperature induces the appearance of subsequent ordered structures of the ‘devil’s staircase’. The corresponding phase diagram of the model has been calculated. The phase behavior of our model agrees qualitatively with the phase behavior of trimesic acid adsorption layer on single crystal surfaces.

Hermitian and non-hermitian higher-order topological states in mechanical metamaterials

Higher-order topological insulators exhibit clear hierarchical boundary states, providing an amazing platform for robust wave manipulations in mechanical or acoustic systems. Recently, this theory has been extended to non-Hermiticity-induced higher-order topology, which enables actively controllable topological transport. Nevertheless, most related studies focus on the non-Hermitian quadrupole topology, associated with the coexistence of negative and positive couplings to constitute a π-flux lattice, which hindered the realizations in classical wave systems. Here, we propose a novel tight-binding model without negative couplings, which supports non-Hermiticity-induced higher-order topological states. In the Hermitian case, the middle band gaps host the vanishing bulk polarization and the associated topology is dependent only upon the associated edge polarization. By introducing the external loss as non-Hermitian components, we reveal that therein the trivial structures can also host topological corner states, featured by the quantized nonzero edge polarizations in the biorthogonal basis. Furthermore, such a topological phase transition induced by non-Hermiticity can be realized for almost all of our lattices, except for the isotropic case where the middle band gaps never open. Basing on the theoretical design, we map the lattice models into the mechanical metamaterials to access the analogous higher-order topology in the elastic wave systems for both Hermitian and non-Hermitian physics. The simulated band structures match well with theoretical solutions. And the robust higher-order topological states are also identified. Our work paves the way to implement the non-Hermitian higher-order topology and offers the possibility for wave manipulations in non-Hermitian systems.

Statistical thermodynamics to assess probability of water channel formation in membrane

In this work, the probability of water channel formation was calculated for several polymeric materials, and with that information, the desalination capacity of each material was assessed. Using a 3D lattice model for a flat sheet, the Gibbs free energy change (ΔG) that results from the formation of the first water channel from the top to the bottom surface of the sheet was calculated as a function of the hydrophilicity/-phobicity of the polymeric material (w), the total fraction of water in the 3D lattice (x), and the thickness of the lattice (n). With this result, an equation was further derived to evaluate (xb) the fraction of water which is related to the channel formation, and (xb/x), the ratio of xb to x. It was found that the values of xb are closely related to the fractional free volume (FFV) measured by positron annihilation lifetime spectroscopy (PALS) and the percent free volume of percolated open spaces where water could pass through obtained by molecular dynamics simulation (MDS).These equations were then used to assess the usefulness of each material for making reverse osmosis membranes. When xb is too large, too many channels form, and those channels join to form large pores through which salt can pass, rendering reverse osmosis unsuccessful. On the other hand, when xb is too small, not enough water channels are formed, so reverse osmosis cannot occur then either. It was found that xb was too small for polyvinylidene fluoride (PVDF) and polyethersulfone (PES); suitable for cellulose acetate (CA), aromatic polyamide (APA) and aromatic polyamidehydrazide (APAH); and too large for cellophane (CE). This paper determines which circumstances allow water to form channels in a membrane, and it provides a novel method to assess a material's suitability for reverse osmosis.

Solvable non-Hermitian skin effects and real-space exceptional points: non-Hermitian generalized Bloch theorem

Non-Hermitian systems can exhibit extraordinary boundary behaviors, known as the non-Hermitian skin effects, where all the eigenstates are localized exponentially at one side of lattice model. To give a full understanding and control of non-Hermitian skin effects, we have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates, in which translation symmetry is broken due to the open boundary condition. By introducing the Vieta’s theorem for any polynomial equation with arbitrary degree, our approach is widely applicable for one-dimensional non-Hermitian tight-binding models. With the non-Hermitian generalized Bloch theorem, we can analyze the condition of existence or non-existence of the non-Hermitian skin effects at a mathematically rigorous level. Additionally, the non-Hermitian generalized Bloch theorem allows us to explore the real-space exceptional points. We also establish the connection between our approach and the generalized Brillouin zone method. To illustrate our main results, we examine two concrete examples including the Su–Schrieffer–Heeger chain model with long-range couplings, and the ladder model with non-reciprocal interaction. Our non-Hermitian generalized Bloch theorem provides an efficient way to analytically study various non-Hermitian phenomena in more general cases.

Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors

Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors

Effective models for dense vortex lattices in the Kitaev honeycomb model

Effective models for dense vortex lattices in the Kitaev honeycomb model

Island myriads in periodic potentials.

A phenomenon of emergence of stability islands in phase space is reported for two periodic potentials with tiling symmetries, one square and the other hexagonal, inspired by bidimensional Hamiltonian models of optical lattices. The structures found, here termed as island myriads, resemble web-tori with notable fractality and arise at energy levels reaching that of unstable equilibria. In general, the myriad is an arrangement of concentric island chains with properties relying on the translational and rotational symmetries of the potential functions. In the square system, orbits within the myriad come in isochronous pairs and can have different periodic closure, either returning to their initial position or jumping to identical sites in neighbor cells of the lattice, therefore impacting transport properties. As seen when compared to a more generic case, i.e., the rectangular lattice, the breaking of square symmetry disrupts the myriad even for small deviations from its equilateral configuration. For the hexagonal case, the myriad was found but in attenuated form, mostly due to extra instabilities in the potential surface that prevent the stabilization of orbits forming the chains.