Regular Lattice Research Articles

PAYOFF-BASED PROBABILISTIC INTERACTION MODEL ON THE EVOLUTION OF COOPERATION IN SPATIAL PUBLIC GOODS GAME

In the spatial public goods game (SPGG), punishment effectively promotes cooperation but often reduces the collective benefits of cooperators and punishers. In order to increase revenue, we propose a probabilistic interaction domain model considering both strategy type and payoff level. In this model, players are divided into two types, successful players with payoffs higher than the payoff threshold and failed players with payoffs lower than the payoff threshold. A successful player is less likely to change the interaction range than a failed player. Through extensive simulations, it is shown to verify that a higher payoff threshold leads to a more pronounced promotion effect on cooperation and corresponds to a higher cooperation return. Moreover, introducing dynamic interaction domain can rapidly remove defectors from the vicinity of cooperative players on regular lattices. Reducing the payoff gap between punishers and cooperators helps mitigate the system’s second-order free-riding problem. Additionally, through analysis of the critical parameters, it is revised that incorporating diversity in interaction structures substantively enhances cooperation level.

Chain-based lattice printing for efficient robotically-assembled structures

Due to the nature of their implementation, nearly all low-level fabrication processes produce solidly filled structures. However, lattice structures are significantly stronger for the same amount of material, resulting in structures that are much lighter and more materially efficient. Here we propose an approach for fabricating lattice structures that echoes 3D printing techniques. In it, a modular chain of specially designed links is “extruded” onto a substrate to produce various lattices configurations depending on the chosen assembly algorithm, ranging from rigid regular lattices with nodal connectivity of 12, octet-truss, to significantly less dense configurations. Compared to conventional additive manufacturing methods, our approach allows for efficient use of nearly any material or combination of materials to construct lattices with programmed arrangements. We experimentally demonstrate that a 3x3x2 lattice structure (287 total links) is fabricated in 27 minutes via a modified robotic arm and can support approximately 1000 N in compression testing.

Skew scattering and ratchet effect in photonic graphene

This paper is devoted to a comprehensive theoretical study of asymmetric (skew) scattering in photonic graphene, with the main focus on its realization with semiconductor microcavity exciton-polaritons. As an important consequence of the skew scattering, we prove the appearance of the ratchet effect in this system. Triangular defects in the form of missing micropillars in a regular honeycomb lattice are considered to be ones that break the spatial inversion symmetry, thus providing the possibility of the ratchet effect. By means of the numerical solution of the effective Schrödinger equation, we provide microscopical insight into the process of skew scattering and determine indicatrices, cross sections, and asymmetry parameters. In a system with multiple coherently oriented triangular defects, a macroscopic ratchet effect occurs as a unidirectional flux upon noiselike initial conditions. Our study broadens the concept of ratchet phenomena in the field of photonics and optics of exciton-polaritons. Published by the American Physical Society 2024

Tunable disorder on the S-state majority-voter model.

We investigate the nonequilibrium phase transition in the S-state majority-vote model for S=2,3, and 4. Each site, k, is characterized by a distinct noise threshold, qk, which indicates its resistance to adopting the majority state of its Nv nearest neighbors. Precisely, this noise threshold is governed by a hyperbolic distribution, P(k)∼1/k, bounded within the limits e-α/2<qk<1/2. Here, the parameter α plays a pivotal role as it determines the extent of disorder in the system through the spread of the threshold distribution. Through Monte Carlo simulations and finite-size scaling analyses on regular square lattices, we deduced that the model undergoes a continuous order-disorder phase transition at a specific α=αc. Interestingly, the critical threshold exhibits a power-law decay, αc∼Nv-δ, as the number Nv of neighboring sites increases. From the least square fits to the data sets results in δ=0.65±0.01 for S=2, δ=0.92±0.01 for S=3, and δ=0.93±0.01 for S=4. Furthermore, the critical exponents β/ν and γ/ν are consistent with those found in the S-state Potts model.

Solving an internal problem for finite regular two-dimensional lattice spiral elements, excitable plate electromagnetic wave

Background. The work is aimed at developing and researching rigorous methods for solving internal problem of electrodynamics for multi-element structures (metastructures) consisting from the final number of elements, as well as to study the physical processes occurring in them. A special case of such structures are two-dimensional lattices with a fixed interelement distance, consisting of identical elements having the same spatial orientation (regular lattices). Aim. In this work, based on an iterative approach, the internal solution is solved. problems of electrodynamics for a finite regular two-dimensional lattice of spiral elements. In order to obtain a priori information about the electrodynamic characteristics of elements lattice and justification for the choice of projection function systems are analyzed spectral characteristics of the integral operator of the internal problem for a single spiral element. Then the currents on the structure elements are calculated, their spectral characteristics are determined. The results of spectral analysis allow increase the efficiency of solving an internal problem. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a finite two-dimensional lattice of spiral elements is proposed radiating structure. For the specified structure, in the case of its excitation by a flat electromagnetic wave, based on the iterative approach, the internal problem of electrodynamics was solved. The following were carried out in a wide frequency range: analysis of the convergence of the iterative process, spectral analysis of the integral operator of the internal problem for a single spiral element, as well as spectral analysis of external field and current functions functions on lattice elements. Conclusion. The feasibility of determining the spectral characteristics of integral operators is shown internal task for the elements forming the metastructure. A relationship has been identified between the frequency dependence eigenvalues of the integral operator of the internal problem of single elements, forming a metastructure, with resonance phenomena arising in the metastructure, the influence of resonances on the convergence of the iterative process was confirmed. The feasibility of considering averaged amplitude current spectra is shown. It was revealed that the averaged spectrum of current functions is close to degenerate, especially near resonant frequencies. This allows for use as projection functions a compact set of eigenfunctions that have significant amplitudes in the vicinity of the frequency under study, which significantly simplifies the solution of the internal problem.

Impact of Surface Finishing on Ti6Al4V Voronoi Additively Manufactured Structures: Morphology, Dimensional Deviation, and Mechanical Behavior

Additively manufactured medical devices require proper surface finishing before their use to remove partially adhered particles and provide adequate surface roughness. The literature widely investigates regular lattice structures—mainly scaffolds with small pores to enhance osseointegration; however, only a few studies have addressed the impact of surface finishing on the dimensional deviation and the global and local mechanical responses of lattice samples. Therefore, the current research investigates the impact of biomedical surface finishing (i.e., corundum sandblasting and zirconia sandblasting) on Voronoi lattice structures produced by laser powder bed fusion (LPBF) with large pores and different thicknesses on the surface morphology and global and local mechanical behaviors. MicroCT and SEM are performed for the assessment of dimensional mismatch and surface evaluation. The mechanical properties are investigated with 2D digital image correlation (DIC) in quasi-static compression tests to estimate the impact of surface finishes on local maps of strain. In the quasi-static tests, both the global mechanical performances, as expected, and local 2D DIC strain maps were mainly affected by the strut thickness, and the impact of different surface finishings was irrelevant; on the contrary, different surface finishing processes led to differences in the dimensional deviation depending on the strut thickness. These results are relevant for designing lattice structures with thin struts that are integrated into medical prostheses that undergo AM.

The immiscible to miscible transition and its consequences for 3-phase displacements in porous media of arbitrary wettability: Comparison of 3D pore network results with basic theory

The theory of the immiscible to miscible transition and its consequences for 3-phase displacements in a system of arbitrary wettability distribution has been studied in a previous paper using a “process based” model through the simplest case possible; a capillary bundle (CB) model. As expected, the CB model was not able to capture many realistic phenomena such as phase trapping, film and layer-flow, topological effects etc. However, it was recognized that it should be able to indicate certain expected qualitative trends in 3-phase displacements in real 3D connected networks.The current paper extends that earlier work by showing the consequences of changing the model of the porous medium to a 3D connected lattice pore network model (PNM) to capture phase trapping and rock connectivity. Initially a simple 3D regular cubic bond lattice is used for this initial work to make a clear comparison with the CB model. Two important characteristics of 3D network refer to (i) displacement phase accessibility, and (ii) defending phase trapping/escape. Three trapping/escape cases based on the probability of invading phase accessibility and defending phase escape have been defined in the 3D lattice network. Networks with different coordination numbers (z = 6 and 4) were studied in order to mimic different rock connectivity and study how and in which way the applied rules result in specific changes in 3-phase saturation paths, 3-phase pore occupancies and phase trapping. Again the focus is on the changes which are predicted to occur in all these quantities as the system moves from an immiscible (IFT σgo ∼ “large”) to a miscible (σgo → 0) case.In this paper, a weakly oil-wet (WOW) wettability distribution is considered and various phase invasions (gas, water, and oil) in the corresponding 2-phase systems are investigated. Both saturation paths and pore occupancy sequences of different phase invasions under different miscibility conditions are presented for both the CB and PNM models. It is found that having a well-connected network and considering a relaxed rule on defending and displacing phases, the results are quite similar to that of the CB model. Also, applying restricted trapping/escaping rules and less connected network mean deviation from the CB model, but the underlying physics of the immiscible to miscible transitions and the central physical parameter of 3-phase displacements in all cases are the same as those observed for the CB model.

Evolution of cooperation with asymmetric rewards

Rewards, as a form of positive reinforcement, effectively encourage cooperation. In this paper, we study a multi-population prisoner's dilemma game with asymmetric rewards, where agents in the same population play prisoner's dilemma game, and agents from the giver population can reward agents from the recipient population only if they make the same choice. In well-mixed populations, asymmetric rewards can facilitate cooperation. Similarly, asymmetric rewards on the regular square lattice can effectively prevent complete defection. In both well-mixed and structured populations, seemingly disadvantageous cooperative givers play an important role in the maintenance and spread of cooperation. Especially on lattice, cooperative givers with asymmetric rewards can be active in the system through diverse cases of cyclic dominance. Our findings provide deeper insights into the impact of asymmetry on cooperative behavior and the development of altruistic behavior in real-world scenarios.

Pore-scale study of coupled heat and mass transfer during primary freeze-drying using an irregular pore network model

This study presents a pore network (PN) model with transient heat transfer and quasi-steady transitional vapor transport that is for the first time applied to irregular porous structures that are obtained by reconstruction of X-ray tomography image data. In contrast to previous studies, the irregular pores are not approximated by spheres but implemented in their original shape. Secondly, instead of assuming cylindrical throats as pore connections, the actual distance between pore centers as well as the pore cross sections are used for the computation of the vapor transport coefficient. The control volume elements of the computational model are matched with the cells obtained by Voronoi tessellation. The improvements have clear advantages over former approaches where the reconstructed void space is usually strongly simplified by balls and sticks confined in a regular lattice structure. A freeze-dried sample of maltodextrin DE12 with 20% (w/w) solid content is used for benchmarking the new methodology. Its morphological and thermal properties are determined by the novel PN model. The simulation results of primary freeze-drying (FD) are compared to reference cases in two ways. First, the differences in heat and mass transfer kinetics as compared to regular PNs are emphasized. Secondly, the PN simulation results are confronted with a simple literature model that neglects pore size distribution (PSD) and transient heat transfer. It is shown that already in small domains with relatively narrow PSD, the variation of the mass transfer coefficient affects the computed sublimation fluxes and yields a significant deviation from the simpler literature model. Moreover, it is revealed in this study that the structure has a significant impact on the sublimation front temperature. This is demonstrated by the comparison of FD in the irregular PN to a regular PN with almost identical PSD but different porosity. The development, verification, and benchmarking of the new PN model can be seen as an important step for studies of the structure dependence of FD.

Laplacian operator and its square lattice discretization: Green function vs. Lattice Green function for the flat 2-torus and other related 2D manifolds

Abstract The paper investigates the truncation error between the Green function and the lattice Green function (LGF) for the Laplacian operator defined on the 2-torus and its discretization on a regular square lattice. Extensions to the cylinder and the rectangular domain with free (or Neumann) boundary conditions are also proposed. In each of these instances, the Green function and its discrete analog are given in exact analytical closed-form allowing to infer accurate estimates as the lattice spacing tends to zero. As expected, it is shown that the continuum limit of the LGF coincides well with the Green function in every case. In particular, the issue of logarithmic singularity regularization of the Green function by the lattice discretization is addressed through two related application examples regarding the rectangular domain, and devoted to the computation of corner-to-corner resistance of an electrical conducting square and the mean first-passage time between the diagonally opposite vertices of a square for a standard Brownian motion, both derived considering the continuum limit.

Development and Analysis of novel Integrable Nonlinear Dynamical Systems on Quasi-One-Dimensional Lattices. Parametrically Driven Nonlinear System of Pseudo-Excitations on a Two-Leg Ladder Lattice

Following the main principles of developing the evolutionary nonlinear integrable systems on quasi-one-dimensional lattices, we suggest a novel nonlinear integrable system of parametrically driven pseudo-excitations on a regular two-leg ladder lattice. The initial (prototype) form of the system is derivable in the framework of semi-discrete zero-curvature equation with the spectral and evolution operators specified by the properly organized 3 × 3 square matrices. Although the lowest conserved local densities found via the direct recursive method do not prompt us the algebraic structure of system’s Hamiltonian function, but the heuristically substantiated search for the suitable two-stage transformation of prototype field functions to the physically motivated ones has allowed to disclose the physically meaningful nonlinear integrable system with time-dependent longitudinal and transverse inter-site coupling parameters. The time dependencies of inter-site coupling parameters in the transformed system are consistently defined in terms of the accompanying parametric driver formalized by the set of four homogeneous ordinary linear differential equations with the time-dependent coefficients. The physically meaningful parametrically driven nonlinear system permits its concise Hamiltonian formulation with the two pairs of field functions serving as the two pairs of canonically conjugated field amplitudes. The explicit example of oscillatory parametric drive is described in full mathematical details.

Measurement of seasonal variations of the NSLS-II circumference and energy

Routine beam-based characterization of the NSLS-II storage ring indicated probable seasonal variations of the ring circumference and energy. We arranged regular direct measurements of the ring circumference during 2023 and compared the results with the archived data of the magnet and undulator settings. A clear correlation between the ring circumference and energy was observed. These seasonal variations of the ring energy are found to be the main reason for regular lattice corrections required to keep the machine performance stable for user operations. The measurement techniques and results are discussed in this article.

Percolation in a three-dimensional nonsymmetric multicolor loop model.

We conduct Monte Carlo simulations to analyze the percolation transition of a nonsymmetric loop model on a regular three-dimensional lattice. We calculate the critical exponents for the percolation transition of this model. The percolation transition occurs at a temperature that is close to, but not exactly, the thermal critical temperature. Our finite-size study on this model yields a correlation length exponent that agrees with that of the three-dimensional XY model with an error margin of 6%.

Fitness noise in the Bak-Sneppen evolution model in high dimensions.

We study the Bak-Sneppen evolution model on a regular hypercubic lattice in high dimensions. Recent work [Phys. Rev. E 108, 044109 (2023)2470-004510.1103/PhysRevE.108.044109] showed the emergence of the 1/f^{α} noise for the fitness observable with α≈1.2 in one-dimension (1D) and α≈2 for the random neighbor (mean-field) version of the model. We examine the temporal correlation of fitness in 2, 3, 4, and 5 dimensions. As obtained by finite-size scaling, the spectral exponent tends to take the mean-field value at the upper critical dimension D_{u}=4, which is consistent with previous studies. Our approach provides an alternative way to understand the upper critical dimension of the model. We also show the local activity power spectra, which offer insight into the return time statistics and the avalanche dimension.

Validity of an approximate electrostatic interaction model

We explain the reasons why a simple approximate expression for the interaction energy between two parallel uniformly charged wires works so well for the calculation of the stored electrostatic energy of a uniformly charged square and/or rectangular plate. The expression under consideration was also found to be very accurate when calculating the total energy of a model consisting of an arbitrary number of uniformly charged wires placed parallel to each other along a one-dimensional regular lattice when the number of wires is not very small. One can use the derived approximate expression for the interaction energy instead of the more elaborate exact one in all circumstances where there is no need for an extremely high accuracy.

HYPERTILING — a high performance Python library for the generation and visualization of hyperbolic lattices

HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincaré disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.

Codebase release 1.3 for HYPERTILING

HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincaré disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.

Forecasting Lattice and Point Spatial Data: Comparison of Unilateral and Multilateral SAR Models

Spatial auto-regressive (SAR) models are widely used in geosciences for data analysis; their main feature is the presence of weight (W) matrices, which define the neighboring relationships between the spatial units. The statistical properties of parameter and forecast estimates strongly depend on the structure of such matrices. The least squares (LS) method is the most flexible and can estimate systems of large dimensions; however, it is biased in the presence of multilateral (sparse) matrices. Instead, the unilateral specification of SAR models provides triangular weight matrices that allow consistent LS estimates and sequential prediction functions. These two properties are strictly related and depend on the linear and recursive nature of the system. In this paper, we show the better performance in out-of-sample forecasting of unilateral SAR (estimated with LS), compared to multilateral SAR (estimated with maximum likelihood, ML). This conclusion is supported by numerical simulations and applications to real geological data, both on regular lattices and irregularly distributed points.

Grid Cells in Cognition: Mechanisms and Function.

The activity patterns of grid cells form distinctively regular triangular lattices over the explored spatial environment and are largely invariant to visual stimuli, animal movement, and environment geometry. These neurons present numerous fascinating challenges to the curious (neuro)scientist: What are the circuit mechanisms responsible for creating spatially periodic activity patterns from the monotonic input-output responses of single neurons? How and why does the brain encode a local, nonperiodic variable-the allocentric position of the animal-with a periodic, nonlocal code? And, are grid cells truly specialized for spatial computations? Otherwise, what is their role in general cognition more broadly? We review efforts in uncovering the mechanisms and functional properties of grid cells, highlighting recent progress in the experimental validation of mechanistic grid cell models, and discuss the coding properties and functional advantages of the grid code as suggested by continuous attractor network models of grid cells.

Disclosing magnetic clusters in the metallic half-Heusler ferromagnet Cr4PtGa17 with a breathing pyrochlore lattice

We report a ferromagnetic resonance (FMR) study of a single crystal of Cr4PtGa17, the first material of a half-Heusler (HH) type with a metallic ferromagnetic breathing pyrochlore structure. The spatial distribution of the magnetic free energy density derived from the FMR data appears to be of a cubic symmetry despite the lower symmetry coordination of magnetic Cr ions. This surprising finding strongly suggests that the Cr4Ga14 structural unit at the Y site of the HH general XYZ formula forms an octahedrally shaped integral magnetic cluster, likely due to strong exchange interaction between the Cr ions via covalent Cr-Ga-Cr bonds. The presence of magnetic clusters within a regular metallic lattice appears to be a new intriguing characteristics of these novel types of HH compounds whereas Cr4PtGa17, at the same time, constitutes the rare example of such metallic pyrochlore-type material.