Binary Lattice Research Articles

Surface pattern formation and scaling described by conserved lattice gases

We extend our 2+1 -dimensional discrete growth model [Odor, Phys. Rev. E 79, 021125 (2009)] with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence. By mapping the slopes onto particles, two-dimensional nonequilibrium binary lattice model emerges, in which the (smoothing or roughening) surface diffusion can be described by attracting or repelling motion of oriented dimers. The binary representation allows simulations on very large size and time scales. We provide numerical evidence for Mullins-Herring or molecular-beam epitaxy class scaling of the surface width. The competition of inverse Mullins-Herring diffusion with a smoothing deposition, which corresponds to a Kardar-Parisi-Zhang (KPZ) process, generates different patterns: dots or ripples. We analyze numerically the scaling and wavelength growth behavior in these models. In particular, we confirm by large size simulations that the KPZ type of scaling is stable against the addition of this surface diffusion, hence this is the asymptotic behavior of the Kuramoto-Sivashinsky equation as conjectured by field theory in two dimensions, but has been debated numerically. If very strong, normal surface diffusion is added to a KPZ process, we observe smooth surfaces with logarithmic growth, which can describe the mean-field behavior of the strong-coupling KPZ class. We show that ripple coarsening occurs if parallel surface currents are present, otherwise logarithmic behavior emerges.

A model for the electrostatic contribution to the pH-dependent nonideal mixing of a binary charged–zwitterionic lipid bilayer

Nonideal mixing provides the physical basis of domain formation and macroscopic phase separation in lipid bilayers. We present a model for the electrostatic contribution to the nonideality of a two-component acidic–zwitterionic lipid membrane. Our model is based on the mean-field Poisson–Boltzmann approach; it includes a protonation/deprotonation equilibrium applicable to acidic lipids such as phosphatidic acid or phosphatidylglycerol. It also includes an electrostatic model for zwitterionic lipids such as phosphatidylcholine or phosphatidylethanolamine that accounts for the spatial separation of the two headgroup charges and the orientational freedom of the headgroup. Modeling the nonelectrostatic contribution to the free energy using the Bragg–Williams approximation of a binary lattice gas enables us to compute binodal lines that reflect the influence of membrane electrostatics on the nonideal mixing properties of the bilayer. If we neglect the zwitterionic lipid's electrostatic contribution, then increasing pH is predicted to always oppose demixing, stabilizing the membrane due to the repulsion between the charged lipids. If the electrostatic properties of the zwitterionic lipids are accounted for, this opposing tendency weakens and may even reverse. In this case, increasing the fraction of charged lipids through increasing pH would, somewhat unexpectedly, promote domain formation. We discuss the corresponding physical mechanism.

특정 상호작용을 갖는 논랜덤 혼합 격자 용액의 깁스 에너지

논랜덤 혼합의 2-성분 격자용액에서 특정상호작용을 갖는 경우의 수에 대한 분포를 난수 모의실험을 통하여 구하였다. 이 분포로부터 2-성분격자용액의 과잉깁스에너지 <TEX>$G^E$</TEX>에 대한 근사식을 유도하였다. 이 식을 사용하여 15개의 2-성분용액에 대한 일정압력에서의 액체-증기 상평형 계산을 하였고 Wilson식, Van Laar식, Redlich-Kister식의 계산 결과와 비교하여 보았다. Performing random number simulations, we obtained an approximate distribution of the number of ways arranging molecules in a binary lattice solution of nonrandom mixing with a specific interaction. From the distribution an approximate equation of excess Gibbs energy for a binary lattice solution was derived. Using the equation, liquid-vapor equilibrium at constant pressure for 15 binary solutions were calculated and compared with the result from Wilson equation, Van Laar equation and Redlich-Kister equation.

Influence of Copper on the Isomerization of Eugenol for as-Synthesized NiCuAl Ternary Hydrotalcites: An Understanding Through Physicochemical Study

Catalysts with the hydrotalcite-like structure and general formula NiCuAlyz-HT having (Ni + Cu)/Al atomic ratio of 3.0 with varying Ni:Cu atomic compositions (100:0–50:50) were synthesized, characterized and tested for isomerization of eugenol to isoeugenol. The decrease in the activity upon addition of copper to NiAl lattice is investigated through temperature programmed reduction and phenol adsorption. Conversion of eugenol over active NiAl hydrotalcite significantly decreased upon incorporation of Cu2+ in the NiAl binary lattice wherein substitution of 25 at% of Ni2+ by Cu2+ annihilated the isomerization activity. The decrease in the activity upon addition of copper to NiAl lattice is investigated through physiochemical studies.

Bloch-Zener Oscillations in Binary Superlattices

Bloch-Zener oscillations, i.e., the coherent superposition of Bloch oscillations and Zener tunneling between minibands of a binary lattice, are experimentally demonstrated for light waves in curved femtosecond laser-written waveguide arrays. Visualization of double-periodicity breathing and oscillation modes is reported, and synchronous tunneling leading to wave reconstruction is demonstrated.

Statistical Thermodynamics and Kinetics of Long-Range Order in Metal-Doped Graphene

The statistical-thermodynamics and kinetics models of atomic ordering in a metal-doped graphene (binary two-dimensional planar graphene-type crystal lattice) at 1/8, 1/4, and 1/2 stoichiometries are proposed. Impossibility of (completely) atomic-ordered distribution at 1/6 and 1/3 stoichiometries is ascertained in a graphene-type crystal lattice (in case of a short-range interatomic interactions at least). If a graphene is doped by the short-range interacting metal atoms, the superstructures described only by a one LRO parameter are possible; and if it is doped by the long-range interacting metal atoms, the new superstructures with the two or three LRO parameters may appear as well. If stoichiometry is 1/4, the structure has a one long-range order (LRO) parameter is more thermodynamically favorable than those have one or two LRO parameters. It is established that kinetics curves of LRO parameters can be non-monotonic for structures where there are two or three LRO parameters (because graphene-type lattice contains two sublattices, and mixing energy is different for each of them). It is shown that the most ordered is structure with equal atomic fractions of carbon and metal atoms, while the least one is structure with a maximal difference of carbon and metal atoms. Kinetics results confirm statistical-thermodynamic ones: firstly, equilibrium values of LRO parameter coincide within the framework of both models, secondly, equilibrium (and instantaneous) value of LRO parameter in a nonstoichiometric binary graphene-type structure (where atomic fraction of a doping component deviates from the stoichiometry to the side of the higher concentrations) may be higher than it is in a stoichiometric one. The dominance of the same physical mechanisms of atomic ordering in both mixed nanosystems and macrosystems is assumed.

Sample-Adaptive Product Quantizers with Affine Index Assignments for Noisy Channels

When we design a robust vector quantizer (VQ) for noisy channels, an appropriate index assignment function should be contrived to minimize the channel-error effect. For relatively high rates, the complexity for finding an optimal index assignment function is too high to be implemented. To overcome such a problem, we use a structurally constrained VQ, which is called the sample-adaptive product quantizer (SAPQ) [12], for low complexities of quantization and index assignment. The product quantizer (PQ) and its variation SAPQ [13], which are based on the scalar quantizer (SQ) and thus belong to a class of the binary lattice VQ [16], have inherent error resilience even though the conventional affine index assignment functions, such as the natural binary code, are employed. The error resilience of SAPQ is observed in a weak sense through worst-case bounds. Using SAPQ for noisy channels is useful especially for high rates, e.g., > 1 bit/sample, and it is numerically shown that the channel-limit performance of SAPQ is comparable to that of the best codebook permutation of binary switching algorithm (BSA) [23]. Further, the PQ or SAPQ codebook with an affine index assignment function is used for the initial guess of the conventional clustering algorithm, and it is shown that the performance of the best BSA can be easily achieved.

Contact line dynamics in binary lattice Boltzmann simulations

We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface velocity.

A large family of pseudorandom binary lattices

Recently P. Hubert, C. Mauduit and A. Sarkozy introduced and studied the notion of pseudorandomness of binary lattices and gave a pseudorandom binary lattice. Later in other papers C. Mauduit and A. Sarkozy constructed some large families of good binary lattices. In this paper a large family of pseudorandom binary lattices is presented by using the multiplicative inverse and the quadratic character of finite fields.

Variable slip coefficient in binary lattice Boltzmann models

Abstract We present a new method in order to obtain variable slip coefficient in binary lattice Boltzmann models to simulate gaseous flows. We present the Boundary layer theory. We study both the single-and multi-fluid BGK-type models as well. The boundary slip and the Knudsen layer are analyzed in detail. Benchmark simulations are carried out in order to compare the analytical derivation with the numerical results. Excellent agreement is found between the two analytical formalism and the numerical simulations.

Represented value sets for integral binary quadratic forms and lattices

A characterization is given for the integral binary quadratic forms for which the set of represented values is closed under products. It is also proved that for an integral binary quadratic lattice over a Dedekind domain, the product of three values represented by the form is again a value represented by the form. This generalizes the trigroup property observed by V. Arnold in the case of integral binary quadratic forms.

Positive definite binary hermitian forms with finitely many exceptions

Let E / F be a CM extension of number fields, and L be a positive definite binary hermitian lattice over the ring of integers of E. An element in F is called an exception of L if it is represented by every localization of L but not by L itself. We show that if E / F and a positive integer k are given, then there are only finitely many similarity classes of positive definite binary hermitian lattices with at most k exceptions. This generalizes the corresponding finiteness result by Earnest and Khosravani [A.G. Earnest, A. Khosravani, Representation of integers by positive definite binary hermitian lattices over imaginary quadratic fields, J. Number Theory 62 (1997) 368–374, Theorem 2.2] for the case F = Q . We also prove that for a fixed totally real field F of odd degree over Q , there are only finitely many CM extensions E / F for which there exists a positive definite regular normal binary hermitian lattice over the ring of integers of E.

Encoding and Decoding Binary Product Lattices

A binary product lattice is generated from two binary component lattices of lower dimensions by employing the Kronecker product. This work focuses on codes carved from binary product lattices. Defined as such, an intriguing problem is that of effectively mapping independent data sequences onto a selected subset of lattice points. A novel approach is disclosed yielding an explicit connection between source bits and lattice points. Decoding methods typically used for binary product codes do not apply for product lattices. Several alternative decoding approaches are discussed. In particular, a provably bounded-distance decoder is presented. It relies on the fact that a product lattice code point may be regarded as a two-dimensional array whose rows and columns are points in the component lattices. The obtained results are compared with classical lattices known in the art

A Molecular-Thermodynamic Lattice Model for Binary Mixtures

Abstract Using a method originally proposed for describing a continuum-space polymer fluid, a new expression for the Helmholtz energy of mixing is proposed for a binary lattice mixture. Molecular size asymmetry and nonrandomness due to segment–segment interactions are taken into account. An expression proposed by Yan, Liu and Hu for a binary lattice mixture of monomers, based on the Ising model, is used as a reference system. Calculated critical constants and liquid–liquid coexistence curves are in good agreement with Monte Carlo simulations for lattice mixtures with modest size asymmetry. Because lattice spacing rises with increasing temperature, comparison of calculated binary liquid–liquid equilibria with experiment requires that calculations take into account that the interchange energy falls as temperature rises. While the new expression for the Helmholtz energy of mixing provides much improvement over the Flory–Huggins equation, calculated liquid–liquid equilibria for three binary systems are similar to those from Guggenheim's quasi-chemical theory.

Violation of Fluctuation–Dissipation Relation in Fragile Glasses

The relationship between correlation and response in the glass state of a binary lattice gas model is explored. In contrast to the Cugliandolo–Kurchan off-equilibrium fluctuation dissipation relation (FDR), we see a violation of the FDR. This collapse of the relation appears for a collective motion among particles of the glassy system. This violation of FDR is related to the inevitable irreversibility that accompanies a quasi-static operation applied to a glassy system.

Multiscale approach for the analysis of channeling profile measurements of ion implantation damage

Coupled binary collision and kinetic lattice Monte Carlo simulations are used to analyze 30keV B channeling profile measurements of damage from 30keV N implants in (110)-Si. Collision cascades are generated in the binary collision approach, while dynamic annealing and post-implant annealing at room temperature are treated within the kinetic lattice Monte Carlo approach. In the binary collision simulations the atom positions of each defect and the lattice strain around the defects are considered. Strain is shown to have a weak but non-negligible effect on the channeling of 30keV B. Comparison of the simulation results with the B profiles measured by SIMS suggests that interstitials and vacancies are attracted by clusters of the opposite type and/or repelled by clusters of the same type.

Coupled BC/kLMC simulations of the temperature dependence of implant damage formation in silicon

We use coupled binary collision (BC) and kinetic lattice Monte Carlo (kLMC) simulations to investigate the temperature dependence of implantation damage around room temperature and below, and the difference between dynamic annealing during the implant and post-implant annealing. Based on our simulations we give a physical explanation of this difference. From comparison with published experimental data on 200keV B implants in Si we conclude that interaction radii or reaction barriers exist that favor recombination over clustering reactions. Moreover, we discuss the point defect parameters required to achieve agreement between simulation and experimental results.

Ambiguities in Powder Indexing: Conjunction of a Ternary and Binary Lattice Metric Singularity in the Cubic System.

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical and theoretical impact on the indexing of powder patterns. For example, in experimental practice an indexing program may find only the lower symmetry member of a singularity. Obviously, it is important to recognize such cases and know how to proceed. Recently, we described: a binary singularity involving a monoclinic and a rhombohedral lattice in a subcell-supercell relationship anda second type of singularity—a ternary singularity–in which two of the three lattices are in a derivative composite relationship. In this work, we describe a ternary lattice metric singularity involving a cubic P, a tetragonal P, and an orthorhombic C lattice. Furthermore, there is a binary singularity, involving a hexagonal P and orthorhombic P lattice, which is characterized by a set of unique d-spacings very close to that of the ternary singularity. The existence of such singularities is more common than once thought and requires a paradigm shift in experimental practice. In addition singularities provide opportunities in material design as they point to highly specialized lattices that may be associated with unusual physical properties.

Phase separation of a multiple occupancy lattice gas

A binary lattice gas model that allows for multiple occupancy of lattice sites, inspired by recent coarse-grained descriptions of solutions of interacting polymers, is investigated by combining the steepest descent approximation with an exploration of the multidimensional energy landscape, and by Gibbs ensemble Monte Carlo simulations. The one-component version of the model, involving on site and nearest neighbour interactions, is shown to exhibit microphase separation into two sub-lattices with different mean occupation numbers. The symmetric two-component version of the multiple occupancy lattice gas is shown to exhibit a demixing transition into two phases above a critical mean occupation number.

Inevitable Irreversibility Generated by the Glass Transition of the Binary Lattice Gas Model

We numerically investigate the thermodynamic properties of the glass state. As the object of our study, we employ a binary lattice gas model. Through Monte Carlo simulations, we find that this model actually experiences a glass transition. We introduce a potential into the model that represents a piston with which we compress the glass. By measuring the work performed in this process, we find that irreversible works exist at the glass state even in the quasistatic limit. This implies that yield stress is created by the glass transition.