Pattern Densities in Non-Frozen Planar Dimer Models

In this paper, we introduce a family of observables for the dimer model on a bi-periodic bipartite planar graph, called pattern density fields. We study the scaling limit of these objects for non-frozen Gibbs measures of the dimer model, and prove that they converge to a linear combination of a derivative of the Gaussian massless free field and an independent white noise.     

Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions: A Fluorescence Study

The fluorescence technique was employed to study thermal phase transitions of iota (ι-) carrageenan (IC) in CaCl₂ solution. IC gels underwent coil to double helix (c-h) and double helix to dimer (h-d) transitions upon cooling. Upon heating IC gels presented dimer to double helix (d-h) and double helix to coil (h-c) transitions, showing hysteresis types of transition paths. Scattered light, I_sc and fluorescence intensity, I, were monitored against temperature to determine phase transitions. Transition temperatures were determined from the derivative of the transition paths. The critical gel fraction exponent, β, was measured and found to be in accord with the classic Flory–Stockmayer model.     

相对论离子与氦二聚体碰撞电离的理论研究

基于对称程函近似,从理论角度研究了相对论离子与氦二聚体碰撞双电离的直接碎裂通道:由入射离子与两个原子的作用造成的双电离。从不同的近似角度出发,建立了两个理论模型,第一个模型将氦二聚体的两个原子看做一个整体,而另外一个模型完全忽略了两个氦原子之间的相互作用。模型的数值计算结果表明,总截面与氦二聚体的空间取向有很强的依赖关系,当氦二聚体与入射离子束流平行时,总截面达到最大值,在垂直时为最小值。进一步研究发现,模型一的结果在氦二聚体核间距较小时更为合理,核间距较大时,模型二更为精确。     

Path of Momentum Integral in the Skorniakov-Ter-Martirosian Equation

The Skorniakov-Ter-Martirosian (STM) integral equation is widely used for the quantum three-body problems of low-energy particles (e.g., ultracold atom gases). With this equation these three-body problems can be efficiently solved in the momentum space. In this approach the boundary condition for the case that all the three particles are gathered together is described by the upper limit of the momentum integral, i.e., the momentum cutoff. On the other hand, in realistic systems, the three-body recombination (TBR) process can occur when all these three particles are close to each other. In this process two particles form a deep dimer and the other particle can gain high kinetic energy and then escape from the low-energy system. In the presence of the TBR process, the momentum-cutoff in the STM equation would include a non-zero imaginary part. As a result, the momentum integral in the STM equation should be done in the complex-momentum plane. In this case the result of the integral depends on the choice of the integral path. Obviously, only one integral path can lead to the correct result. In this paper we consider how to correctly choose the integral path for the STM equation. We take the atom-dimer scattering problem in a specific ultracold atom gas as an example, and show the results given by different integral paths. Based on the result for this case we explore the reasonable integral paths for general case.     

聚对苯二甲酸丁二醇酯二聚体键离能的理论研究

采用密度泛函理论方法对聚对苯二甲酸丁二醇酯(PBT)二聚体的键离能进行了计算.为了选取较为精确的方法来计算PBT各个键的键离能,以与PBT具有相同的酯基官能团的乙酸乙酯为模型参照物.采用M062X, B3P86, M06, PBE0, wB97xD方法分别在基组6-31G(d), 6-311G(d), 6-311+G(d, p), 6-311++G(d, p), cc-pVDZ, cc-pVTZ水平下对乙酸乙酯的键离能进行计算.通过对比计算结果与iBonD数据库的乙酸乙酯实验测定值可知,M062X在基组6-311G(d)水平下计算结果与实验值最为接近.因此,本研究采用M062X方法在基组6-311G(d)水平下对聚对苯二甲酸丁二醇酯(PBT)二聚体的键离能进行计算.计算结果表明：在PBT的各键中C-C_arcmatic键的键离能最大,主链上的C-C键离能最小,为370.9 kJ/mol.其次就是C-O键,为404.6 kJ/mol.基于PBT键离能的计算结果,设计了3条PBT二聚体热降解过程可能形成的反应路径,分析了热解产物的形成机理.结果表明PBT二聚体热解过程可...     

Diffusion of Al dimers on the surface of Mg clusters

The surface diffusion of Al dimmers on Mg clusters with hexahedral structure was studied using the combination of quenched molecular dynamics and the embedded atom method. The system energy barriers of typical minimum energy diffusion paths for Al dimers on the Mg clusters were calculated using the Nudged Elastic Band method. In our study range (153–4061 atoms), the binding energies on the (0001) facets and the (1\(\hbox{$\overline 1 $}\)01) facets differed, the binding energy on the former was lower than that on the latter. Moreover, cluster size only slightly influenced the binding energy values. Two possible diffusion paths were studied. Results showed that the diffusion of the dimer on the (0001) facet easily occurred at low temperatures. Furthermore, the interaction between the two atoms of the dimer facilitated the dimer crossing of the step edge between the (1\(\hbox{$\overline 1 $}\)01) facets by hopping mechanism.     

Cu dimer diffusion on strained Cu(0 0 1)

Cu dimer diffusion energy barrier on strained Cu(0 0 1) surfaces has been studied with nudged elastic band method (NEB) and embedded atom method (EAM). Dimer exchange and hopping mechanisms are chosen as the initial diffusion paths in the NEB method. It is shown here that the dimer exchange is dominant on tensile surfaces and the dimer hopping is dominant on compressive surfaces. For most strain conditions Cu dimer diffusion energy barrier is lower than Cu monomer diffusion barrier. The concerted movement of the remaining adatom toward the hopping adatom lowers the dimer hopping barrier. The adsorption induced relaxation makes the dimer exchange barriers lower than the monomer exchange barriers on tensile surfaces. Transition state theory is used to calculate the diffusion frequencies as a function of temperature. No surface crowdion is observed on the shear strained surfaces for the dimer diffusion.     

Defect-induced dimer pinning on the Si(0 0 1) surface

Room-temperature STM images frequently show regions of antisymmetric dimer ordering surrounding certain types of defect on the Si(0 0 1) surface. While it has been generally believed that any defect asymmetric with respect to the dimer row would induce this dimer pinning effect, recent experimental results have shown that this is not the case. We present a model, based on a nearest-neighbour Ising treatment of the surface, which allows the extent of pinning caused by a dimer to be predicted from ab initio calculations. We use this model to predict the pinning extent for three phosphorus-containing structures important in a proposed silicon-based quantum computer fabrication scheme, and identify one of these asymmetric features as causing no appreciable pinning. In addition, we use ab initio calculations to identify the effects governing the interaction between neighbouring dimers.     

Finding the dominant energy transmission paths in statistical energy analysis

A key issue for noise, vibration and harshness purposes, when modelling the vibroacoustic behaviour of a system, is that of determining how energy is transmitted from a given source, where external energy is being input, to a target where energy is to be reduced. In many situations of practical interest, a high percentage of the transmitted energy is driven by a limited set of dominant paths. For instance, this is at the core of the existence of transmission loss regulations between dwellings. In this work, it is shown that in the case of a system modelled with statistical energy analysis (SEA), the problem of ranking dominant paths can be posed as a variation of the so-called K shortest path problem in graph theory. An algorithm for the latter is then modified and adapted to obtain the sorted set of K dominant energy transmission paths in a SEA model. A numerical example to show its potential for practical applications is included.     

The effect of random errors on a large statistical energy analysis model

The framework of analysis known as Statistical Energy Analysis has many important applications particularly in systems where detailed information is not available. As a result of the approximations made, to simplify the calculations, random error can be introduced into the SEA model. For large systems this gives rise to uncertainty in the energy levels. It is shown that the effect of these errors on the model depends on the “shape” of the model. A compact model dominated by short paths is less affected than a model controlled by long paths. In either case the ratio of the average error in the resultant energy level to the average error in the coupling loss factor decreases as the errors increase. This means that large models may be used with confidence even when based on data that is known to be approximate.     

Accelerating regular polygon beams

Beams that possess high-intensity peaks that follow curved paths of propagation under linear diffraction have recently been shown to have a multitude of interesting uses. In this Letter, a family of phase-only masks is derived, and each mask gives rise to multiple accelerating intensity maxima. The curved paths of the peaks can be described by the vertices of a regular polygon that is centered on the optic axis and expands with propagation.     

Simulation of the Double Proton Transfer Dynamics in the Benzoic Acid Dimer

A numerical simulation of the rate constants of the double proton transfer in the benzoic acid dimer at partial and complete deuteration of hydrogen bonds in the dimer as well as at different hydrostatic pressures applied to the sample has been carried out on the basis of the model of a multistage process activated by equilibrium radiation. It has been shown that this model, as opposed to the known approach based on the synthesis of two processes — activation (Boltzmann–Arrhenius model) and molecular tunneling (Goldanskii model) — can describe both low- and high-temperature rate constants of reactions using a single set of parameters characterizing the process of interaction of the transforming molecule with the thermal field.     

3D reconstruction of the hemocyanin subunit dimer from the chiton Acanthochiton fascicularis

Procedures are presented for the purification of the subunit dimer from Acanthochiton fasicularis hemocyanin. Electron microscopy of negatively stained specimens revealed a uniform population of macromolecules possessing the characteristic "boat shape". A 3D reconstruction from this EM data generated a approximately 3 nm resolution model that correlates well with earlier data of the purported subunit dimer, extracted from the 3D reconstruction of the didecamer of Haliotis tuberculata hemocyanin type 1.     

Spin quantum tunneling via entangled states in a dimer of exchange-coupled single-molecule magnets

A new family of supramolecular, antiferromagnetically exchange-coupled dimers of single-molecule magnets (SMMs) has recently been reported. Each SMM acts as a bias on its neighbor, shifting the quantum tunneling resonances of the individual SMMs. Hysteresis loop measurements on a single crystal of SMM dimers have now established quantum tunneling of the magnetization via entangled states of the dimer. This shows that the dimer really does behave as a quantum mechanically coupled dimer, and also allows the measurement of the longitudinal and transverse superexchange coupling constants.     

Theory of monomer-dimer systems

We investigate the general monomer-dimer partition function,P(x), which is a polynomial in the monomer activity,x, with coefficients depending on the dimer activities. Our main result is thatP(x) has its zeros on the imaginary axis when the dimer activities are nonnegative. Therefore, no monomer-dimer system can have a phase transition as a function of monomer density except, possibly, when the monomer density is minimal (i.e.x=0). Elaborating on this theme we prove the existence and analyticity of correlation functions (away fromx=0) in the thermodynamic limit. Among other things we obtain bounds on the compressibility and derive a new variable in which to make an expansion of the free energy that converges down to the minimal monomer density. We also relate the monomer-dimer problem to the Heisenberg and Ising models of a magnet and derive Christoffell-Darboux formulas for the monomer-dimer and Ising model partition functions. This casts the Ising model in a new light and provides an alternative proof of the Lee-Yang circle theorem. We also derive joint complex analyticity domains in the monomer and dimer activities. Our considerations are independent of geometry and hence are valid for any dimensionality.Work supported by National Science Foundation Grant GP-26526.     

Structural phase transitions of the Si(100) surface

A Monte Carlo study of the structural phase transitions on the Si(100) surface for both the “(2×1)” and “c(2×2)” reconstruction families is carried out using the asymmetric dimer model. A second order phase transition is observed at about 250 K from a p(2×2) (layered antiferromagnetic) to a disordered (paramagnetic) state in the “2×1” family. A similar transition is observed about 800 K from a c(2×2) (ferromagnetic) to a disordered state in the “c(2×2)” family. These results are in agreement with real-space renormalization group results. The variation of the specific heat, susceptability and the absolute value of the order parameter as a function of temperature is obtained in the range 200 to 300 K for the “2×1” family and 750 to 850 K for the “c(2×2)” family. Also, the order parameter correlation function is computed for ten different temperatures in the above ranges.     

On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms

In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.     

Tungsten cluster migration on nanoparticles: minimum energy pathway and migration mechanism

Saddle point searches have been employed to investigate the migration mechanisms of W clusters on W nanoparticles, and to determine the corresponding migration energies for the possible migration paths of these clusters. The tungsten clusters containing up to four adatoms are found to prefer 2D-compact structures with relatively low binding energies. The effect of interface and vertex regions on the migration behavior of the clusters is significantly strong, as compared to that of nanoparticle size. The migration mechanisms are quite different when the clusters are located at the center of the nanoparticle and near the interface or vertex areas. Near the interfaces and vertex areas, the substrate atoms tend to participate in the migration processes of the clusters, and can join the adatoms to form a larger cluster or lead to the dissociation of a cluster via the exchange mechanism, which results in the adatom crossing the facets. The lowest energy paths are used to be determined the energy barriers for W cluster migrations (from 1- to 4-atoms) on the facets, edges and vertex regions. The calculated energy barriers for the trimers suggest that the concerted migration is more probable than the successive jumping of a single adatom in the clusters. In addition, it of interest to note that the dimer shearing is a dominant migration mechanism for the tetramer, but needs to overcome a relatively higher migration energy than other clusters.     

The Height Fluctuations of an Off-Critical Dimer Model on the Square Grid

The dimer model on a planar bipartite graph can be viewed as a random surface measure. We study these fluctuations for a dimer model on the square grid with two different classes of weights and provide a condition for their equivalence. In the thermodynamic limit and scaling window, these height fluctuations are shown to be non-Gaussian.     

Adsorption and reactions of HN3 on Si(1 0 0)-2 × 1: A computational study

We have studied the adsorption and decomposition of HN₃ on Si(1 0 0)-2 × 1 surface using the hybrid density functional B3LYP method and effective core potential basis, LanL2DZ, with Si₁₅H₁₆ as a double dimer surface model for cluster calculations. The result shows that the barriers for the dissociative adsorption of HN₃ forming HN(a) + N₂(g) are quite low by stepwise dissociation processes occurring either on a dimer or across the dimers. The low activation energies are consistent with previous experimental observations that the molecularly adsorbed HN₃(a) can undergo decomposition producing HN(a) at low surface temperatures. On the other hand, the predicted activation energies for the N₃(a) + H(a) formation processes are all relatively higher. These results also explain the absence of the N₃(a) species in HREELS measurements following each annealing experiment. Several selected reaction paths were also confirmed with slab model calculations using an optimization approach coupling the energy and gradient calculations by the slab model with the geometrical optimization using Berny algorithm.In addition, the adsorbate effect was examined for the end-on and side-on molecular configurations. For the side-on adsorption configuration, all possible combinations with 1-4 adsorbates can exist on the four surface Si sites of the double dimers, with adsorption energies lying closely to the multiples of that of a single side-on adsorbate (LM2); i.e., adsorption energies are nearly additive. Interestingly, for the end-on adsorption, only 1 and 2 HN₃ molecules can adsorb on a dimer due to the presence of the negative charges on the remaining Si sites in the neighboring dimer. For the two end-on adsorbates on the same dimer, the total adsorption energy is close to two times that of HN₃(a) or LM1. For the mixed end-on/side-on configurations, only one of each type can co-exist on a single dimer pair (Si₁-Si₂ or Si₃-Si₄) sites with adsorption energy close to the sum of those of one end-on and one side-on adsorbate. Finally, the predicted reaction routes and vibrational frequencies showed good agreement with previous experimental results. The stabilities of many ad-species involved in these reactions with end-on and/or side-on configurations have been predicted together with the transition states connecting those species.