Dimer statistics of honeycomb lattices on Klein bottle,Möbius strip and cylinder

Dimer statistics is a central problem in statistical physics. In this paper the enumerations of close-packed dimers of honeycomb lattices on Klein bottle, Möbius strip and cylinder are considered. By establishing a Pfaffian orientation or a crossing orientation, and then computing the determinants of the skew-symmetric matrices of the resulting orientation graphs, we obtain explicit expressions of the number of close-packed dimers of the Klein-bottle polyhex, the Möbius polyhex and the cylindrical polyhex.     

Dimer statistics on the Möbius strip and the Klein bottle

Closed-form expressions are obtained for the generating function of close-packed dimers on a 2M×2N simple quartic lattice embedded on a Möbius strip and a Klein bottle. Finite-size corrections are also analyzed and compared with those under cylindrical and free boundary conditions. Particularly, it is found that, for large lattices of the same size and with a square symmetry, the number of dimer configurations on a Möbius strip is 70.2% of that on a cylinder. We also establish two identities relating dimer generating functions for Möbius strips and cylinders.     

Dimer problem on the cylinder and torus

We obtain explicit expressions of the number of close-packed dimers and entropy for three types of lattices (the so-called 8.8.6, 8.8.4, and hexagonal lattices) with cylindrical boundary condition and the entropy of the 8.8.6 lattice with toroidal boundary condition. Our results and the one on 8.8.4 and hexagonal lattices with toroidal boundary condition by Salinas and Nagle [S.R. Salinas, J.F. Nagle, Theory of the phase transition in the layered hydrogen-bonded SnCl²⋅2H₂O crystal, Phys. Rev. B 9 (1974) 4920-4931] and Wu [F.Y. Wu, Dimers on two-dimensional lattices, Inter. J. Modern Phys. B 20 (2006) 5357-5371] imply that the 8.8.6 (or 8.8.4) lattices with cylindrical and toroidal boundary conditions have the same entropy whereas the hexagonal lattices have not. Based on these facts we propose the following problem: under which conditions do the lattices with cylindrical and toroidal boundary conditions have the same entropy?     

Klein bottles and simple currents

The standard Klein bottle coefficient in the construction of open descendants is shown to equal the Frobenius-Schur indicator of a conformal field theory. Other consistent Klein bottle projections are shown to correspond to simple currents. These observations enable us to generalize the standard open string construction from C-diagonal parent theories to include non-standard Klein bottles. Using (generalizations of) the Frobenius-Schur indicator we prove positivity and integrality of the resulting open and closed string state multiplicities for standard as well as non-standard Klein bottles.     

BML model on non-orientable surfaces

Two-dimensional Biham-Middleton-Levine traffic model on a N×N square lattice embedded on a Klein bottle and a projective plane is investigated by computer simulations. The behavior of the model with these boundary conditions is compared with the model under toroidal boundary conditions. Our numerical results show that the phase diagram depends strongly on the underlying topology. We also investigate the influence of the ratio between the number of red and blue particles has over the speed of the system and conclude that the projective plane case differs considerably from the other cases reviewed here.     

Interacting classical dimers on the square lattice

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)]. By means of Monte Carlo and transfer matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.     

铁的冲击相变机制的分子动力学研究

 用分子动力学方法模拟计算了在冲击波加载条件下，单晶铁中的结构相变（由体心立方结构α相到六角密排结构ε相），相互作用势采用铁的嵌入式原子势（EAM），单晶铁样品的尺寸为28.7 nm×22.9 nm×22.9 nm，总原子数为1.28×10⁶个。通过推动一个运动活塞对静止靶的作用来产生冲击压缩，加载方向沿单晶铁的[100]晶向。通过对原子位置的追踪，揭示了铁的冲击相变机制，计算结果表明相变机制包括两步：首先是在{011}面上的原子受到沿〈100〉晶向的压缩，使{011}面转化成正六角形密排面；然后是在{011}面上原子沿〈0-11〉晶向的滑移，完成由bcc结构到hcp结构的相变。同时发现滑移面只出现在与冲击波加载方向平行的(011)和(0-11)面上。     

Carbide induced reconstruction of monatomic steps on Ni(1 1 1) - A density functional study

We present density functional calculations for carbon adsorption at the two types of monatomic steps on a Ni(1 1 1) surface. We show that it is thermodynamically favourable to make a carbon induced clock-type reconstruction at the close-packed step with a [1 1 1] step geometry, which creates fourfold sites at the step-edge. It is furthermore possible to extend the carbide with the clock reconstructed geometry onto the upper terrace with a net energy gain compared to adsorption of carbon on unreconstructed close-packed steps or terrace sites on Ni(1 1 1). Our findings explain the fact that carbide islands start to grow preferentially on the close-packed steps as has been observed using scanning tunneling microscopy.     

Parameter identification of chaos system based on unknown parameter observer

Parameter identification of chaos system based on unknown parameter observer is discussed generally. Based on the work of Guan et al. [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26], the design of unknown parameter observer is improved. The application of the improved approach is extended greatly. The works in some literatures [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26; J.H. Lü, S.C. Zhang, Phys. Lett. A 286 (2001) 148; X.Q. Wu, J.A. Lu, Chaos Solitons Fractals 18 (2003) 721; J. Liu, S.H. Chen, J. Xie, Chaos Solitons Fractals 19 (2004) 533] are only the special cases of our Corollaries 1 and 2. Some observers for Lü system and a new chaos system are designed to test our improved method, and simulations results demonstrate the effectiveness and feasibility of the improved approach.     

Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology??after Merleau-Ponty, Heidegger and Rosen??and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown??s primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard??s gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above.     

The Klein-Gordon Operator on Möbius Strip Domains and the Klein Bottle in ℝ n

In this paper we present explicit formulas for the fundamental solution to the Klein-Gordon operator on some higher dimensional generalizations of the Möbius strip and the Klein bottle with values in distinct pinor bundles. The fundamental solution is described in terms of generalizations of the Weierstraß $\wp $ -function that are adapted to the context of these geometries. The explicit formulas for the kernel then allow us to express all solutions to the homogeneous and inhomogeneous Klein-Gordon problem with given boundary data in the context of these manifolds. In the case of the Klein bottle we are able to describe all null solutions of the Klein-Gordon equation in terms of finite linear combinations of the fundamental solution and its partial derivatives.     

Strings on orientifolds

We construct several examples of compactification of type IIB theory on orientifolds and discuss their duals. In six dimensions we obtain models with N = 1 supersymmetry, multiple tensor multiplets, and different gauge groups. In nine dimensions we obtain a model that is dual to M-theory compactified on a Klein bottle.     

Resonance transition energies and oscillator strengths in lutetium and lawrencium

The transition energies and oscillator strengths for nd (2)D(3/2)-(n+1)p (2)P(o)(1/2,3/2) transitions in Lu ( n = 5, Z = 71) and Lr ( n = 6, Z = 103) were calculated with the multiconfiguration Dirac-Hartree-Fock method. The present study confirmed that the ground state of atomic Lr is [Rn]5f(14)7s(2)7p (2)P(o)(1/2). The calculation for Lr required wave function expansions of more than 330 000 configuration states. In Lu, the transition energies, with Breit and QED corrections included, agree with experiment to within 126 cm(-1). In lighter elements, core correlation is usually neglected but was found to be of extreme importance for these heavy elements, affecting the oscillator strengths by a factor of 3 and 2 in Lu and Lr, respectively.     

Water dimer diffusion on Pd[111] assisted by an H-bond donor-acceptor tunneling exchange

Based on the results of density functional theory calculations, a novel mechanism for the diffusion of water dimers on metal surfaces is proposed, which relies on the ability of H bonds to rearrange through quantum tunneling. The mechanism involves quasifree rotation of the dimer and exchange of H-bond donor and acceptor molecules. At appropriate temperatures, water dimers diffuse more rapidly than water monomers, thus providing a physical explanation for the experimentally measured high diffusivity of water dimers on Pd[111] [Science 297, 1850 (2002)]].     

Magnetic properties of liquid crystalline iron complexes

We report on the magnetic properties of liquid crystalline iron complexes with 1,4,7-tris[3,4-bis(decyloxy)-benzyl]-1,4,7-triazacyclononane. Mössbauer spectroscopy in external magnetic fields reveals two different molecular configurations: monomers form magnetic single domain particles while dimers are found to behave diamagnetic.

     

Response to the Comment on ‘Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices’

The error of Equation (15b) in my article [Z.D. Zhang, Phil. Mag. 87 (2007) p.5309] in the application of the Jordan–Wigner transformation does not affect the validity of the putative exact solution, since the solution is not derived directly from that equation. Other objections of Perk's comment [J.H.H. Perk, Phil. Mag. 89 (2009) p.761] are the same as those in Wu et al.'s comments [F.Y. Wu et al., Phil. Mag. 88 (2008) p.3093; p.3103], which do not stand on solid ground and which I have sought to refute in my previous response [Z.D. Zhang, Phil. Mag. 88 (2008) p.3097]. The conjectured solution can be utilized to understand critical phenomena in various systems, whereas the conjectures are open to rigorous proof.     

Identification of syllables in noise: electrophysiological and behavioral correlates

This study was designed to characterize the effect of background noise on the identification of syllables using behavioral and electrophysiological measures. Twenty normal-hearing adults (18-30 years) performed an identification task in a two-alternative forced-choice paradigm. Stimuli consisted of naturally produced syllables [da] and [ga] embedded in white noise. The noise was initiated 1000 ms before the onset of the speech stimuli in order to separate the auditory event related potentials (AERP) response to noise onset from that to the speech. Syllables were presented in quiet and in five SNRs: +15, +3, 0, -3, and -6 dB. Results show that (1) performance accuracy, d', and reaction time were affected by the noise, more so for reaction time; (2) both N1 and P3 latency were prolonged as noise levels increased, more so for P3; (3) [ga] was better identified than [da], in all noise conditions; and (4) P3 latency was longer for [da] than for [ga] for SNR 0 through -6 dB, while N1 latency was longer for [ga] than for [da] in most listening conditions. In conclusion, the unique stimuli structure utilized in this study demonstrated the effects of noise on speech recognition at both the physical and the perceptual processing levels.     

香兰素对甲苯胺希夫碱稀土配合物的红外光声光谱

研究了香兰素对甲苯胺希夫碱及其金属配合物在３８００－２００ ｃｍ＾－１范围的傅里叶变换红外光谱光谱，对主要谱带进行了经验归属。     

Surface atom displacement processes

Progress in field ion microscope studies of adatom displacements on metal surfaces is reviewed. It is concluded that of the displacement processes that contribute to surface diffusion only displacements between low-coordination (terrace) sites are well characterised. Procedures and preliminary results of FIM studies of adatom displacement over steps are described. Activation energies measured for passage of Ta, W, Re, Ir and Pt adatoms across (110) W steps are found to equal activation energies for diffusion over (110) W, despite the highly reflecting character of the step for all the adsorbates except Pt. Displacements of adatoms interacting with other adatoms are discussed. Results presented show that interaction of transition metal adatoms forming close-packed dimers on (110) W is rather weak, with a minimum interaction energy [?U(r) < 4kJ/mol] for Re₂ corresponding to a very weak attraction for Re adatoms 0.27 nm apart.     

Dimers on the kagome lattice I: Finite lattices

We report exact results on the enumeration of close-packed dimers on a finite kagome lattice with general asymmetric dimer weights under periodic and cylindrical boundary conditions. For symmetric dimer weights, the resulting dimer generating functions reduce to very simple expressions, and we show how the simple expressions can be obtained from the consideration of a spin-variable mapping.