New Correlation Duality Relations for the Planar Potts Model

We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. We show that generally it is linear combinations of correlation functions, not the individual correlations, that are related by dualities. The method is illustrated in several non-trivial cases, and the relation to earlier results is explained. A graph-theoretical formulation of our results in terms of rooted dichromatic, or Tutte, polynomials is also given.     

Discrete network models for the low-field Hall effect near a percolation threshold: Theory and simulations

The critical behavior of the weak-field Hall effect near a percolation threshold is studied with the help of two discrete random network models. Many finite realizations of such networks at the percolation threshold are produced and solved to yield the potentials at all sites. A new algorithm for doing that was developed that is based on the transfer matrix method. The site potentials are used to calculate the bulk effective Hall conductivity and Hall coefficient, as well as some other properties, such as the Ohmic conductivity, the size of the backbone, and the number of binodes. Scaling behavior for these quantities as power laws of the network size is determined and values of the critical exponents are found.School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel     

Critical temperature for two-dimensional ising ferromagnets with quenched bond disorder

The configuration-averaged free energy of a quenched, random bond Ising model on a square lattice which contains an equal mixture of two types of ferromagnetic bonds J₁ and J₂ is shown to obey the same duality relation as the ordered rectangular model with the same two bond strengths. If the random.system has a single, sharp critical point, the critical temperature T_c must be identical to that of the ordered system, i.e., sinh(2J ₁/kT _c) sinh(2J ₂/kT _c) = 1. Since _c ^(B) = 1/2, we can takeJ ₂ 0 and use Bergstresser-type inequalities to obtain(/dp) exp(–2J ₁/kT_c¦_p=p_c + = 1, in agreement with Bergstresser's rigorous result for the diluted ferromagnet near the percolation threshold.Work supported in part by National Science Foundation Grant No. DMR 76-21703, Office of Naval Research Grant No. N00014-76-C-0106, and National Science Foundation MRL program Grant No. DMR 76-00678.Paper presented at the 37th Yeshiva University Statistical Mechanics Meeting, May 10, 1977.     

The Duality Transformation for an n-Species Ising Model Interacting with Z2 Gauge Fields on a Random Surface

The duality transformation is carried out for an n-species Ising spin system interacting with Z₂ gauge fields. For n > 1, we find that the dual model has topological terms when the surface is topologically nontrivial. The plaquette interaction of the gauge fields is dual to an n-spin coupling in the dual model.     

Percolation of level sets for two-dimensional random fields with lattice symmetry

Let (x),x², be a random field, which may be viewed as the potential of an incompressible flow for which the trajectories follow the level lines of . Percolation methods are used to analyze the sizes of the connected components of level sets {x:(x)=h} and sets {x:(x)h} in several classes of random fields with lattice symmetry. In typical cases there is a sharp transition at a critical value ofh from exponential boundedness for such components to the existence of an unbounded component. In some examples, however, there is a nondegenerate interval of values ofh where components are bounded but not exponentially so, and in other cases each level set may be a single infinite line which visits every region of the lattice.     

Exact Results for the Universal Area Distribution of Clusters in Percolation, Ising, and Potts Models

At the critical point in two dimensions, the number of percolation clusters of enclosed area greater than A is proportional to A ^–1, with a proportionality constant C that is universal. We show theoretically (based upon Coulomb gas methods), and verify numerically to high precision, that . We also derive, and verify to varying precision, the corresponding constant for Ising spin clusters, and for Fortuin–Kasteleyn clusters of the Q = 2, 3 and 4-state Potts models.     

String Cosmological Solutions with O(d,d) Duality Symmetry and Matter Coupling

The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.     

Diamond Composites with TiC,SiC and Ti 3 SiC 2 Bonding Phase

The problems connected with producing diamond composites with 30 wt.% of bonding phase in form of: SiC, TiC, and Ti 3 SiC 2 are presented in the paper. Increasing the fraction of the bonding phase within the composite generally helps to reduce internal stresses. Composites were sintered at pressure 8.0 - 0.2 GPa and temperature of 2070 - 50 K using the Bridgman type high pressure apparatus. Interactions in the diamond-SiC, the diamond-TiC, and the diamond-Ti 3 SiC 2 systems were studied by means of transmission electron microscope (TEM) and X-ray diffraction. Density was measured pycnometrically. The wear resistance studies of these composites were carried out using pin - on disc type laboratory equipment. Hardness was measured with Vickers apparatus. Results of measurements of physical and mechanical properties are reported.     

Mean-Field Behavior for Long- and Finite Range Ising Model,Percolation and Self-Avoiding Walk

We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion we prove mean-field behavior for these models if d>2(α ∧2) for self-avoiding walk and the Ising model, and d>3(α ∧2) for percolation, where d denotes the dimension and α the power-law decay exponent of the coupling function. We provide a simplified analysis of the lace expansion based on the trigonometric approach in Borgs et al. (Ann. Probab. 33(5):1886–1944, 2005).      

Modification of a Theoretical Model for the Prediction of the Thermal Expansion Behavior of Particulate Composites: Application to Poly(vinyl chloride)/Talc Composites

The coefficients of thermal expansion (CTE) of poly(vinyl chloride) (PVC)/talc composites were tested and the experimental data showed that the CTE of PVC/talc composites were closely related to the talc particle size and its distribution; for a given talc volume fraction, the smaller the talc particle size, and the lower the CTE of the PVC/talc composites. The theoretical equations proposed by Sideridis and Papanicolaou and by Lombardo, which were based on a single, spherical particle size, were found to predict well the CTE of PVC/talc composites, but with the obtained interphase thicknesses were too large to be believed. In order to overcome the shortcomings of these equations, being without variation of filler particle size and its distribution, a modified model was proposed. It was found that the modified model can predict well the CTE of PVC/talc composites, with almost the same and more reliable interphase thicknesses for different talc particle sizes, confirming the correctness of the modified model to some extent.     

Carbon materials with quasi-graphene layers: the dielectric, percolation properties and the electronic transport mechanism

We investigate the dielectric properties of multi-walled carbon nanotubes (MWCNTs) and graphite filling in SiO₂ with the filling concentration of 2-20 wt.% in the frequency range of 10²-10⁷ Hz. MWCNTs and graphite have general electrical properties and percolation phenomena owing to their quasi-structure made up of graphene layers. Both permittivity ε and conductivity σ exhibit jumps around the percolation threshold. Variations of dielectric properties of the composites are in agreement with the percolation theory. All the percolation phenomena are determined by hopping and migrating electrons, which are attributed to the special electronic transport mechanism of the fillers in the composites. However, the twin-percolation phenomenon exists when the concentration of MWCNTs is between 5-10 wt.% and 15-20 wt.% in the MWCNTs/SiO₂ composites, while in the graphite/SiO₂ composites, there is only one percolation phenomenon in the graphite concentration of 10-15 wt.%. The unique twin-percolation phenomenon of MWCNTs/SiO₂ is described and attributed to the electronic transfer mechanism, especially the network effect of MWCNTs in the composites. The formation of network plays an essential role in determining the second percolation threshold of MWCNTs/SiO₂.     

Phase transitions, interfacial fluctuations and hidden symmetries for fluids near structured walls

Fluids adsorbed at micro-patterned and geometrically structured substrates can exhibit novel phase transitions and interfacial fluctuation effects distinct from those characteristic of wetting at planar, homogeneous walls. We review recent theoretical progress in this area paying particular attention to filling transitions pertinent to fluid adsorption near wedges, which have highlighted a deep connection between geometrical and contact angles. We show that filling transitions are not only characterized by large scale interfacial fluctuations leading to universal critical singularities but also reveal hidden symmetries with short-ranged critical wetting transitions and properties of dimensional reduction. We propose a non-local interfacial model which fulfills all these properties and throws light on long-standing problems regarding the order of the 3D short-range critical wetting transition.     

Thermal,Mechanical, and Dielectric Properties of a Dielectric Elastomer for Actuator Applications

Dielectric elastomers (DE) are a new type of electro-active material, which is able to produce a large degree of deformation under electrical stimulation. The thermal, mechanical, and dielectric properties of the most widely used dielectric acrylic elastomer (VHB 4910), commercially available from the company 3M, were studied by differential scanning calorimetry (DSC), thermal gravimetric analysis (TGA), dynamic mechanical analysis (DMA), and broadband dielectric spectroscopy (BDS) analyzer, respectively. DSC experiments on the VHB 4910 showed a glass transition at about ?40°C. VHB 4910 started to lose weight at about 250°C from the TGA study. The results of DMA indicated the storage modulus of VHB 4910 increased with frequency and had a strong temperature dependence of elasticity. The dielectric constant of VHB 4910 increased as a function of temperature up to 0°C, followed by a drop till 100°C. The mechanical and electrical efficiency of dielectric elastomer actuators (DEA) of VHB 4910 were analyzed. It was demonstrated that the actuation performance is dominated by the mechanical properties of the elastomer and is less influenced by the frequency and the temperature dependence of the dielectric properties; this may be used to guide the design of actuator configurations, as well as the choice of actuator materials.     

Electrical properties of nanocrystalline magnetite with large non-stoichiometry, near Verwey transition

DC electrical measurements were carried out on compacted powders of magnetite with an average particle diameter of 50 nm over the temperature range 10-300 K. The non-stoichiometry was estimated from Mossbauer spectroscopy analysis. High-resolution X-ray diffraction studies in the temperature range 93-300 K did not show any phase transition. There was a drastic change in resistivity around 80 K but no discontinuity thereof. Electrical resistivity vs. temperature data were analysed on the basis of Mott's small polaron and variable-range hopping models, respectively. The Verwey temperature as estimated from this analysis was 93 K. From voltage-current characteristics it was concluded that there was a small intrinsic gap at the Fermi level above the transition temperature and the same increased drastically below the transition temperature. This was ascribed to a transition from short-range order to long-range order as the temperature was lowered.     

Effect of Wood Flour on the Curing Behavior,Mechanical Properties,and Water Absorption of Natural Rubber/Wood Flour Composites

The preparation of natural rubber/wood flour (NR/WF) composites and the influence of WF content, modification, and particle size on the vulcanizing behavior, mechanical properties, and water absorption of NR/WF composites are described. Results show that the addition of WF into NR delayed the scorching time and vulcanizing time of NR. The appropriate WF contents can improve the mechanical properties of NR. However, the overloading of WF destroys the mechanical properties of NR. The addition of WF increased the water absorption of NR. The silicone couple agents that were used to modify the WF had little effect on the water absorption of NR/WF composites. Decreasing the WF particle size enhanced the water absorption of NR/WF composites because the water-absorbing surface area increased with decreasing WF particle size. The water absorption of sisal-fiber-filled NR-based composites was larger than that of the WF-filled NR-based composites. A useful equation, w=ktⁿ , was inferred from the water absorption results to calculate the water absorption (w) of the NR/WF composites as a function of time (t), where k was a constant concerning the compounds’ character that was primarily determined by the WF's character and n was the power of time that was related to the NR's inherent character, such as cross-linking density, and primarily determined the water absorption rate.     

Phase Structure,Thermal, and Mechanical Properties of Polypropylene/Hollow Glass Microsphere Composites Modified with Maleated Poly(ethylene-octene)

Maleated poly(ethylene-octene) (POE-g-MAH), as a compatilizer and toughener, was incorporated in polypropylene/hollow glass microspheres (PP/HGM) binary composites, and the phase structure and thermal and mechanical properties of these composites were investigated. Scanning electron microscopy analysis indicated that the phase structure of ternary composites could be controlled by POE-g-MAH and the surface treatment of HGM. Fourier transform infrared spectroscopy revealed that there was an amidation reaction between the treated HGM and POE-g-MAH during melt compounding. Differential scanning calorimetry suggested that the crystallization and melting behaviors of ternary composites were influenced by phase structure. Evaluation of mechanical properties showed that the amide linkage between the treated HGM and POE-g-MAH was favorable for improving the properties of ternary composites.     

Relations,analogous to Snoek's one,for domain wall processes

The suitability of relations having a formal similarity with the known Snoek's law is analysed for polycrystalline ferrites (PF) in their typical domain wall process frequency range. The parameters used in these relations are the saturation magnetization and those taken from the complex permeability spectrum and from microstructure of PF sample.     

Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations

We study the behavior of the wave part of asymptotic solutions to the Cauchy problem for linearized shallow water equations with initial perturbations localized near the origin. The global representation for these solutions based on the generalized Maslov canonical operator was given earlier. The asymptotic solutions are also localized in the neighborhood of certain curves (fronts). The simplification of general formulas and the behavior of asymptotic solutions in a neighborhood of the regular part of fronts was also given earlier. Here the behavior of asymptotic solutions in a neighborhood of the focal point of the fronts is discussed in detail and the proof of formulas announced earlier for the wave equation is given. This paper can be regarded as a continuation of the paper in Russiian Journal of Mathematical Physics 15 (2), 192–221 (2008). In memoriam V.A. Borovikov     

Organic Nano-Montmorillonite for Simultaneously Improving the Flame Retardancy,Thermal Stability,and Mechanical Properties of Intumescent Flame-Retardant Silicone Rubber Composites

The flammability of room temperature vulcanized silicone rubber (RTVSR) composites filled with melamine phosphate (MP) as intumescent flame-retardant additives was characterized by limiting oxygen index (LOI), UL-94 test, and cone calorimeter. In addition, the thermal degradation of the composites was studied using thermogravimetric analysis (TGA). Furthermore, in order to relate to actual application requirements, the comprehensive performance of the RTVSR/MP composites was optimized by adding organic nano-montmorillonite (OMMT) as a partial substitute for the MP. The as-prepared intumescent flame-retardant RTVSR/MP/OMMT nanocomposites were characterized by LOI, UL-94 test, TGA, cone calorimetry, scanning electron microscopy (SEM), and mechanical tests. The residue morphology formed after the burning of the nanocomposites was analyzed by its SEM and digital photographs. The results showed that the flame-retardant nanocomposites filled with 10 phr OMMT and 35 phr MP displayed the best comprehensive performance in terms of the flame retardancy, mechanical properties, and heat stability at low cost. It is expected that the intumescent flame-retardant silicone rubber composites with simultaneously improved flame retardancy, thermal stability, and mechanical properties will meet more requirements of the increasingly complex applications.     

Applications to metal K pre-edges of transition metal dimers illustrate the approximate origin independence for the intensities in the length representation

ABSTRACT

X-ray absorption spectroscopy (XAS) in the metal K pre-edge is a standard probe of electronic and geometric structure of transition metal complexes. Simulating the K pre-edge spectra requires contributions beyond the electric dipole, but if that term is non-zero, the second-order terms, e.g. electric quadrupoles, are no longer origin-independent. In the velocity representation, complete origin independence can be achieved by including all terms to the same order in the oscillator strength. Here, we implement that approach in the length representation and use it for restricted active space (RAS) simulations of metal K pre-edges of iron monomers and dimers. Complete origin independence is not achieved and the size of the remaining errors depends on the electric dipole oscillator strength and its ratio in length and velocity representations. The error in the origin independence is in the ANO basis sets two orders of magnitude smaller than the value of the individual contributions. For systems with strong electric dipole contributions, the errors are not significant within 3 Å from a metal centre, far enough to handle many multi-metal systems. Furthermore, we discuss the convergence of the multipole expansion, the possibility to assign spectral contributions, and the origin of negative absorption intensities.