Typical Exponent Research Articles

Asymptotic Description of Fast Thermal Processes in Scalar Harmonic Lattices

Thermal vibrations in a d-dimensional (d = 1, 2) scalar harmonic lattice of a simple structure are under consideration. Redistribution of the averaged kinetic and potential energies of particles after instantaneous thermal excitation (fast process) is described. It is established that the difference between the kinetic and potential energies undergoes power-law damped oscillations at times much longer than the characteristic atomic-vibration period. A typical exponent is –d/2. The oscillation frequencies are determined from the dispersion relation for the lattice. The algorithm of proving allows generalization to scalar and vector lattices with a complex structure and different dimensions. Thermal vibrations in a two-dimensional hexagonal lattice (graphene lattice) are considered as an example of this generalization.

Electric conductivity in silicone-carbon black nanocomposites: percolation and variable range hopping on a fractal

Effects of various experimental parameters on dc conductivity of Silicone-Carbon Black (CB) nanocomposites are measured and correlated to the fractal morphology of CB network. The influence of filler volume fraction, temperature and electric field strength, are discussed using percolation and variable range hopping on a fractal as theoretical background. One also investigates effects of curing rate and CB content on both surface’s morphology and conductivity. The fractal aspect of CB network is studied by optical microscopy (OM). Electric conductivity is measured using four points setup. AFM and STM are used to study respectively surface morphology and conductivity. Low percolation threshold ϕc = 0,15% and scaling exponent μ ≅ 2,6 of conductivity with CB volume fraction is correlated to the measured fractal dimension df = 2,4. Conduction at low temperature proceeds by mean of variable range hopping on the CB fractal network with a Mott’s exponent m = 0,65 and temperature T0 = 64 K. Non-Ohmic conductivity curves at different temperatures could be superposed into a unique master curve and the onset field of non-linearity Scales with temperature with a typical exponent XT ≅ 1,2. At low curing rate, capillary forces have time to bring down all CB particles from the surface into the bulk whereas at fast curing rate the roughness and conductivity of the surface remain high.

Investigation of magnetic and relaxor dielectric properties of polycrystalline gadolinium iron garnet by Bi substitution

We have synthesized Bi-substituted gadolinium iron garnet [(Gd3−xBix)Fe5O12] samples with x = 0, 0.5, and 1.0 and studied their structural, magnetic, and dielectric properties. All samples are found to be in single-phase form with cubic structure as per the Rietveld analysis based on $$Ia\bar{3}d$$ space group. Bi substitution leads to increase in lattice constant, Fe(a)–Fe(d) bond length and Fe(a)–O–Fe(d) bond angles, and they have direct influence on magnetic properties. All samples undergo ferrimagnetic transition followed by magnetic compensation behavior at low temperature. The ferrimagnetic transition temperature (Tc) is found to increase from 576 K for x = 0 to 596 K for x = 1.0. However, the magnetic compensation temperature (Tcomp) decreases from 296 to 176 K. They are explained in terms of increase in Fe(a)–O–Fe(d) bond angle and the dilution of magnetic moment at Gd site. The analysis of impedance spectra at room temperature and at higher temperature shows that Bi substitution gives rise to larger impedance due to the localization as well as reduction in the concentration of charge carriers. The activation energy of charge-carrier relaxation is found to be in the range of 0.9–1.0 eV. The temperature variation of dielectric constant data and their analysis based on modified Curie–Weiss law show the relaxor ferroelectric transition with a typical diffuseness exponent, γ close to 2.0.

Three-dimensional characterization of micro-fractures in shale reservoir rocks

Fractures are crucial for unconventional hydrocarbon exploitation, but it is difficult to accurately observe the 3D spatial distribution characteristics of fractures. Microtomography (micro-CT) technology makes it possible to observe the 3D structures of fractures at micro-scale. In this study, micron-CT scanning is conducted on multiple mud-shale samples of source rocks in the Permian Lucaogou Formation, Junggar Basin. The Avizo® software is applied to process and segment the micron-CT images, so as to obtain the 3D fracture structure model inside rock core. Therefore, the independently-developed CTSTA program is adopted to quantitatively describe the micro-fractures inside rock core, including fracture dimension, extension direction and extension scale. Meanwhile, this study summarizes the classification characteristics of fractures and their anisotropy. On this basis, the fractal dimensions of fractures can also be extracted. Previous studies show that the geometric features of fractures have self-similarity at large and small scales, which can be described by exponential laws; and the fractal dimension is a typical exponent. Through the quantitative description or characterization of 3D fractures at micro-scale, the distribution characteristics of fractures in large scales could be known.

Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

We study the critical order parameter fluctuations of the absorbing-state phase-transition exhibited by branching and annihilating random walkers performing anomalous diffusion in a linear chain. The diffusion process is considered to follow a power-law distribution of jump lengths with a typical decay exponent α. We focus in the case of parity conserving dynamics for which deviations from the usual directed percolation universality class have been previously demonstrated even for the limiting cases of normal diffusion. Anomalous diffusion induces a continuous change of the critical exponents. By performing a finite-size scaling analysis of simulation data, we show that the critical order parameter moment ratio also varies continuously with α. We unveil that the critical order parameter distribution evolves from a nearly Gaussian to an exponential form as the range of the jump distribution is increased up to the limit on which the active state predominates for any finite branching probability.

Selecting Parameters of the Fuzzy Possibilistic Clustering Algorithm

Clustering has been widely used in pattern recognition, image processing, and data analysis. It aims to organize a collection of data items into clusters, such that items within a cluster are more similar to each other than they are in other clusters. The Fuzzy Possibilistic C-Means (FPCM) is one of the most popular clustering methods based on minimization of a criterion function. So the implementation of this algorithm requires a priori selection of some parameters: the fuzzy and the typical exponent, initialization of cluster centers. But the definition of these parameters at the moment is fixed in advanced and the initialization of centers is random; so the algorithm can give results not consistent. The determination of an optimal value for these parameters and the cluster centers at the beginning are problematic and remains an open problem. New procedures for choice of the optimal values of parameters and for initialization of centers were developed. Numerical results using data sets are used to illustrate the simplicity and effectiveness of the proposed procedures. General Terms Pattern Recognition, Clustering, Algorithms et. al.

The random transverse field Ising model in d = 2: analysis via boundary strong disorder renormalization

To avoid the complicated topology of surviving clusters induced by standard strong disorder RG in dimension d > 1, we introduce a modified procedure called ‘boundary strong disorder RG’ where the order of decimations is chosen a priori. We apply this modified procedure numerically to the random transverse field Ising model in dimension d = 2. We find that the location of the critical point, the activated exponent ψ ≃ 0.5 of the infinite-disorder scaling, and the finite-size correlation exponent νFS ≃ 1.3 are compatible with the values obtained previously using standard strong disorder RG. Our conclusion is thus that strong disorder RG is very robust with respect to changes in the order of decimations. In addition, we analyze the RG flows within the two phases in more detail, to show explicitly the presence of various correlation length exponents: we measure the typical correlation exponent νtyp ≃ 0.64 for the disordered phase (this value is very close to the correlation exponent of the pure two-dimensional quantum Ising model), and the typical exponent νh ≃ 1 for the ordered phase. These values satisfy the relations between critical exponents imposed by the expected finite-size scaling properties at infinite-disorder critical points. We also measure, within the disordered phase, the fluctuation exponent ω ≃ 0.35 which is compatible with the directed polymer exponent in (1 + 1) dimensions.

Classical Random Graphs with Unbounded Expected Degrees are Locally Scale-Free

A common property of many, though not all, massive real-world networks, including the World- Wide Web, the Internet, and social networks, is that the connectivity of the various nodes follows a scale-free distribution, P(k) ∞ k-α, with typical scaling exponent 2≤α≤3. In this letter, we prove that the Erdős-Ŕenyi random graph with unbounded expected degrees has a scale-free behaviour with scaling exponent 1=2 in a neighbourhood of expected degree hki. This interesting phenomenon shows a discrepancy from the Erdős-Ŕenyi random graph with bounded expected degree, which has a bell shaped connectivity distribution, peaking at 〈k〉, and decaying exponentially for large k.

A critical Dyson hierarchical model for the Anderson localization transition

A Dyson hierarchical model for Anderson localization, containing non-random hierarchicalhoppings and random on-site energies, has been studied in the mathematicalliterature since its introduction by Bovier (1990 J. Stat. Phys. 59 745), with theconclusion that this model is always in the localized phase. Here we show that if oneintroduces alternating signs in the hoppings along the hierarchy (instead of choosingall hoppings of the same sign), it is possible to reach an Anderson localizationcritical point presenting multifractal eigenfunctions and intermediate spectralstatistics. The advantage of this model is that one can write exact renormalizationequations for some observables. In particular, we obtain that the renormalized on-siteenergies have the Cauchy distributions for exact fixed points. Another output of thisrenormalization analysis is that the typical exponent of critical eigenfunctions is alwaysαtyp = 2, independentlyof the disorder strength. We present numerical results concerning the whole multifractal spectrumf(α) and thecompressibility χ of the level statistics, for both the box and the Cauchy distributions of the random on-siteenergies. We discuss the similarities and differences with the ensemble of ultrametricrandom matrices introduced recently by Fyodorov, Ossipov and Rodriguez (2009 J. Stat.Mech. L12001).

Statistical properties of two-particle transmission at an Anderson transition

The ensemble of L × L power-law random banded matrices, where the random hopping Hi,j decays as a power-law (b/|i − j|)a, is known to present an Anderson localization transition at a = 1, where one-particle eigenfunctions are multifractal. Here we study numerically, at this critical point, the statistical properties of the transmission T2 for two distinguishable particles, two bosons or two fermions, in the non-interacting case. We find that the statistics of T2 is multifractal, i.e. the probability to have T2(L) ∼ 1/Lκ behaves as , where the multifractal spectrum Φ2(κ) for fermions is different from the common multifractal spectrum concerning distinguishable particles and bosons. However, in the three cases, the typical transmission Ttyp2(L) is governed by the same exponent κtyp2, which is much smaller than the naive expectation 2κtyp1, where κtyp1 is the typical exponent of the one-particle transmission T1(L).

Félix Vicq d’Azyr (1748–1794)

Félix Vicq d’Azyr (1748–1794)

A Multiphysics Model of Myoma Growth

We present a first attempt to create an in-silico model of a uterine leiomyoma, a typical exponent of a common benign tumor. We employ a finite element model to investigate the interaction between a chemically driven growth of the pathology and the mechanical response of the surrounding healthy tissue. The model includes neoplastic tissue growth, oxygen and growth factor transport as well as angiogenic sprouting. Neovascularisation is addressed implicitly by modeling proliferation of endothelial cells and their migration up the gradient of the angiogenic growth factor, produced in hypoxic regions of the tumor. The response of the surrounding healthy tissue in our model is that of a viscoelastic material, whereby a stress exerted by expanding neoplasm is slowly dissipated. By incorporating the interplay of four underlying processes we are able to explain experimental findings on the pathology's phenotype. The model has a potential to become a computer simulation tool to study various growing conditions and treatment strategies and to predict post-treatment conditions of a benign tumor.

A staggered six-vertex model with non-compact continuum limit

The antiferromagnetic critical point of the Potts model on the square lattice was identified by Baxter [R.J. Baxter, Proc. R. Soc. London A 383 (1982) 43] as a staggered integrable six-vertex model. In this work, we investigate the integrable structure of this model. It enables us to derive some new properties, such as the Hamiltonian limit of the model, an equivalent vertex model, and the structure resulting from the Z 2 symmetry. Using this material, we discuss the low-energy spectrum, and relate it to geometrical excitations. We also compute the critical exponents by solving the Bethe equations for a large lattice width N. The results confirm that the low-energy spectrum is a collection of continua with typical exponent gaps of order ( log N ) −2 .

In situ Ni–Si nanowire junction based on substrate sourced growth and its electrical transport behavior

The authors report on formation of high current carrying Ni–Si nanowires between Ni/heavily doped polycrstaliine Si contacts using substrate sourced growth without any supply of Si source gas. The conductance (G) of a 18nm diameter nanowire bridge in the temperature range of 13–293K showed a power function of temperature Tα, with a typical exponent α≈0.62±0.06, and the dI∕dV were fitted to the Vα with α≈0.55±0.15. Although the power law dependence of the G and dI∕dV, which provides evidence for the interaction of the electrons in a low-dimensional infinite conductor, corresponds to the featured behavior of the interacting electrons within an error tolerance, the strength of the interaction is very weak due to the highly metallic characteristics with finite length and lack of purity of the channel. As a result, the in situ high current carrying Ni-Si nanowire junction can be utilized not only as a nanointerconnector, but also as a tool to study low-dimensional electrical transport properties.

Sixfold bond orientational properties of a model liquid crystal in the dimensional crossover of B phases: A computer simulation study

A wide range of NPT simulations of a bead necklace liquid crystal model in the crystal B, smectic B, smectic A, and nematic phases have been performed. Systems with up to 21 600 molecules have been studied to observe the behavior of slowly decaying spatial correlation functions. The pair correlation function and its in-plane restriction are consistent with a crystalline phase made of independent two-dimensional crystalline layers. Smectic B phase is studied by the bond orientational pair correlation functions g(6) and its extension g(6ext). The first reaches a constant value, which seems to rule out a classical hexatic phase. The latter shows a power-law decay within the layers: its typical decay exponent (eta(6ext)) is evaluated. Relationships between multiple harmonics of the C(6n) order parameter have been evaluated through the whole range of existence of B phases (crystalline and smectic): the extension to the crystalline phase holds and provides an excellent fit of the simulation data.

The variation of Zipf?s law in human language

Words in humans follow the so-called Zipf’s law. More precisely, the word frequency spectrum follows a power function, whose typical exponent is β≈2, but significant variations are found. We hypothesize that the full range of variation reflects our ability to balance the goal of communication, i.e. maximizing the information transfer and the cost of communication, imposed by the limitations of the human brain. We show that the higher the importance of satisfying the goal of communication, the higher the exponent. Here, assuming that words are used according to their meaning we explain why variation in β should be limited to a particular domain. From the one hand, we explain a non-trivial lower bound at about β=1.6 for communication systems neglecting the goal of the communication. From the other hand, we find a sudden divergence of β if a certain critical balance is crossed. At the same time a sharp transition to maximum information transfer and unfortunately, maximum communication cost, is found. Consistently with the upper bound of real exponents, the maximum finite value predicted is about β=2.4. It is convenient for human language not to cross the transition and remain in a domain where maximum information transfer is high but at a reasonable cost. Therefore, only a particular range of exponents should be found in human speakers. The exponent β contains information about the balance between cost and communicative efficiency.

Renormalization group for network models of quantum Hall transitions

We analyze in detail the renormalization group flows which follow from the recently proposed all orders β functions for the Chalker–Coddington network model. The flows in the physical regime reach a true singularity after a finite scale transformation. Other flows are regular and we identify the asymptotic directions. One direction is in the same universality class as the disordered XY model. The all orders β function is computed for the network model of the spin quantum Hall transition and the flows are shown to have similar properties. It is argued that fixed points of general current–current interactions in 2d should correspond to solutions of the Virasoro master equation. Based on this we identify two coset conformal field theories osp(2 N|2 N) 1/ u(1) 0 and osp(4 N|4 N) 1/ su(2) 0 as possible fixed points and study the resulting multifractal properties. We also obtain a scaling relation between the typical amplitude exponent α 0 and the typical point contact conductance exponent X t which is expected to hold when the density of states is constant.

Electrical conduction processes in silicon nitride thin films prepared by r.f. magnetron sputtering using nitrogen gas

Silicon nitride (Si3N4) is an important VLSI material owing to its high resistivity and breakdown strength and its use in surface encapsulation during ion implantation and annealing. Previous work has focused on films prepared by low-pressure and plasma-enhanced chemical vapour deposition (LPCVD and PECVD), but in the present work the DC electrical properties of films prepared by r.f. magnetron sputtering were investigated. Al-Si3N4-Al sandwich structures were fabricated from a Si3N4 target at a discharge power of 100 W using N2 as the sputtering gas at a pressure of approximately 0.5 Pa. Capacitance was independent of voltage, indicating the absence of a Schottky barrier at the Al/Si3N4 interface. Measurements of the capacitance as a function of inverse dielectric thickness implied a relative permittivity value of 6.3. However, although films prepared using PECVD exhibited Poole–Frenkel conductivity and tunnelling at higher voltages, the present sputtered films showed space-charge-limited conductivity (SCLC). Conductivity was dominated by an exponential distribution of trap levels, as indicated by a power-law dependence of current density J on applied voltage V, with a typical exponent value of 3.2. Measurements of J as a function of temperature confirmed the appearance of SCLC and indicated that the bulk trap density was of the order of 2×1024m−3 as observed in LPCVD and PECVD films, with the appearance of hopping conductivity at low temperatures.

Structure of the attraction zones of the final states in the presence of dynamical period doubling bifurcations

The structure of the attraction zones of the final states associated with dynamical period doubling bifurcations is investigated. It is found that on the “initial value—transition rate” plane the attraction zones of the two possible final states alternate with each other and that a subdivision of the attraction regions occurs with a decrease in the transition rate. It is shown that the boundaries of the attraction zones are smeared out because of the effect of noise and in this situation the fine structure of the attraction zones is destroyed. As analytical and numerical calculations have shown, the critical value of the noise variance, corresponding to the boundary between the dynamical (or predictable) and stochastic (or unpredictable) modes, has a power-law dependence on the transition rate with a typical exponent value of one. The existence of “noise” invariants is also observed: the integrated (over all initial values) probability of achieving the final state is invariant with respect to the noise level.

A Typological Study on the Grammatical Encoding of the Causee in Causative Constructions

The causative introduces an external agent into the clausal structure. When an additional agent is introduced into the event, and when it is construed as the agent ultimately responsible for the occurrence of the event, then this ultimate agent is encoded as the subject, and the one that is less responsible for the event is encoded as the direct or oblique object. Causative constructions can be classified according to two parameters; one is a formal (or morphological) parameter and the other is semantic. As for the semantic distinction, we have shown that the difference between distant and contact causation is reflected formally in many languages including Korean. In Korean, semantic differences between distant and contact causatives generally correspond to those between the analytic and the morphological types. The essential difference between distant and contact causatives is the degree of control exercised by the causee. The causee in distant causatives has some control over the action, whereas the causee in contact causatives has no control over the action. That is, the causer of contact causatives behaves like the agent of a typical transitive verb, in that he or she both initiates and directly carries out the action. One interesting aspect of this, with respect to the control parameter of the causee, is that distant causatives usually require animate causes. Where the causee is inanimate, the distant causative suggests that the causer might invoke some external force, such as "magical power", in view of the indication that there is an absence of physical contact between causer and causee. The other issue that we have investigated is the morphological encoding of the causee. We established the case hierarchy for the Korean causative construction as accusative > dative > nominative, which coincides with the degree of control exercised by the causee, from least to greatest. We also investigated the validity of Comrie's (1981) hierarchy account through a careful examination of data from Korean. We have shown that there are many languages that do not conform to this hierarchy, and that allow doubling on certain grammatical relations. Korean permits doubling on Direct Object, Indirect Object, and even on subject positions. Most importantly, Comrie's hierarchy account fails to explain why case-markings are used contrastively. For example, the case-marking contrast of the causee between the accusative and the dative/oblique indicates a semantic contrast. Basically, Comrie's hierarchy account is rooted in a purely syntactic perspective without considering the semantic function of case-markers. We have shown that there is a possible semantic contrast between different encodings of the causee in causative constructions. As the basic morphological encoding of the patient, the accusative typically refers to an entity (causee) with a very low degree of control. On the other hand, the oblique case (or whatever case that might be selected for passive agents) is frequently used for an entity with a high degree of control. As the typical exponent of the experiencer or recipient role, the dative occupies an intermediate position.