The calculation of electrical parameters of AT-cut quartz crystal resonators with the consideration of material viscosity

Electrical parameters like resistance and quality factor of a quartz crystal resonator cannot be determined through vibration analysis without considering the presence of material dissipation. In this study, we use the first-order Mindlin plate equations of piezoelectric plates for thickness-shear vibrations of a simple resonator model with partial electrodes. We derive the expressions of electrical parameters with emphasis on the resistance that is related to the imaginary part of complex elastic constants, or the viscosity, of quartz crystal. Since all electrical parameters are frequency dependent, this procedure provides the chance to study the frequency behavior of crystal resonators with a direct formulation. We understand that the electrical parameters are strongly affected by the manufacturing process, with the plating techniques in particular, but the theoretical approach we presented here will be the first step for the precise estimation of such parameters and their further applications in the analysis of nonlinear behavior of resonators. We calculated the parameters from our simple resonator model of AT-cut quartz crystal with the first-order Mindlin plate theory to demonstrate the procedure and show that the numerical results are consistent with earlier measurements.     

Exploring the operation of a tiny heat engine

We model a tiny heat engine as a Brownian particle that moves in a viscous medium in a sawtooth potential (with or without load) assisted by alternately placed hot and cold heat baths along its path. We find closed form expression for the steady-state current as a function of the model parameters. This enables us to deal with the energetics of the model and evaluate either its efficiency or its coefficient of performance depending upon whether the model functions either as a heat engine or as a refrigerator, respectively. We also study the way current changes with changes in parameters of interest. When we plot the phase diagrams showing the way the model operates, we not only find regions where it functions as a heat engine and as a refrigerator but we also identify a region where the model functions as neither of the two.     

Can we explain the coexistence of ferromagnetism and superconductivity based on two parameters model?

A possible explanation about the coexistence of ferromagnetism (FM) and superconductivity (SC) based on a two parameters mean field model in a two-dimensional system is discussed. The key feature of this model is that there are two independent parameters which are responsible for ferromagnetism and superconductivity, respectively. We point out that the coexisting FM and s-wave pairing SC state is energetically not favorable among all possible state. We generalize the two parameter model to include the coexistence of FM with p-wave SC. We find that the phase diagram is not consistent with what experimentally discovered in UGe₂.     

Slave fermion formalism for the tetrahedral spin chain

We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.     

Connectivity degrees in the threshold preferential attachment model

In this paper we present a study of the connectivity degrees of the threshold preferential attachment model, a generalization of the Barabási-Albert model to heterogeneous complex networks. The threshold model incorporates the states of the nodes in its preferential linking rule and assumes that the affinity between network nodes follows an inverse relationship with the distance between their states. We numerically analyze the connectivity degrees of the model, studying the influence of the main parameters on the distribution of connectivity degrees and its statistics, the average degree and highest degree of the network. We show that such statistics exhibit markedly different behaviors in the dependence on the model parameters, particularly as regards the interaction threshold. Nevertheless, we show that the two statistics converge in the limit of null threshold and often exhibit scaling that can be described by power laws of the model parameters.     

Single particle models in the shell correction approach

We investigate the dependence of the shell correction energy on the parameters as they occur in the Nilsson model and the single particle model with a Woods-Saxon potential. We give criteria, how these parameters should be chosen in order that the shell correction energies become fairly model-independent. The different models yield now a value of about ?20 MeV for²⁰⁸Pb, substantially larger than in previous work. Its relation to the remainder of the mass formula fit is discussed. We find that shell energies have an extremum. The minimum occurs close to the conventional parameter values (except the potential diffuseness of the protons) and close to the minimum of the total binding energy. The minimum in shell energy corresponds to a maximum bunching of single particle states. The gross properties of these extremal shells agree considerably better with the experimental spectra (for both the neutrons and the protons) than those of conventional model parameters.     

Synchronization of the time—varying parameter chaotic system and its application to secure communication

In this paper we propose and investigate the synchronization of a new chaotic model with time-varying parameters and apply it to improve the security of chaotic communication. In this model, the chaotic system is modulated by both the message and the varying parameters. The varying parameters distort the phase space so heavily that they prevent the carrier from being broken by nonlinear dynamic forecasting method. Theory and simulation experiments with speech signal communication indicate that the receiver can gain a perfect synchronization with the transmitter, and the intruder cannot break down this communication system. We also discuss the robustness of the new communication system.     

Evolution of the Internet AS-level ecosystem

We present an analytically tractable model of Internet evolution at the level of autonomous systems (ASs). We call our model the multiclass preferential attachment (MPA) model. As its name suggests, it is based on preferential attachment. All of its parameters are measurable from available Internet topology data. Given the estimated values of these parameters, our analytic results predict a definitive set of statistics characterizing the AS topology structure. These statistics are not part of the model formulation. The MPA model thus closes the “measure-model-validate-predict” loop, and provides further evidence that preferential attachment is a driving force behind Internet evolution.     

Application of the two-liquid model for the interpretation of the observed electrophysical properties of supercooled water in nanopores

We propose a model combining the first-order liquid-liquid and the second-order ferroelectric phase transitions phenomenology to explain various features of the λ-point of liquid water. We suggest that the long-range dipole-dipole interaction of water molecules leads to a ferroelectric phase transition, which occurs only in the low-density component of the liquid and is the origin of the singularity of the dielectric constant recently observed in experiments with supercooled liquid water in nanoporous materials. Finally, we establish the model parameters and prove the consistency of the combined model by comparing its predictions with experimental data and the results of recent molecular-dynamics simulations.     

Mathematical modeling of the thermal and optical parameters of the zone of laser influence for determining the feedback parameters for a system of adaptive precision laser material processing

We develop a mathematical model of channel formation in the ablation regime at the initial non-stationary stage of growth that establishes the relationship between channel parameters such as temperature, optical parameters of the irradiated surface and erosion flow, and the parameters of laser action. The solution to a two-dimensional heat equation, coordinated with the solution to the problem of propagation of an ablation front and the formation of flows of evaporated material and plasma, is found in a grid with variable boundaries.     

Bounds for the chaotic region in the Lorenz model

In a previous paper, the authors made an extensive numerical study of the Lorenz model, changing all three parameters of the system. We conjectured that the region of parameters where the Lorenz model is chaotic is bounded for fixed r. In this paper, we give a theoretical proof of the conjecture by obtaining theoretical bounds for the chaotic region and by using Fenichel theory. The theoretical bounds are complemented with numerical studies performed using the Maximum Lyapunov Exponent and OFLI2 techniques, and a comparison of both sets of results is shown. Finally, we provide a complete three-dimensional model of the chaotic regime depending on the three parameters.     

Threshold resummation for the production of a color sextet (antitriplet) scalar at the LHC

This paper is devoted to the study of warm inflation using vector fields in the background of a locally rotationally symmetric Bianchi type I model of the universe. We formulate the field equations, and slow-roll and perturbation parameters (scalar and tensor power spectra as well as their spectral indices) in the slow-roll approximation. We evaluate all these parameters in terms of the directional Hubble parameter during the intermediate and logamediate inflationary regimes by taking the dissipation factor as a function of the scalar field as well as a constant. In each case, we calculate the observational parameter of interest, i.e., the tensor–scalar ratio in terms of the inflaton. The graphical behavior of these parameters shows that the anisotropic model is also compatible with WMAP7 and the Planck observational data.     

Constraints on the parameters of the left-right symmetric gauge models

We find an important constraint on the parameters of the general four-parameter left-right symmetric model. The constraint links the v-hadron sector of the model with the parity-violation sector. Using this constraint along with the available neutral-current data from neutrino-hadron and electron-deuteron scattering we find that, except for a narrow region amounting to essentially one point in the four-parameter space, the model is excluded.     

Calculation of concentrational dependence of equilibrium lattice parameters for the alloys Al-Cu and Al-Ag

We fit the Animalu model potential by using the crystal equation of state. We give the fitted parameters for 25 metals that have a cubic lattice. We calculate the concentrational dependence of the lattice parameters for the alloys Al-Cu and Al-Ag. The derivative da/dc in these alloys agrees well with the experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 30–34, June, 1986.     

Scaling property of the critical hopping parameters for the Bose-Hubbard model

Recently precise results for the boundary between the Mott insulator phase and the superfluid phase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor g and any lattice dimension d ≥ 2. We use these data for demonstrating that the critical hopping parameters obey a scaling relationship which allows one to map results for different g onto each other. Unexpectedly, the mean-field result captures the dependence of the exact critical parameters on the filling factor almost fully. We also present an approximation formula which describes the critical parameters for d ≥ 2 and any g with high accuracy.     

Universality and the weak neutral current

We consider the possibility that the weak neutral current displays both muon-electron and quark-lepton universality. Such a model contains three parameters which we determine, within limits, from existing data on deep inelastic scattering of neutrinos off nucleons and elastic scattering of neutrinos off leptons. We show that such a model is consistent with other results on elastic neutrino-nucleon scattering and neutrino-induced production of single pions.     

A new look at the accelerating universe

We show that the cosmological model having zero cosmological constant, but containing the vacuum energy of a simple quantized free scalar field of low mass (VCDM model), agrees with the cosmic microwave background radiation (CMBR) and supernova (SNe-Ia) data at least as well as the classical cosmological model with a small nonzero cosmological constant. We also show that in the VCDM model the ratio of vacuum pressure to vacuum energy density is less than -1. We display the VCDM results for a set of parameters that give a very good fit to the CMBR power spectrum, and show that the same parameters also give a good fit to the SNe-Ia data.     

On the theory of the oscillatory survival probability in noble gas ion-surface scattering

We present a simple analytic model of neutralisation of ions colliding with solid surfaces. The model is applied to 0.3–2.0 keV He⁺ scattered from Pb and Ga. We obtain, for appropriate values of the parameters, good agreement with the experimental data.     

\mu-e conversion in nuclei in the left-right supersymmetric model

We investigate the contributions to conversion in nuclei in a supersymmetric model with left-right symmetry, motivated by the new data on neutrino oscillations. We study the dependence of the conversion rate on the various parameters of the model, and show that light-mass or large scenarios are severely restricted. We analyse the effect of several popular mecahnisms of neutrino mixing on the conversion rate as well as the influence of the right-handed scale on the conversion rate. We compare the conversion rate to the branching ratio for and discuss their relative accessibility at future experiments, their sensitivity to various parameters of the model, as well as their relative importance in providing signals for new Physics. Received: 31 May 2000 / Published online: 31 August 2000     

Comparison of the energetic properties and the dynamical stability in a mathematical model of the stretch reflex

The previous studies on finite-time thermodynamic engines have shown that some of the parameters affecting their thermodynamic performance also affect their stability. Moreover, such parameters have to be tuned to reach an optimal trade-off between these two generic properties. In the present work we carry out a similar analysis on a mathematical model of the stretch reflex regulatory pathway, which is a simplified version of a previously published model. We show that the model has a unique stable fixed point in the absence of time delays. However, when the system inherent time delays are considered, they can destabilize the fixed point and engender a stable limit cycle. We further explore the parameter space to analyse the sensitivity of the system stability to variations in the parameter values. Particular attention is paid to the parameter here denoted as α, which has been shown to determine the muscle thermodynamic properties during steady-state contractions: larger values of α mean more powerful and less efficient muscles. Our results indicate that the stretch reflex pathway is less stable in the more powerful and less efficient muscles. We finally compare these observations with those obtained on thermal engines.