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We consider the non-perturbative renormalization group (RG) equations, obtained as approximations of the exact Wetterich RG flow equation within the Blaizot-Mendez-Wschebor (BMW) truncation scheme. For the first time, we derive explicit RG flow equations for the scalar model at the arbitrary order of truncation. Moreover, we consider original, as well as modified, approximations, used to obtain a set of closed equations. We compare these equations at the s = 2 order of truncation with those recently derived in J. Phys. A: Math. Theor. 53, 415002 (2020) within a new truncation scheme and find a striking similarity. Namely, the first-order equations of the latter scheme, those of the original BMW scheme, and those of the modified BMW scheme (at s = 2) differ only in one term. We solved these equations by a recently proposed and tested method of semianalytic approximations. Thus, the critical exponents η, ν, and ω were evaluated, recovering also the known results of the original BMW scheme. In addition, we estimated the subleading correction-to-scaling exponent ω2 for the three equations considered. To the best of our knowledge, this exponent has not yet been extracted from the Wetterich equation beyond the local potential (the zeroth order) approximation. Our current estimate for the 3D Ising model is ω2 = 2.02 (40), where the error bars include the expected truncation error in the BMW scheme. [ABSTRACT FROM AUTHOR]

Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to L = 3 4 5 6. Our estimated values of the correction-to-scaling exponent ω tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. L < L min with L min ∈ [ 6 , 6 4 ] , are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. ω ≈ 0. 7 and ω = 0. 7 5 (5). We discuss the possibilities that ω is either really smaller than usually expected or these values of ω describe some transient behavior which, eventually, turns into the correct asymptotic behavior at L min > 6 4. We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents η and ν provide stable values η = 0. 0 3 6 3 2 (1 3) and ν = 0. 6 3 0 1 7 (3 1) , which well agree with those of the conformal bootstrap method, i.e. η = 0. 0 3 6 2 9 7 8 (2 0) and ν = 0. 6 2 9 9 7 0 9 (4 0). [ABSTRACT FROM AUTHOR]

The known approximation schemes for the solution of the Wetterich exact renormalization group (RG) equation are critically reconsidered, and a new truncation scheme is proposed. In particular, the equations of the derivative expansion up to the ∂2 order for a scalar model are derived in a suitable form, clarifying the role of the off-diagonal terms in the matrix of functional derivatives. The natural domain of validity of the derivative expansion appears to be limited to small values of q/k in the calculation of the critical two-point correlation function, depending on the wave-vector magnitude q and the infrared cut-off scale k. The new approximation scheme has the advantage to be valid for any q/k, and, therefore, it can be auspicious in many current and potential applications of the celebrated Wetterich equation and similar models. Contrary to the derivative expansion, derivatives are not truncated at a finite order in the new scheme. The RG flow equations in the first approximation of this new scheme are derived and approximately solved as an example. It is shown that the derivative expansion up to the ∂2 order is just the small-q approximation of our new equations at the first order of truncation. [ABSTRACT FROM AUTHOR]

A static and dynamic analysis of the combined and self-consistent influence of spontaneous polarization, piezoelectric effects, lattice mismatch, and strain effects is presented for a three-layer one-dimensional AlN/GaN wurtzite quantum-well structure (with GaN as the central quantum-well layer). It is shown that, contrary to the assumption of Fonoberov and Balandin [J. Appl. Phys. 94, 7178 (2003); J. Vac. Sci. Technol. B 22, 2190 (2004)], even in cases with no current transport through the structure, the strain distributions are not well captured by minimization of the strain energy only and not, as is in principle required, the total free energy including electric and piezoelectric coupling and spontaneous polarization contributions. Furthermore, we have found that, when an ac signal is imposed through the structure, resonance frequencies exist where strain distributions are even more strongly affected by piezoelectric-coupling contributions depending on the amount of mechanical and electrical losses in the full material system. [ABSTRACT FROM AUTHOR]

Corrections to scaling in the 3D Ising model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes . Analytical arguments show the existence of corrections with the exponent , the leading correction-to-scaling exponent being . A numerical estimation of from the susceptibility data within yields , in agreement with this statement. We reconsider the MC estimation of from smaller lattice sizes, , using different finite-size scaling methods, and show that these sizes are still too small, since no convergence to the same result is observed. In particular, estimates ranging from to are obtained, using MC data for thermodynamic average quantities, as well as for partition function zeros. However, a trend toward smaller values is observed in one of these cases in a refined estimation from extended data up to . We discuss the influence of on the estimation of critical exponents and . [ABSTRACT FROM AUTHOR]

Corrections to scaling in the two-dimensional (2D) scalar model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L () and different values of the coupling constant , i.e. , 1, 10. According to our analysis, amplitudes of the nontrivial correction terms with the correction-to-scaling exponents become small when approaching the Ising limit (), but such corrections generally exist in the 2D model. Analytical arguments show the existence of corrections with the exponent . The numerical analysis suggests that there exist also corrections with the exponent and, perhaps, also with the exponent about , which are detectable at . The numerical tests provide an evidence that the structure of corrections to scaling in the 2D model differs from the usually expected one in the 2D Ising model. [ABSTRACT FROM AUTHOR]

This paper presents a detailed investigation of the effects of piezoelectricity, spontaneous polarization and charge density on the electronic states and the quasi-Fermi level energy in wurtzite-type semiconductor heterojunctions. This has required a full solution to the coupled Schrödinger-Poisson-Navier model, as a generalization of earlier work on the Schrödinger-Poisson problem. Finite-element-based simulations have been performed on a quantum well by using both one-step calculation as well as the self-consistent iterative scheme. Results have been provided for field distributions corresponding to cases with zero-displacement boundary conditions and also stress-free boundary conditions. It has been further demonstrated by using four case study examples that a complete self-consistent coupling of electromechanical fields is essential to accurately capture the electromechanical fields and electronic wavefunctions. We have demonstrated that electronic energies can change up to approximately 0.5 eV when comparing partial and complete coupling of electromechanical fields. Similarly, wavefunctions are significantly altered when following a self-consistent procedure as opposed to the partial-coupling case usually considered in literature. Hence, a complete self-consistent procedure is necessary when addressing problems requiring more accurate results on optoelectronic properties of low-dimensional nanostructures compared to those obtainable with conventional methodologies. A complete self-consistent procedure has been developed for analyzing optoelectromechanical properties of low-dimensional semiconductor nanostructures. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations of magnetization and susceptibility in the 3D XY model are performed for system sizes up to L=384 (significantly exceeding the largest size L=160 considered in work published previously), and fields h ≥ 0.0003125 at two different coupling constants β=0.5, and β=0.55 in the ordered phase. We examine the prediction of the standard theory that the longitudinal susceptibility χ∥ has a Goldstone mode singularity such that χ∥ ∝h-1/2 holds when h↦0. Most of our results, however, support another theoretical prediction that the singularity is of a more general form χ∥ ∝hρ-1, where 1/2<ρ<1 is a universal exponent related to the ∼hρ variation of the magnetization. [ABSTRACT FROM AUTHOR]

Using mathematical modeling and computer simulation, nonlinear dynamics of rubber-based polymers has been studied with due regard for the effect of thermal relaxation. Main results have been obtained for the case of elongational oscillations of a ring-shaped body subjected to periodic (“internal”)boundary conditions. Particular emphasis has been placed on high-frequency and short spatial variations of temperature and displacement, in which the role of nonlinearities in the dynamics of the material and their close connection with the effect of thermal relaxation time can be best appreciated. It is shown how the vanishing relaxation time can lead to an attenuation of nonlinear effects in the thermomechanical system. [ABSTRACT FROM AUTHOR]

Nanostructures, created by confinement of the motion of an electron from all three dimensions and known as quantum dots (QDs), provide materials scientists with a wide range of potential applications. These structures are produced today with advances of QD growth technology, and computational tools are fundamental in providing a better understanding of such structures. In this paper QD nanostructures are analysed with due account for coupling effects between electronic states in the dot and the wetting layer regions. The analysis, performed on the basis of the finite element methodology and Arnoldi iterations, demonstrates that the effect of coupling may be essential. The numerical procedure applied here is more efficient compared to the QR algorithm typically used in the context of modelling low-dimensional nanostructures. We report results of computational experiments for cylindrical and truncated conical QDs and compare them with the earlier results obtained for fully conical QD nanostructures. [ABSTRACT FROM AUTHOR]

Many problems in applications of piezoelectric materials are essentially time-dependent, and a conventional treatment of such problems with analytical or semi-analytical techniques based on the analysis of harmonic oscillations become inadequate in those cases where a complete dynamic picture of electromechanical energy transfer is required. For such situations we have developed an efficient explicit numerical methodology allowing us to compute dynamic electromechanical characteristics of piezoelectric structures and devices under various loading conditions. In this paper we demonstrate that the stability conditions for our numerical approximation can be obtained from a discrete conservation law, and can be cast in a form similar to that of the classical CFL condition. However, in our case the velocities of wave propagations, participating in the formulation of the stability conditions, are clearly dependent on the pattern of electroraectromechanical coupling. Our discussion in this paper, including computational examples, is centred around finite piezoelectric shells of cylindrical shape. [ABSTRACT FROM AUTHOR]

Using models incorporating a thermal relaxation time (hyperbolic models), we study the properties of spatially periodic thermoelastic waves propagating in an infinite rod. Analyzing the Lord-Schulman and Green-Lindsay linear models, we reveal dependencies of decay rates and frequency shifts of temperature and displacement upon the wave number for the case of weak thermoelastic coupling. We explore numerically a general nonlinear hyperbolic model, describing the time evolution of initially sinusoidal distributions of displacement and temperature. Mechanisms of nonlinear interaction between thermal and mechanical fields are qualitatively analyzed. It is demonstrated that larger relaxation times may provide smoother temperature profiles at an intermediate stage of the dynamics. [ABSTRACT FROM AUTHOR]

In this paper we deal with a model of coupled non-stationary electroelasticity with displacements and potential given on the boundary of a body. We construct a numerical scheme for modelling electromechanical interactions in the body, and present a spectrum of a priori estimates for the solution of this scheme. Such estimates allow us to prove the convergence of the scheme to a generalized solution of the differential problem from W22(QT) with the second order of accuracy in a weaker than L2 metric. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]