Classical Degrees Research Articles

Efficiency of the spectral element method with very high polynomial degree to solve the elastic wave equation

The spectral element method (SEM) has gained tremendous popularity within the seismological community to solve the wave equation at all scales. Classic SEM applications mostly rely on degrees 4–8 elements in each tensorial direction. Higher degrees are usually not considered due to two main reasons. First, high degrees imply large elements, which make the meshing of mechanical discontinuities difficult. Second, the SEM’s collocation points cluster toward the edge of the elements with the degree, degrading the time-marching stability criteria and imposing a small time step and a high numerical cost. Recently, the homogenization method has been introduced in seismology. This method can be seen as a preprocessing step before solving the wave equation that smooths out the internal mechanical discontinuities of the elastic model. It releases the meshing constraint and makes use of very high degree elements more attractive. Thus, we address the question of memory and computing time efficiency of very high degree elements in SEM, up to degree 40. Numerical analyses reveal that, for a fixed accuracy, very high degree elements require less computer memory than low-degree elements. With minimum sampling points per minimum wavelength of 2.5, the memory needed for a degree 20 is about a quarter that of the one necessary for a degree 4 in two dimensions and about one-eighth in three dimensions. Moreover, for the SEM codes tested in this work, the computation time with degrees 12–24 can be up to twice faster than the classic degree 4. This makes SEM with very high degrees attractive and competitive for solving the wave equation in many situations.

Improved Possibility Degree Method for Intuitionistic Fuzzy Multi-Attribute Decision Making and Application in Aircraft Cockpit Display Ergonomic Evaluation

It is very important for the intuitionistic fuzzy decision making to rank the different intuitionistic fuzzy numbers (IFNs). Based on the full information of the membership degree and non-membership degree, an improved possibility degree method is defined for dealing with multi-attribute decision making (MADM) problems in this paper. Firstly, the limitations of the existing possibility degree are discussed, and then an improved one is defined to overcome these shortcomings. Subsequently, six properties of the proposed possibility degree, which are similar to that of the classic possibility degree, are presented and proved. Moreover, some numerical examples are provided to illustrate the superiority of the proposed method. And the calculation method of membership degree and non-membership degree from the statistical viewpoint is developed to construct the intuitionistic fuzzy evaluation matrix considering that the decision-makers are difficult to give exact values of the two variables directly. Furthermore, depending on the proposed possibility degree and the intuitionistic fuzzy generalized ordered weighted geometric average (IFGOWGA) operator, a new MADM approach is employed and used to solve the practical problem of aircraft cockpit display ergonomic evaluation under the intuitionistic fuzzy set environment. Finally, an evaluation example is examined to manifest the effectiveness and feasibility of the proposed decision-making method.

The matrix product approximation for the dynamic cavity method

Stochastic dynamics of classical degrees of freedom, defined on vertices of locally tree-like graphs, can be studied in the framework of the dynamic cavity method which is exact for tree graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, and other technical, biological, and social networks. The central objects in the cavity method are edge messages—conditional probabilities of two vertex variable trajectories. In this paper, we discuss a rather pedagogical derivation for the dynamic cavity method, give a detailed account of the novel matrix product edge message (MPEM) algorithm for the solution of the dynamic cavity equation as introduced in Barthel et al (2018 Phys. Rev. E 97 010104 (R)), and present optimizations and extensions. Matrix product approximations of the edge messages are constructed recursively in an iteration over time. Computation costs and precision can be tuned by controlling the matrix dimensions of the MPEM in truncations. Without truncations, the dynamics is exact. Data for Glauber–Ising dynamics shows a linear growth of computation costs in time. In contrast to Monte Carlo simulations, the approach has a much better error scaling. Hence, it gives for example access to low probability events and decaying observables like temporal correlations. We discuss optimized truncation schemes and an extension that allows to capture models which have a continuum time limit.

Diversified viral marketing: The power of sharing over multiple online social networks

The popularity of online social networks (OSNs) makes them attractive platforms to advertise products. Previous work on marketing in OSNs utilized older diffusion models that do not capture the interactions of modern OSNs and hence there is a need to develop a model that accounts for the interactions that occur in current OSNs. In this paper, we introduce a new model for information flow in online social networks that captures the sharing behavior exercised by users when they pass information from one online social network to their social circles in another network. We, then, formulate a problem of maximizing the marketing reach where the diversity of users’ other social networks is taken as a constraint. We also propose a greedy algorithm to solve the aforementioned optimization problem. Numerical results show that the proposed algorithm achieves better results than algorithms that are based on classical degree centrality metric and with comparable running time.

Improvising at rest: Differentiating jazz and classical music training with resting state functional connectivity

Jazz improvisation offers a model for creative cognition, as it involves the real-time creation of a novel, information-rich product. Previous research has shown that when musicians improvise, they recruit regions in the Default Mode Network (DMN) and Executive Control Network (ECN). Here, we ask whether these findings from task-fMRI studies might extend to intrinsic differences in resting state functional connectivity. We compared Improvising musicians, Classical musicians, and Minimally Musically Trained (MMT) controls in seed-based functional connectivity and network analyses in resting state functional MRI. We also examined the functional correlates of behavioral performance in musical improvisation and divergent thinking. Seed-based analysis consistently showed higher connectivity in ventral DMN (vDMN) and bilateral ECN in both groups of musically trained individuals as compared to MMT controls, with additional group differences in primary visual network. In particular, primary visual network connectivity to DMN and ECN was highest in Improvisational musicians, as was connectivity between ECN and DMN; in contrast, connectivity between vDMN and frontal pole was highest in Classical musicians. Furthermore, graph-theoretical analysis indicated heightened network measures in both musician groups, with betweenness centrality, clustering, and local efficiency showing highest levels in Classical musicians, and degrees and strengths showing highest levels in Improvisational musicians. Taken together, results suggest that heightened functional connectivity among musicians can be explained by higher within-network connectivity (more tight-knit cortical networks) in Classical musicians, as opposed to more disperse, globally-connected cortical networks in Improvisational musicians.

Multilayered triangular and quadrilateral flat shell elements based on the Refined Zigzag Theory

The paper presents a class of C0-continuous, flat shell elements based on the Refined Zigzag Theory (RZT) for the analysis of multilayered and curved composite and sandwich structures. The use of the interdependent interpolation strategy allows eliminating the shear-locking phenomenon and introducing the drilling rotation necessary to complete the set of classical nodal degrees of freedom (three displacements and three rotations). Additional kinematic variables are present in RZT, the zigzag rotations around the in-plane axes that measure the normal distortion typical of multilayered structures. An additional “drilling” zigzag rotation is therefore included among the nodal degrees of freedom in order to properly model curved and built-up structures. A stabilization procedure is adopted to suppress spurious zero-energy modes. A three-node triangular and a four-node quadrilateral flat shell element are formulated with 9 degrees of freedom per node. Example problems involving flat and curved multilayered structures are presented and discussed in order to assess the accuracy and convergence properties of the presented elements. Both static response predictions and free vibrations analyses are considered and the comparison is made with analytic RZT solutions, high-fidelity 3D finite element models and FSDT-based flat shell elements.

Complex time route to quantum backreaction

We consider the backreaction of a quantum system q on an effectively classical degree of freedom C that is interacting with it. The backreaction equation based on the standard path integral formalism gives the so-called ‘in-out’ backreaction equation, which has several serious pathologies. One can use a different backreaction prescription, referred to as the ‘in-in’ approach, which resolves all the issues of ‘in-out’ backreaction equation. However, this procedure is usually invoked in a rather ad hoc manner. Here we provide a rigorous path integral derivation of the ‘in-in’ approach by exploiting the concept of quantum evolution along complex time contours. It turns out that, this approach can also be used to study both the ‘in-in’ and ‘in-out’ backreaction equations in a unified manner.

Reversible time travel with freedom of choice

General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or more generally local operations, lead to inconsistencies and should thus be forbidden. Here we consider the most general deterministic dynamics connecting classical degrees of freedom defined on a set of bounded space-time regions, requiring that it is compatible with arbitrary operations performed in the local regions. We find that any such dynamics can be realised through reversible interactions. We further find that consistency with local operations is compatible with non-trivial time travel: three parties can interact in such a way to be all both in the future and in the past of each other, while being free to perform arbitrary local operations.

N‐space collision model for rotation‐translation energy exchange in DSMC collisions

SummaryA new discrete simulation Monte Carlo (DSMC) collision model for molecules possessing an integer number of classical degrees of freedom for molecular structure energy is proposed. The total molecular energy (translation plus molecular structure) is represented by a velocity in five‐dimensional space. Each collision is an elastic N‐sphere collision in N‐space, where N= 3, 4, or 5. For N=5, there is a maximum chance of exchange of energy between the two components of velocity, which represent the rotation energy and the three components that represent the translational velocity. For N=3, there is no change in the rotation energy of each molecule, and for N=4, there is an intermediate chance that rotation and translation energy will be exchanged. The exchange probability ϕ can be set to give the desired rotational relaxation rate. To achieve any realistic viscosity μ(T), the N‐space model must be coupled with a modified collision procedure known as ν‐DSMC. The new model is shown to match the results of molecular dynamics calculations for the internal structure of a Mach 7 shock, with a saving of about 20% in CPU time compared to standard DSMC using the standard Borgnakke‐Larsen exchange model.

Phase space quantum–classical hybrid model

In this work we provide a complete model of semiclassical theories by including back-reaction and correlation into the picture. We specially aim at the interaction between light and a two-level atom, and we also illustrate it via the coupling of two harmonic oscillators. Quantum and classical systems are treated on the same grounds via the Wigner–Weyl phase-space correspondence of the quantum theory. We show that this model provides a suitable mixture of the quantum and classical degrees of freedom, including the fact that the evolution transfers nonclassical features to the classical subsystem and nonquantum behaviour to the quantum subsystem. In that sense, we can no longer distinguish between classical and quantum variables and we need to talk about a hybrid model.

DIGITAL MARKETING STRATEGY BASED ON HOTEL INDUSTRY STUDY IN TBILISI

Digital Marketing is a processual and causeful, accomplishment of daily obstacles mix. It is a broad term, refers to advertising using offline and online marketing channels. As long as there are no widely available and complete educational courses of digital marketing it becomes highly demanded almost in every field in Tbilisi, Georgia. Digital marketing requires a unique set of knowledge and a person with a classical marketing degree cannot sufficiently run digital campaigns, thus organizations mainly outsource the digital marketing to agencies or do it independently and frequently with major mistakes. Even though “Digital marketing” is a new term in Tbilisi, Georgia, still many realize its importance for business. Proper digital marketing campaigns are most vital for some business industries. One of those industries is a tourism sector, in particular the hotel business. Tourism industry is one of the successful and rapidly growing spheres in Georgia, where digital marketing channels play a huge role for finding customers. The key determinant of the hotel business success is the proper digital marketing campaign, though inaccuracy and lack of knowledge of managing digital marketing channels negatively affect the hotels' sustainable development. Goal of the paper is to investigate, develop and define digital marketing online communication channel strategy based on the hotel industry. Research Objectives: • Investigate online marketing channels in the hotel industry; • Create online marketing channels’ allocation guide; Research Question: • Which are the most effective online marketing channels in hotel business? This work aims to come up with a practical digital marketing online communication channel strategy and ready to use guidelines in hotel industry. Research Methods: As mentioned before, the aim of this paper is to investigate, analyze and develop digital marketing online channels strategy for hotel industry. Accordingly quantitative approach was conducted during the research. From quantitative data sources was conducted: • Questionnaire – 70 hotels (in Tbilisi).

Correlation between intensity fluctuations and degree of cross-polarization of light waves on scattering

Correlation between intensity fluctuations (CIF) in the three-dimensional scattered field has been deduced, only provided that the fluctuating electric field obeys Gaussian statistics. This discussion results in the introduction of a new definition of the degree of cross-polarization (DCP) which depends on two locations and can reduce to the classical degree of polarization as its two locations coinciding. The concept of DCP in the general three-dimensional scattered field is considered to be especially useful, for instance, in inverse problems of scattering.

In-parallel resonators to increase the absorption of subwavelength acoustic absorbers in the mid-frequency range

The acoustic effects of in-parallel resonators is compared to the behavior of a classical single degree of freedom resonator for which the resistance and the mass are in series. In-parallel resonators serve to enhance the acoustic absorption for mid-frequencies thereby extending the active frequency range of perfect acoustic absorbers. Two implementations of these in-parallel absorbers are presented and investigated experimentally as well as numerically. In the first demonstration, the resistance is a perforated plate with a wiremesh and the oscillating mass is the air that fills a tube passing through the plate. The second implementation consists of a thin flexible beam that oscillates and where the resistance is due to the micro-slit resulting from the cutting of the beam.

Quantum mechanical MRI simulations: Solving the matrix dimension problem.

We propose a solution to the matrix dimension problem in quantum mechanical simulations of MRI (magnetic resonance imaging) experiments on complex molecules. This problem is very old; it arises when Kronecker products of spin operators and spatial dynamics generators are taken-the resulting matrices are far too large for any current or future computer. However, spin and spatial operators individually have manageable dimensions, and we note here that the action by their Kronecker products on any vector may be computed without opening those products. This eliminates large matrices from the simulation process. MRI simulations for coupled spin systems of complex metabolites in three dimensions with diffusion, flow, chemical kinetics, and quantum mechanical treatment of spin relaxation are now possible. The methods described in this paper are implemented in versions 2.4 and later of the Spinach library.

Clustering and phase transitions in a 2D superfluid with immiscible active impurities

Phase transitions of a finite-size two-dimensional superfluid of bosons in presence of active impurities are studied by using the projected Gross–Pitaevskii model. Impurities are described with classical degrees of freedom. A spontaneous clustering of impurities during the thermalization is observed. Depending on the interaction among impurities, such clusters can break due to thermal fluctuations at temperatures where the condensed fraction is still significant. The emergence of clusters is found to increase the condensation transition temperature. The condensation and the Berezinskii–Kosterlitz–Thouless transition temperatures, determined numerically, are found to strongly depend on the volume occupied by the impurities: a relative increase up to a of their respective values is observed, whereas their ratio remains approximately constant.

Classical and Quantum Liquids Induced by Quantum Fluctuations.

Geometrically frustrated interactions may render classical ground states macroscopically degenerate. The connection between classical and quantum liquids and how the degeneracy is affected by quantum fluctuations is, however, not completely understood. We study a simple model of coupled quantum and classical degrees of freedom, the so-called Falicov-Kimball model, on a triangular lattice and away from half-filling. For weak interactions the phase diagram features a charge disordered state down to zero temperature. We provide compelling evidence that this phase is a liquid and show that it is divided by a crossover line that terminates in a quantum critical point. Our results offer a new vantage point to address how quantum liquids can emerge from their classical counterparts.

Hybrid quantum-classical simulation of quantum speed limits in open quantum systems

The quantum speed limit (QSL) provides a fundamental upper bound on the speed of quantum evolution, but its evaluation in generic open quantum systems still presents a formidable computational challenge. Herein, we introduce a hybrid quantum-classical method for computing QSL times in multi-level open quantum systems. The method is based on a mixed Wigner–Heisenberg representation of the composite quantum dynamics, in which the open subsystem of interest is treated quantum mechanically and the bath is treated in a classical-like fashion. By solving a set of coupled first-order deterministic differential equations for the quantum and classical degrees of freedom, one can compute the QSL time. To demonstrate the utility of the method, we study the unbiased spin-boson model and provide a detailed analysis of the effect of the subsystem-bath coupling strength and bath temperature on the QSL time. In particular, we find a turnover of the QSL time in the strong coupling regime, which is indicative of a speed-up in the quantum evolution. We also apply the method to the Fenna–Matthews–Olson complex model and identify a potential connection between the QSL time and the efficiency of the excitation energy transfer at different temperatures.

Two-dimensional vibronic spectra from classical trajectories.

We present a semiclassical procedure for calculating nonlinear optical spectra from a quantum Hamiltonian with discrete electronic states. The purely electronic Hamiltonian for N states is first mapped to the associated Meyer-Miller Hamiltonian for N quantum harmonic oscillators. The classical limit is then taken, and classical nuclear degrees of freedom are introduced. Spectra are calculated by propagating the classical analogs of transition dipole operators subject to semiclassical quantization conditions on action variables. This method generalizes the optimized-mean-trajectory approach, originally developed for nonlinear vibrational spectroscopy and subsequently extended to vibronic spectroscopy, to models with multiple interacting electronic states. Calculations for two electronic excited states with displaced harmonic nuclear potentials illustrate the implementation of this approach.

Effective potentials from semiclassical truncations

Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order in moments for a single classical degree of freedom and to second order for a pair of classical degrees of freedom are derived and applied to several model systems. It is shown that these new canonical variables facilitate the derivation of quantum-statistical quantities and effective potentials. Moreover, by formulating quantum dynamics in classical language, these methods result in new heuristic pictures, for instance of tunneling, that can guide further investigations.

Interaction between active particles and quantum vortices leading to Kelvin wave generation

One of the main features of superfluids is the presence of topological defects with quantised circulation. These objects are known as quantum vortices and exhibit a hydrodynamic behaviour. Nowadays, particles are the main experimental tool used to visualise quantum vortices and to study their dynamics. We use a self-consistent model based on the three-dimensional Gross-Pitaevskii (GP) equation to explore theoretically and numerically the attractive interaction between particles and quantized vortices at very low temperature. Particles are described as localised potentials depleting the superfluid and following Newtonian dynamics. We are able to derive analytically a reduced central-force model that only depends on the classical degrees of freedom of the particle. Such model is found to be consistent with the GP simulations. We then generalised the model to include deformations of the vortex filament. The resulting long-range mutual interaction qualitatively reproduces the observed generation of a cusp on the vortex filament during the particle approach. Moreover, we show that particles can excite Kelvin waves on the vortex filament through a resonance mechanism even if they are still far from it.