Search results for: fractal symmetry

Authors: Ibrahim Alsendid, Rob Sturman, Benjamin Sharp

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In this paper, we consider a family of 2-dimensional nonlinear area-preserving transformations on the torus. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results, we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments that define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated and compared with the distribution of periodic points of the system.

Keywords: Discrete-time dynamical systems, Fractal geometry, Multifractal behaviour of the Perturbed map, Multifractal of Dynamical systems

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Authors: Heerak Banerjee, Sourov Roy

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Supersymmetry, one of the most celebrated fields of study for explaining experimental observations where the standard model (SM) falls short, is reeling from the lack of experimental vindication. At the same time, the idea of additional gauge symmetry, in particular, the gauged Lμ-Lτ symmetric models have also generated significant interest. They have been extensively proposed in order to explain the tantalizing discrepancy in the predicted and measured value of the muon anomalous magnetic moment alongside several other issues plaguing the SM. While very little parameter space within these models remain unconstrained, this work finds that the γ + Missing Energy (ME) signal at the Belle-II detector will be a smoking gun for supersymmetry (SUSY) in the presence of a gauged U(1)Lμ-Lτ symmetry. A remarkable consequence of breaking the enhanced symmetry appearing in the limit of degenerate (s)leptons is the nondecoupling of the radiative contribution of heavy charged sleptons to the γ-Z΄ kinetic mixing. The signal process, e⁺e⁻ →γZ΄→γ+ME, is an outcome of this ubiquitous feature. Taking the severe constraints on gauged Lμ-Lτ models by several low energy observables into account, it is shown that any significant excess in all but the highest photon energy bin would be an undeniable signature of such heavy scalar fields in SUSY coupling to the additional gauge boson Z΄. The number of signal events depends crucially on the logarithm of the ratio of stau to smuon mass in the presence of SUSY. In addition, the number is also inversely proportional to the e⁺e⁻ collision energy, making a low-energy, high-luminosity collider like Belle-II an ideal testing ground for this channel. This process can probe large swathes of the hitherto free slepton mass ratio vs. additional gauge coupling (gₓ) parameter space. More importantly, it can explore the narrow slice of Z΄ mass (MZ΄) vs. gₓ parameter space still allowed in gauged U(1)Lμ-Lτ models for superheavy sparticles. The spectacular finding that the signal significance is independent of individual slepton masses is an exciting prospect indeed. Further, the prospect that signatures of even superheavy SUSY particles that may have escaped detection at the LHC may show up at the Belle-II detector is an invigorating revelation.

Keywords: additional gauge symmetry, electron-positron collider, kinetic mixing, nondecoupling radiative effect, supersymmetry

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Authors: S. De Curtis, L. Delle Rose, S. Moretti, K. Yagyu

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Supersymmetry and compositeness are the two prevalent paradigms providing both a solution to the hierarchy problem and motivation for a light Higgs boson state. An open door towards the solution is found in the context of 2-Higgs Doublet Models (2HDMs), which are necessary to supersymmetry and natural within compositeness in order to enable Electro-Weak Symmetry Breaking. In scenarios of compositeness, the two isospin doublets arise as pseudo Nambu-Goldstone bosons from the breaking of SO(6). By calculating the Higgs potential at one-loop level through the Coleman-Weinberg mechanism from the explicit breaking of the global symmetry induced by the partial compositeness of fermions and gauge bosons, we derive the phenomenological properties of the Higgs states and highlight the main signatures of this Composite 2-Higgs Doublet Model at the Large Hadron Collider. These include modifications to the SM-like Higgs couplings as well as production and decay channels of heavier Higgs bosons. We contrast the properties of this composite scenario to the well-known ones established in supersymmetry, with the MSSM being the most notorious example. We show how 2HDM spectra of masses and couplings accessible at the Large Hadron Collider may allow one to distinguish between the two paradigms.

Keywords: beyond the standard model, composite Higgs, supersymmetry, Two-Higgs Doublet Model

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Authors: Vramori Mitra, Bornali Sarma, Arun K. Sarma

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Recurrence is a ubiquitous feature of any real dynamical system. The states in phase space trajectory of a system have an inherent tendency to return to the same state or its close state after certain time laps. Recurrence quantification analysis technique, based on this fundamental feature of a dynamical system, detects evaluation of state under variation of control parameter of the system. The paper presents the investigation of nonlinear dynamical behavior of plasma floating potential fluctuations obtained by using a Langmuir probe in different magnetic field under the variation of discharge voltages. The main measures of recurrence quantification analysis are considered as determinism, linemax and entropy. The increment of the DET and linemax variables asserts that the predictability and periodicity of the system is increasing. The variable linemax indicates that the chaoticity is being diminished with the slump of magnetic field while increase of magnetic field enhancing the chaotic behavior. Fractal property of the plasma time series estimated by DFA technique (Detrended fluctuation analysis) reflects that long-range correlation of plasma fluctuations is decreasing while fractal dimension is increasing with the enhancement of magnetic field which corroborates the RQA analysis.

Keywords: detrended fluctuation analysis, chaos, phase space, recurrence

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Authors: Sanjeet Kumar Singh, Shanatanu Bhattacharaya

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Design of high- efficiency low, frequency (<1000Hz) soundproof window or wall absorber which is transparent to airflow is presented. Due to the massive rise in human population and modernization, environmental noise has significantly risen globally. Prolonged noise exposure can cause severe physiological and psychological symptoms like nausea, headaches, fatigue, and insomnia. There has been continuous growth in building construction and infrastructure like offices, bus stops, and airports due to urban population. Generally, a ventilated window is used for getting fresh air into the room, but at the same time, unwanted noise comes along. Researchers used traditional approaches like noise barrier mats in front of the window or designed the entire window using sound-absorbing materials. However, this solution is not aesthetically pleasing, and at the same time, it's heavy and not adequate for low-frequency noise shielding. To address this challenge, we design a transparent hexagonal panel based on Sierpiński fractal triangle, which is aesthetically pleasing, demonstrates normal incident sound absorption coefficient more than 0.96 around 700 Hz and transmission loss around 23 dB while maintaining e air circulation through triangular cutout. Next, we present a concept of fabrication of large acoustic panel for large-scale applications, which lead to suppressing the urban noise pollution.

Keywords: acoustic metamaterials, noise, functional materials, ventilated

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Authors: Sanjeet Kumar Singh, Shantanu Bhatacharya

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Design of high-efficiency low, frequency (<1000Hz) soundproof window or wall absorber which is transparent to airflow is presented. Due to the massive rise in human population and modernization, environmental noise has significantly risen globally. Prolonged noise exposure can cause severe physiological and psychological symptoms like nausea, headaches, fatigue, and insomnia. There has been continuous growth in building construction and infrastructure like offices, bus stops, and airports due to the urban population. Generally, a ventilated window is used for getting fresh air into the room, but at the same time, unwanted noise comes along. Researchers used traditional approaches like noise barrier mats in front of the window or designed the entire window using sound-absorbing materials. However, this solution is not aesthetically pleasing, and at the same time, it's heavy and not adequate for low-frequency noise shielding. To address this challenge, we design a transparent hexagonal panel based on the Sierpiński fractal triangle, which is aesthetically pleasing and demonstrates a normal incident sound absorption coefficient of more than 0.96 around 700 Hz and transmission loss of around 23 dB while maintaining e air circulation through the triangular cutout. Next, we present a concept of fabrication of large acoustic panels for large-scale applications, which leads to suppressing urban noise pollution.

Keywords: acoustic metamaterials, ventilation, urban noise pollution, noise control

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Authors: Akanksha Indora

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Environmental problems are considered a vital social issue in terms of the world’s problems with pollution, environmental degradation, and resource depletion. And populism is about appropriating the social issues according to the social condition for mobilizing a mass and constructing a ‘general will’. Populism encourages a move towards a common cause, it channelizes the emotions of the ‘common people’ towards a nation and nature. The Gandhian ideology has been received as a dominant ideology and the ‘only’ solution to environmental problems. This paper strives to understand the symmetry of environmentalism and Gandhianismi.e., how the debate on the environment in India has been primarily studied through the Gandhian ideology. The Indian Social Sciences visualize the broader issues of the environment from these perspectives, thus, making it a hegemonic approach. Being anti pluralist rhetoric is major rhetoric in the becoming of a populist. This paper shall focus on the idea that how this hegemonic construction of Gandhian ideology in the debates on environmentalism has contributed to the making of anti-pluralistic rhetoric. This anti-pluralistic rhetoric has eliminated the possibility of a pluralistic perspective in the debates on the environment. The quest for a moral inspiration embedded in Gandhianism, whose situatedness is found in the Hindu Social order, seems to have been completely rationalized through the larger politics of knowledge and thus making it appear as the only way forward when it is not.

Keywords: environmental populism, gandhianism, populist rhetoric, environmentalism

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Authors: Juan Xia, Jiaxu Yan, Ze Xiang Shen

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The tuneable interlayer interactions in two-dimensional (2D) transition metal dichlcogenides (TMDs) offer an exciting platform for exploring new physics and applications by material variety, thickness, stacking sequence, electromagnetic filed, and stress/strain. Compared with the five methods mentioned above, high pressure is a clean and powerful tool to induce dramatic changes in lattice parameters and physical properties for 2D TMD materials. For instance, high pressure can strengthen the van der Waals interactions along c-axis and shorten the covalent bonds in atomic plane, leading to the typical first-order structural transition (2Hc to 2Ha for MoS2), or metallization. In particular, in the case of WTe₂, its unique symmetry endows the significant anisotropy and the corresponding unexpected properties including the giant magnetoresistance, pressure-induced superconductivity and Weyl semimetal states. Upon increasing pressure, the Raman peaks for WTe₂ at ~120 cm⁻¹, are gradually red-shifted and totally suppressed above 10 GPa, attributed to the possible structural instability of orthorhombic Td phase under high pressure and phase transition to a new monoclinic T' phase with inversion symmetry. Distinct electronic structures near Fermi level between the Td and T' phases may pave a feasible way to achieve the Weyl state tuning in one material without doping.

Keywords: 2D TMDs, electronic property, high pressure, first-principles calculations

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Authors: V. Batishchev, V. Getman

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We study the self-similar fluid flows in the Marangoni layers with the axial symmetry. Such flows are induced by the radial gradients of the temperatures whose distributions along the free boundary obey some power law. The self-similar solutions describe thermo-capillar flows both in the thin layers and in the case of infinite thickness. We consider both positive and negative temperature gradients. In the former case the cooling of free boundary nearby the axis of symmetry gives rise to the rotation of fluid. The rotating flow concentrates itself inside the Marangoni layer while outside of it the fluid does not revolve. In the latter case we observe no rotating flows at all. In the layers of infinite thickness the separation of the rotating flow creates two zones where the flows are directed oppositely. Both the longitudinal velocity and the temperature have exactly one critical point inside the boundary layer. It is worth to note that the profiles are monotonic in the case of non-swirling flows. We describe the flow outside the boundary layer with the use of self-similar solution of the Euler equations. This flow is slow and non-swirling. The introducing of an outer flow gives rise to the branching of swirling flows from the non-swirling ones. There is such the critical velocity of the outer flow that a non-swirling flow exists for supercritical velocities and cannot be extended to the sub-critical velocities. For the positive temperature gradients there are two non-swirling flows. For the negative temperature gradients the non-swirling flow is unique. We determine the critical velocity of the outer flow for which the branching of the swirling flows happens. In the case of a thin layer confined within free boundaries we show that the cooling of the free boundaries near the axis of symmetry leads to the separating of the layer and creates two sub-layers with opposite rotations inside. This makes sharp contrast with the case of infinite thickness. We show that such rotation arises provided the thickness of the layer exceed some critical value. In the case of a thin layer confined within free and rigid boundaries we construct the branching equation and the asymptotic approximation for the secondary swirling flows near the bifurcation point. It turns out that the bifurcation gives rise to one pair of the secondary swirling flows with different directions of swirl.

Keywords: free surface, rotation, fluid flow, bifurcation, boundary layer, Marangoni layer

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Authors: Ozgu Hafizoglu

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Analogy is an essential tool of human cognition that enables connecting diffuse and diverse systems with attributional, deep structural, casual relations that are essential to learning, to innovation in artificial worlds, and to discovery in science. Cognitive Model of Analogy (CMA) leads and creates information pattern transfer within and between domains and disciplines in science. This paper demonstrates the Cognitive Model of Analogy (CMA) as an evolutionary approach to scientific research. The model puts forward the challenges of deep uncertainty about the future, emphasizing the need for flexibility of the system in order to enable reasoning methodology to adapt to changing conditions. In this paper, the model of analogical reasoning is created based on brain cells, their fractal, and operational forms within the system itself. Visualization techniques are used to show correspondences. Distinct phases of the problem-solving processes are divided thusly: encoding, mapping, inference, and response. The system is revealed relevant to brain activation considering each of these phases with an emphasis on achieving a better visualization of the brain cells: glial cells, axons, axon terminals, and neurons, relative to matching conditions of analogical reasoning and relational information. It’s found that encoding, mapping, inference, and response processes in four-term analogical reasoning are corresponding with the fractal and operational forms of brain cells: glial, axons, and neurons.

Keywords: analogy, analogical reasoning, cognitive model, brain and glials

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Authors: Rafal Michalski, Jakub Zygadlo

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We present the concept and scientific methods and algorithms of our computation system called ATOMIC MATTERS. This is the first presentation of the new computer package, that allows its user to describe physical properties of atomic localized electron systems subject to electromagnetic interactions. Our solution applies to situations where an unclosed electron 2p/3p/3d/4d/5d/4f/5f subshell interacts with an electrostatic potential of definable symmetry and external magnetic field. Our methods are based on Crystal Electric Field (CEF) approach, which takes into consideration the electrostatic ligands field as well as the magnetic Zeeman effect. The application allowed us to predict macroscopic properties of materials such as: Magnetic, spectral and calorimetric as a result of physical properties of their fine electronic structure. We emphasize the importance of symmetry of charge surroundings of atom/ion, spin-orbit interactions (spin-orbit coupling) and the use of complex number matrices in the definition of the Hamiltonian. Calculation methods, algorithms and convention recalculation tools collected in ATOMIC MATTERS were chosen to permit the prediction of magnetic and spectral properties of materials in isostructural series.

Keywords: atomic matters, crystal electric field (CEF) spin-orbit coupling, localized states, electron subshell, fine electronic structure

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Saad M. Darwish, Adel A. El-Zoghabi, Moustafa F. Ashry

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The popularity of the Internet and the availability of powerful computers and high-speed networks as low-cost commodity components are changing the way we use computers today. These technical opportunities have led to the possibility of using geographically distributed and multi-owner resources to solve large-scale problems in science, engineering, and commerce. Recent research on these topics has led to the emergence of a new paradigm known as Grid computing. To achieve the promising potentials of tremendous distributed resources, effective and efficient load balancing algorithms are fundamentally important. Unfortunately, load balancing algorithms in traditional parallel and distributed systems, which usually run on homogeneous and dedicated resources, cannot work well in the new circumstances. In this paper, the concept of a fast fractal transform in heterogeneous grid computing based on R-tree and the domain-range entropy is proposed to improve fault tolerance and load balancing algorithm by improve connectivity, communication delay, network bandwidth, resource availability, and resource unpredictability. A novel two-dimension figure of merit is suggested to describe the network effects on load balance and fault tolerance estimation. Fault tolerance is enhanced by adaptively decrease replication time and message cost while load balance is enhanced by adaptively decrease mean job response time. Experimental results show that the proposed method yields superior performance over other methods.

Keywords: Grid computing, load balancing, fault tolerance, R-tree, heterogeneous systems

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Authors: Steven D. P Moore

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A novel method referred to asKýklos(Ky) dimensional geometry is proposed as an entity specific core geometric dimensional measurement system. Ky geometric measures can constructscaled multi-dimensionalmodels using regular and irregular sets in IRn. This entity specific-derived geometric measurement system shares similar fractal methods in which a ‘fractal transformation operator’ is applied to a set S to produce a union of N copies. The Kýklos’ inputs use 1D geometry as a core measure. One-dimensional inputs include the radius interval of a circle/sphere or the semiminor/semimajor axes intervals of an ellipse or spheroid. These geometric inputs have finite values that can be measured by SI distance units. The outputs for each interval are divided and subdivided 1D subcomponents with a union equal to the interval geometry/length. Setting a limit of subdivision iterations creates a finite value for each 1Dsubcomponent. The uniqueness of this method is captured by allowing the simplest 1D inputs to define entity specific subclass geometric core measurements that can also be used to derive length measures. Current methodologies for celestial based measurement of time, as defined within SI units, fits within this methodology, thus combining spatial and temporal features into geometric core measures. The novel Ky method discussed here offers geometric measures to construct scaled multi-dimensional structures, even models. Ky classes proposed for consideration include celestial even subatomic. The application of this offers incredible possibilities, for example, geometric architecture that can represent scaled celestial models that incorporates planets (spheroids) and celestial motion (elliptical orbits).

Keywords: Kyklos, geometry, measurement, celestial, dimension

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Authors: Abdalla Manur, Daniel Offin, Alessandro Arsie

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In this paper, we study the extension of the minimizing equal mass parallelogram solutions which was derived by Chen in 2001. Chen’s solution was minimizing for one quarter of the period [0; T], where numerical integration had been used in his proof. This paper focuses on extending the minimization property to intervals of time [0; 2T] and [0; 4T].

Keywords: action, Hamiltoian, N-body, symmetry

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Authors: Veronique Jubera, Ka-Young Kim, U-Chan Chung, Amelie Veillere, Jean-Marc Heintz

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Emitting materials and all solid state lasers are widely used in the field of optical applications and materials science as a source of excitement, instrumental measurements, medical applications, metal shaping etc. Recently promising optical efficiencies were recorded on ceramics which result from a cheaper and faster ways to obtain crystallized materials. The choice and optimization of the sintering process is the key point to fabricate transparent ceramics. It includes a high control on the preparation of the powder with the choice of an adequate synthesis, a pre-heat-treatment, the reproducibility of the sintering cycle, the polishing and post-annealing of the ceramic. The densification is the main factor needed to reach a satisfying transparency, and many technologies are now available. The symmetry of the unit cell plays a crucial role in the diffusion rate of the material. Therefore, the cubic symmetry compounds having an isotropic refractive index is preferred. The cubic Y3NbO7 matrix is an interesting host which can accept a high concentration of rare earth doping element and it has been demonstrated that SPS is an efficient way to sinter this material. The optimization of diffusion losses requires a microstructure of fine ceramics, generally less than one hundred nanometers. In this case, grain growth is not an obstacle to transparency. The ceramics properties are then isotropic thereby to free-shaping step by orienting the ceramics as this is the case for the compounds of lower symmetry. After optimization of the synthesis route, several SPS parameters as heating rate, holding, dwell time and pressure were adjusted in order to increase the densification of the Eu3+ doped Y3NbO7 pellets. The luminescence data coupled with X-Ray diffraction analysis and electronic diffraction microscopy highlight the existence of several distorted environments of the doping element in the studied defective fluorite-type host lattice. Indeed, the fast and high crystallization rate obtained to put in evidence a lack of miscibility in the phase diagram, being the final composition of the pellet driven by the ratio between niobium and yttrium elements. By following the luminescence properties, we demonstrate a direct impact on the SPS process on this material.

Keywords: emission, niobate of rare earth, Spark plasma sintering, lack of miscibility

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Authors: Mounir Zili

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We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-markovian and that it has non-stationary increments. We will also give the conditions under which it is a semi-martingale. Finally, the main features of its sample paths will be specified.

Keywords: fractal dimensions, mixed gaussian processes, sample paths, sub-fractional brownian motion

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Authors: Sami Houry

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Complex systems exhibit universal characteristics as they near a tipping point. Among them are common generic early warning signals which precede critical transitions. These signals include: critical slowing down in which the rate of recovery from perturbations decreases over time; an increase in the variance of the state variable; an increase in the skewness of the state variable; an increase in the autocorrelations of the state variable; flickering between different states; and an increase in spatial correlations over time. The presence of the signals has management implications, as the identification of the signals near the tipping point could allow management to identify intervention points. Despite the applications of the generic early warning signals in various scientific fields, such as fisheries, ecology and finance, a review of literature did not identify any applications that address the program student withdrawal problem at the undergraduate distance universities. This area could benefit from the application of generic early warning signals as the program withdrawal rate amongst distance students is higher than the program withdrawal rate at face-to-face conventional universities. This research specifically assessed the generic early warning signals through an intensive case study of undergraduate program student withdrawal at a Canadian distance university. The university is non-cohort based due to its system of continuous course enrollment where students can enroll in a course at the beginning of every month. The assessment of the signals was achieved through the comparison of the incidences of generic early warning signals among students who withdrew or simply became inactive in their undergraduate program of study, the true positives, to the incidences of the generic early warning signals among graduates, the false positives. This was achieved through significance testing. Research findings showed support for the signal pertaining to the rise in flickering which is represented in the increase in the student’s non-pass rates prior to withdrawing from a program; moderate support for the signals of critical slowing down as reflected in the increase in the time a student spends in a course; and moderate support for the signals on increase in autocorrelation and increase in variance in the grade variable. The findings did not support the signal on the increase in skewness of the grade variable. The research also proposes a new signal based on the fractal-like characteristic of student behavior. The research also sought to extend knowledge by investigating whether the emergence of a program withdrawal status is self-similar or fractal-like at multiple levels of observation, specifically the program level and the course level. In other words, whether the act of withdrawal at the program level is also present at the course level. The findings moderately supported self-similarity as a potential signal. Overall, the assessment of the signals suggests that the signals, with the exception with the increase of skewness, could be utilized as a predictive management tool and potentially add one more tool, the fractal-like characteristic of withdrawal, as an additional signal in addressing the student program withdrawal problem.

Keywords: critical transitions, fractals, generic early warning signals, program student withdrawal

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Authors: S.I.Mukhin, S. Seidov, A. Mukherjee

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The Dicke model is a key tool for the description of correlated states of quantum atomic systems, excited by resonant photon absorption and subsequently emitting spontaneous coherent radiation in the superradiant state. The Dicke Hamiltonian (DH) is successfully used for the description of the dynamics of the Josephson Junction (JJ) array in a resonant cavity under applied current. In this work, we have investigated a generalized model, which is described by DH with a frustrating interaction term. This frustrating interaction term is explicitly the infinite coordinated interaction between all the spin half in the system. In this work, we consider an array of N superconducting islands, each divided into two sub-islands by a Josephson Junction, taken in a charged qubit / Cooper Pair Box (CPB) condition. The array is placed inside the resonant cavity. One important aspect of the problem lies in the dynamical nature of the physical observables involved in the system, such as condensed electric field and dipole moment. It is important to understand how these quantities behave with time to define the quantum phase of the system. The Dicke model without frustrating term is solved to find the dynamical solutions of the physical observables in analytic form. We have used Heisenberg’s dynamical equations for the operators and on applying newly developed Rotating Holstein Primakoff (HP) transformation and DH we have arrived at the four coupled nonlinear dynamical differential equations for the momentum and spin component operators. It is possible to solve the system analytically using two-time scales. The analytical solutions are expressed in terms of Jacobi's elliptic functions for the metastable ‘bound luminosity’ dynamic state with the periodic coherent beating of the dipoles that connect the two double degenerate dipolar ordered phases discovered previously. In this work, we have proceeded the analysis with the extended DH with a frustrating interaction term. Inclusion of the frustrating term involves complexity in the system of differential equations and it gets difficult to solve analytically. We have solved semi-classical dynamic equations using the perturbation technique for small values of Josephson energy EJ. Because the Hamiltonian contains parity symmetry, thus phase transition can be found if this symmetry is broken. Introducing spontaneous symmetry breaking term in the DH, we have derived the solutions which show the occurrence of finite condensate, showing quantum phase transition. Our obtained result matches with the existing results in this scientific field.

Keywords: Dicke Model, nonlinear dynamics, perturbation theory, superconductivity

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Authors: Hikari Ryu, Yuki Fukuda, Kento Oishi, Chiharu Igarashi, Shogo Kiryu

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Recently, wireless power transfer has been developed in various fields. Magnetic coupling is popular for feeding power at a relatively short distance and at a lower frequency. Electro-magnetic wave coupling at a high frequency is used for long-distance power transfer. The wireless power transfer has attracted attention in e-textile fields. Rigid batteries are required for many body-worn electric systems at the present time. The technology enables such batteries to be removed from the systems. Flexible coils have been studied for such applications. Coils with a high Q factor are required in the magnetic-coupling power transfer. Antennas with low return loss are needed for the electro-magnetic coupling. Litz wire is so flexible to fabricate coils and antennas sewn on fabric and has low resistivity. In this study, the electric characteristics of some coils and antennas fabricated with the Litz wire by using two sewing techniques are investigated. As examples, a coil and an antenna are described. Both were fabricated with 330/0.04 mm Litz wire. The coil was a planar coil with a square shape. The outer side was 150 mm, the number of turns was 15, and the pitch interval between each turn was 5 mm. The Litz wire of the coil was overstitched with a sewing machine. The coil was fabricated as a receiver coil for a magnetic coupled wireless power transfer. The Q factor was 200 at a frequency of 800 kHz. A wireless power system was constructed by using the coil. A power oscillator was used in the system. The resonant frequency of the circuit was set to 123 kHz, where the switching loss of power FETs was small. The power efficiencies were 0.44 – 0.99, depending on the distance between the transmitter and receiver coils. As an example of an antenna with a sewing technique, a fractal pattern antenna was stitched on a 500 mm x 500 mm fabric by using a needle punch method. The pattern was the 2nd-oder Vicsec fractal. The return loss of the antenna was -28 dB at a frequency of 144 MHz.

Keywords: e-textile, flexible coils and antennas, Litz wire, wireless power transfer

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Authors: Ghulam Hussain, Herrington Lee, Comfort Paul, Jones Richard

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Background: To determine the functional limitations of the lower limbs or readiness to return to sport, most rehabilitation programs use some form of testing; however, it is still unknown what the pass criteria is. This study aims to investigate the differences between the dominant and non-dominant leg performances across several lower limb tasks, which are hop tests, two-dimensional (2D) frontal plane projection angle (FPPA) tests, and isokinetic muscle tests. This study also provides the reference values for the limb symmetry index (LSI) for the hop and isokinetic muscle strength tests. Twenty recreationally active participants were recruited, 11 males and 9 females (age 23.65±2.79 years; height 169.9±3.74 cm; and body mass 74.72±5.81 kg. All tests were undertaken on the dominant and non-dominant legs. These tests are (1) Hop tests, which include horizontal hop for distance and crossover hop tests, (2) Frontal plane projection angle (FPPA): 2D capturing from two different tasks, which are forward hop landing and squatting, and (3) Isokinetic muscle strength tests: four different muscles were tested: quadriceps, hamstring, ankle plantar flexor, and hip extensor muscles. The main outcome measurements were, for the (1) hop tests: maximum distance was taken when undertaking single/crossover hop for distance using a standard tape measure, (2) for the FPPA: the knee valgus angle was measured from the maximum knee flexion position using a single 2D camera, and (3) for the isokinetic muscle strength tests: three different variables were measured: peak torque, peak torque to body weight, and the total work to body weight. All the muscle strength tests have been applied in both concentric and eccentric muscle actions at a speed of 60°/sec. This study revealed no differences between the dominant and non-dominant leg performance, and 85% of LSI was achieved by the majority of the subjects in both hop and isokinetic muscle tests, and; therefore, one leg’s hop performance can define the other.

Keywords: 2D FPPA, hop tests, isokinetic testing, LSI

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Authors: Gurcharan Singh Buttar

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It has been discovered that although these two areas, statistics, and information theory, are independent in their nature, they can be combined to create applications in multidisciplinary mathematics. This is due to the fact that where in the field of statistics, statistical parameters (measures) play an essential role in reference to the population (distribution) under investigation. Information measure is crucial in the study of ambiguity, assortment, and unpredictability present in an array of phenomena. The following communication is a link between the two, and it has been demonstrated that the well-known conventional statistical measures can be used as a measure of information.

Keywords: probability distribution, entropy, concavity, symmetry, variance, central tendency

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Authors: Shankha Sanyal, Archi Banerjee, Sayan Biswas, Sourya Sengupta, Sayan Nag, Ranjan Sengupta, Dipak Ghosh

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The term ‘gestalt’ has been widely used in the field of psychology which defined the perception of human mind to group any object not in part but as a 'unified' whole. Music, in general, is polyphonic - i.e. a combination of a number of pure tones (frequencies) mixed together in a manner that sounds harmonious. The study of human brain response due to different frequency groups of the acoustic signal can give us an excellent insight regarding the neural and functional architecture of brain functions. Hence, the study of music cognition using neuro-biosensors is becoming a rapidly emerging field of research. In this work, we have tried to analyze the effect of different frequency bands of music on the various frequency rhythms of human brain obtained from EEG data. Four widely popular Rabindrasangeet clips were subjected to Wavelet Transform method for extracting five resonant frequency bands from the original music signal. These frequency bands were initially analyzed with Detrended/Adaptive Fractal analysis (DFA/AFA) methods. A listening test was conducted on a pool of 100 respondents to assess the frequency band in which the music becomes non-recognizable. Next, these resonant frequency bands were presented to 20 subjects as auditory stimulus and EEG signals recorded simultaneously in 19 different locations of the brain. The recorded EEG signals were noise cleaned and subjected again to DFA/AFA technique on the alpha, theta and gamma frequency range. Thus, we obtained the scaling exponents from the two methods in alpha, theta and gamma EEG rhythms corresponding to different frequency bands of music. From the analysis of music signal, it is seen that loss of recognition is proportional to the loss of long range correlation in the signal. From the EEG signal analysis, we obtain frequency specific arousal based response in different lobes of brain as well as in specific EEG bands corresponding to musical stimuli. In this way, we look to identify a specific frequency band beyond which the music becomes non-recognizable and below which in spite of the absence of other bands the music is perceivable to the audience. This revelation can be of immense importance when it comes to the field of cognitive music therapy and researchers of creativity.

Keywords: AFA, DFA, EEG, gestalt in music, Hurst exponent

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Authors: Amar Partap Singh Pharwaha, Shweta Rani

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To develop a reliable and cost effective communication platform for the telemedicine applications, novel antenna design has been presented using bacterial foraging optimization (BFO) technique. The proposed antenna geometry is achieved by etching a modified Koch curve fractal shape at the edges and a square shape slot at the center of the radiating element of a patch antenna. It has been found that the new antenna has achieved 43.79% size reduction and better resonating characteristic than the original patch. Representative results for both simulations and numerical validations are reported in order to assess the effectiveness of the developed methodology.

Keywords: BFO, electrical permittivity, fractals, Koch curve

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Authors: L. Tonia, I. Daglis, W. Kurth

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The sound of the universe creates an affinity with the sounds of music. The analysis of the sound of space focuses on the existence of a tone material, the microstructure and macrostructure, and the form of the sound through the signals recorded during the flight of the spacecraft Van Allen Probes and Cassini’s mission. The sound becomes from the frequencies that belong to electromagnetic waves. Plasma Wave Science Instrument and Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) recorded the signals from space. A transformation of that signals to audio gave the opportunity to study and analyze the sound. Due to the fact that the musical tone pitch has a frequency and every electromagnetic wave produces a frequency too, the creation of a musical score, which appears as the sound of space, can give information about the form, the symmetry, and the harmony of the sound. The conversion of space radio emissions to audio provides a number of tone pitches corresponding to the original frequencies. Through the process of these sounds, we have the opportunity to present a music score that “composed” from space. In this score, we can see some basic features associated with the music form, the structure, the tone center of music material, the construction and deconstruction of the sound. The structure, which was built through a harmonic world, includes tone centers, major and minor scales, sequences of chords, and types of cadences. The form of the sound represents the symmetry of a spiral movement not only in micro-structural but also to macro-structural shape. Multiple glissando sounds in linear and polyphonic process of the sound, founded in magnetic fields around Earth, Saturn, and Jupiter, but also a spiral movement appeared on the spectrogram of the sound. Whistles, Auroral Kilometric Radiations, and Chorus emissions reveal movements similar to musical excerpts of works by contemporary composers like Sofia Gubaidulina, Iannis Xenakis, EinojuhamiRautavara.

Keywords: space sound analysis, spiral, space music, analysis

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Authors: Adil Murtaza, Muhammad Tahir Khan, Awais Ghani, Chao Zhou, Sen Yang, Xiaoping Song

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The morphotropic phase boundary (MPB); a boundary between two different crystallographic symmetries in the composition–temperature phase diagram has been widely studied in ferroelectrics and recently has drawn interest in ferromagnets for obtaining enhanced large field-induced strain. At MPB, the system gets a compressed free energy state, which allows the polarization to freely rotate and hence results in a high magnetoelastic response (e.g., high magnetization, low coercivity, and large magnetostriction). Based on the same mechanism, we designed MPB in a ferromagnetic Tb₁₋ₓNdₓCo₂ system. The temperature-dependent magnetization curves showed spin reorientation (SR); which can be explained by a two-sublattice model. Contrary to previously reported MPB involved ferromagnetic systems, the MPB composition of Tb₀.₃₅Nd₀.₆₅Co₂ exhibits a low saturation magnetization (MS), indicating a compensation of the Tb and Nd magnetic moments at MPB. The coercive field (HC) under a low magnetic field and first anisotropy constant (K₁) shows a minimum value at MPB composition of x=0.65. A detailed spin configuration diagram is provided for the Tb₁₋ₓNdₓCo₂ around the composition for the anisotropy compensation; this can guide the development of novel magnetostrictive materials. The anisotropic magnetostriction (λS) first decreased until x=0.8 and then continuously increased in the negative direction with further increase of Nd concentration. In addition, the large ratio between magnetostriction and the absolute values of the first anisotropy constant (λS/K₁) appears at MPB, indicating that Tb₀.₃₅Nd₀.₆₅Co₂ has good magnetostrictive properties. Present work shows an anomalous type of MPB in ferromagnetic materials, revealing that MPB can also lead to a weakening of magnetoelastic behavior as shown in the ferromagnetic Tb₁₋ₓNdₓCo₂ system. Our work shows the universal presence of MPB in ferromagnetic materials and suggests the differences between different ferromagnetic MPB systems that are important for substantial improvement of magnetic and magnetostrictive properties. Based on the results of this study, similar MPB effects might be achieved in other ferroic systems that can be used for technological applications. The finding of magnetic MPB in the ferromagnetic system leads to some important significances. First, it provides a better understanding of the fundamental concept of spin reorientation transitions (SRT) like ferro-ferro transitions are not only reorientation of magnetization but also crystal symmetry change upon magnetic ordering. Second, the flattened free energy corresponding to a low energy barrier for magnetization rotation and enhanced magnetoelastic response near MPB. Third, to attain large magnetostriction with MPB approach two terminal compounds have different easy magnetization directions below Curie temperature Tc in order to accomplish the weakening of magnetization anisotropy at MPB (as in ferroelectrics), thus easing the magnetic domain switching and the lattice distortion difference between two terminal compounds should be large enough, e.g., lattice distortion of R symmetry ˃˃ lattice distortion of T symmetry). So that the MPB composition agrees to a nearly isotropic state along with large ‘net’ lattice distortion, which is revealed in a higher value of magnetostriction.

Keywords: magnetization, magnetostriction, morphotropic phase boundary (MPB), phase transition

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Authors: Anca Radulescu, Danae Evans

Abstract:

The relationship between a network’s hardwiring and its emergent dynamics are central to neuroscience. We study the principles of this correspondence in a canonical setup (in which network nodes exhibit well-studied complex quadratic dynamics), then test their universality in biological networks. By extending methods from discrete dynamics, we study the effects of network connectivity on temporal patterns, encapsulating long-term behavior into the rich topology of network Mandelbrot sets. Then elements of fractal geometry can be used to predict and classify network behavior.

Keywords: canonical model, complex dynamics, dynamic networks, fractals, Mandelbrot set, network connectivity

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Authors: Jiwuer Jilili, Fabrizio Cossu, Udo Schwingenschlogl

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By first-principles calculations we investigate the structural, electronic, and magnetic properties of the (LaMnO3)2/(SrTiO3)2 superlattice. We find that a monoclinic C2h symmetry is energetically favorable and that the spins order ferromagnetically. Under both compressive and tensile uniaxial strain the electronic structure of the superlattice shows a half-metallic character. In particular, a fully spin-polarized two-dimensional electron gas, which traces back to the Ti 3dxy orbitals, is achieved under compressive uniaxial strain.

Keywords: manganite, strain, 2DEG, superlattice

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Authors: Makamas Kumprou, Pipatana Amatachaya, Sugalya Amatachaya, Thiwabhorn Thaweewannakij, Preeda Arayawichanon

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Many individuals with spinal cord injury (SCI) need an ambulatory assistive device (AAD) to promote their independence and experience of task-specific walking practice. Without a periodic follow-up for their walking progression, however, many individuals may use the same AAD even though up to 66% of them had the potential to progress walking ability. This may distort their optimal ability and increase the possibility of having negative impacts due to the long-lasting used of an AAD. However, these findings were cross-sectionally collected without data confirmation for the benefit or negative impacts of those who changed the types of AAD used. Therefore, this study prospectively assessed the proportion of ambulatory individuals with SCI who were able to progress their walking ability as determined using a type of AAD, and the changes of their functional ability as well as the incidence of falls over 6 months. Twenty-four subjects with SCI who daily walked with an AAD were involved in the study for 2 visits over 6 months. At the first visit (baseline assessments), the subjects were assessed for their spatiotemporal variables (i.e., cadence, step length, stride length, and step symmetry) and walking ability using the 10-meter walk test (10MWT). Then, they were assessed for the possibility of their walking progression as determined using the ability of walking with the least support AAD with no more than contact guarding assist. Those who were capable of changing an AAD were trained for the ability to walk with a new AAD. Thereafter, all subjects were monthly monitored for incidence of fall over 6 months. At the second visit (after 6 months followed-up), subjects were reassessed for their spatiotemporal variables and 10MWT. The findings indicated that, of all 24 subjects, 8 subjects (33.3%) were able to walk with less support AAD than their usual one. The walking cadence, step length symmetry, and walking ability of these subjects improved significantly greater than those who walked with the same AAD (p < 0.05). Among these subjects, one subject (12.5%) reported fell (3 times) during the follow-up period, whereas 5 subjects (31.3%) who walked with the same AAD experienced at least one fall (range 1 – 16 times). The findings indicated that a large proportion of ambulatory individuals with SCI who daily walked with an AAD could progress their walking ability, whereby their walking ability and safety also significantly improved after they walked with an optimal AAD. The findings suggest the need for a periodic follow-up for an appropriate AAD used for these individuals.

Keywords: walking device, walker, crutches, cane, rehabilitation

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Authors: Manish Saha, Manish Kumar Niranjan, Saket Asthana

Abstract:

The K₀.₅Na₀.₅NbO₃ (KNN) system has emerged as one of the most promising lead-free piezoelectric over the years. In this work, we perform a comprehensive investigation of electronic structure, lattice dynamics and dielectric/ferroelectric properties of the room temperature phase of KNN by combining ab-initio DFT-based theoretical analysis and experimental characterization. We assign the symmetry labels to KNN vibrational modes and obtain ab-initio polarized Raman spectra, Infrared (IR) reflectivity, Born-effective charge tensors, oscillator strengths etc. The computed Raman spectrum is found to agree well with the experimental spectrum. In particular, the results suggest that the mode in the range ~840-870 cm-¹ reported in the experimental studies is longitudinal optical (LO) with A_1 symmetry. The Raman mode intensities are calculated for different light polarization set-ups, which suggests the observation of different symmetry modes in different polarization set-ups. The electronic structure of KNN is investigated, and an optical absorption spectrum is obtained. Further, the performances of DFT semi-local, metal-GGA and hybrid exchange-correlations (XC) functionals, in the estimation of KNN band gaps are investigated. The KNN bandgap computed using GGA-1/2 and HSE06 hybrid functional schemes are found to be in excellant agreement with the experimental value. The COHP, electron localization function and Bader charge analysis is also performed to deduce the nature of chemical bonding in the KNN. The solid-state reaction and hydrothermal methods are used to prepare the KNN ceramics, and the effects of grain size on the physical characteristics these ceramics are examined. A comprehensive study on the impact of different synthesis techniques on the structural, electrical, and photocatalytic properties of ferroelectric ceramics KNN. The KNN-S prepared by solid-state method have significantly larger grain size as compared to that for KNN-H prepared by hydrothermal method. Furthermore, the KNN-S is found to exhibit higher dielectric, piezoelectric and ferroelectric properties as compared to KNN-H. On the other hand, the increased photocatalytic activity is observed in KNN-H as compared to KNN-S. As compared to the hydrothermal synthesis, the solid-state synthesis causes an increase in the relative dielectric permittivity (ε^') from 2394 to 3286, remnant polarization (P_r) from 15.38 to 20.41 μC/cm^², planer electromechanical coupling factor (k_p) from 0.19 to 0.28 and piezoelectric coefficient (d_33) from 88 to 125 pC/N. The KNN-S ceramics are also found to have a lower leakage current density, and higher grain resistance than KNN-H ceramic. The enhanced photocatalytic activity of KNN-H is attributed to relatively smaller particle sizes. The KNN-S and KNN-H samples are found to have degradation efficiencies of RhB solution of 20% and 65%, respectively. The experimental study highlights the importance of synthesis methods and how these can be exploited to tailor the dielectric, piezoelectric and photocatalytic properties of KNN. Overall, our study provides several bench-mark important results on KNN that have not been reported so far.

Keywords: lead-free piezoelectric, Raman intensity spectrum, electronic structure, first-principles calculations, solid state synthesis, photocatalysis, hydrothermal synthesis

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