Degeneracy Properties Research Articles

Impact of valley degeneracy on the thermoelectric properties of zig-zag graphene nanoribbons with staggered sublattice potentials and transverse electric fields.

This study investigates the band inversion of flat bands in zig-zag graphene nanoribbons (ZGNRs) using a tight-binding model. The band inversion results from symmetry breaking in the transverse direction, achievable through deposition on specific substrates such as separated silicon carbide or hexagonal boron nitride sheets. Upon band inversion, ZGNRs exhibit electronic structures characterized by valley degeneracy and band gap properties, which can be modulated by transverse electric fields. To explore the impact of this level degeneracy on thermoelectric properties, we employ Green's function techniques to calculate thermoelectric quantities in ZGNR segments with staggered sublattice potentials and transverse electric fields. Two carrier transport scenarios are considered: the chemical potential is positioned above and below the highest occupied molecular orbital. We analyze thermionic-assisted transport (TAT) and direct ballistic transport (DBT). Level degeneracy enhances the electric power factors of ZGNRs by increasing electrical conductance, while the Seebeck coefficient remains robust in the TAT scenario. Conversely, in DBT, the enhancement of the power factor primarily stems from improvements in the Seebeck coefficient at elevated temperatures.

The stochastic fast logarithmic equation in [formula omitted] with multiplicative Stratonovich noise

This paper is concerned with the existence and uniqueness of the solution for the stochastic fast logarithmic equation with Stratonovich linear multiplicative noise in Rd for d⩾3. It provides an answer to a critical case (morally speaking, corresponding to the porous media operator ΔXm for m=0) left as an open problem in the paper Barbu-Röckner-Russo [8]. We face several technical difficulties related both to the degeneracy properties of the logarithm and to the fact that the problem is treated in an unbounded domain. Firstly, the order in which the approximations are considered is very important and different from previous methods. As a by-product of this choice, leading only to weak convergence of relevant terms, identifying the relevant part of the equation in the domain of the nonlinear operator is more fastidious. Secondly, the energy estimates (see eq. (33)) needed in the last step can only be achieved with a well-chosen Stratonovich-type rectification of the noise.

Unraveling parameter degeneracy in GRB data analysis

ABSTRACT Gamma-ray burst (GRB) afterglow light curves and spectra provide information about the density of the environment, the energy of the explosion, the properties of the particle acceleration process, and the structure of the decelerating jet. Due to the large number of parameters involved, the model can present a certain degree of parameter degeneracy. In this paper, we generated synthetic photometric data points using a standard GRB afterglow model and fit them using the Markov chain Monte Carlo (MCMC) method. This method has emerged as the preferred approach for analysing and interpreting data in astronomy. We show that, depending on the choice of priors, the parameter degeneracy can go unnoticed by the MCMC method. Furthermore, we apply the MCMC method to analyse the GRB 170817A afterglow. We find that there is a complete degeneracy between the energy of the explosion E, the density of the environment n, and the microphysical parameters describing the particle acceleration process (e.g. ϵe and ϵB), which cannot be determined by the afterglow light curve alone. Our results emphasize the importance of gaining a deep understanding of the degeneracy properties which can be present in GRB afterglows models, as well as the limitations of the MCMC method. In the case of GRB 170817, we get the following values for the physical parameters: E = 8 × 1050–1 × 1053 erg, n = 7 × 10−5–9 × 10−3, ϵe = 10−3–0.3, ϵB = 10−10–0.3.

The uniqueness of the solution of a mixed problem for three-dimensional hyperbolic equations with type and order degeneracy property

Abstract The relevance of the stated subject is conditioned upon the presence of a real possibility to simulate vibrations of elastic membranes in space according to the Hamilton principle using degenerate three-dimensional hyperbolic equations, which is of particular practical importance from the standpoint of the prospects for mathematical modelling of the heat propagation process in oscillating elastic membranes. The purpose of this paper is to study the sequence of the procedure for mathematical modelling of heat propagation in oscillating elastic membranes which is leading to degenerate three-dimensional hyperbolic equations. The methodological approach of this study is based on a combination of theoretical study of the possibilities of constructing mathematical models of heat propagation in oscillating elastic membranes with the practical application of methods for constructing three-dimensional hyperbolic equations with type and order degeneracy to find a single solution to a mixed problem. In the course of this study, the results were presented in the form of a mathematical proof of the possibility of obtaining a single solution to a mixed problem for three-dimensional hyperbolic equations with type and order degeneracy. The results obtained in this study and the conclusions formulated on their basis are of significant practical importance for developers of methods of mathematical modelling of heat propagation processes in oscillating artificial membranes, which is of key importance from the standpoint of prospects for improving methods of mathematical modelling of processes occurring in technical devices used in various fields of modern industries.

Nodal degeneracy of guided modes in uniaxial crystal slabs

We study the dispersions of the guided modes in the continuous uniaxial crystal slab waveguide and engineer their degeneracies through dielectric anisotropy. By switching the uniaxial positivity and negativity, we can obtain distinctive nodal types, point and line, for the lowest degeneracy in frequency. The mirror symmetry protections, Mx and My, are pointed out, and the degeneracy properties are intuitively analyzed through comparing the approximate slopes of the guided modes. Our results reveal a link between the lowest nodal types and the positivity/negativity of the uniaxial crystal, and provide a new approach to regulate the topology of degeneracy in two-dimensional photonic bands.

HDR Degree Bassed Indices and Mhr-Polynomial for the Treatment of COVID-19

In this research work, We introduce topological indices, namely as an HDR version of Modified Zagreb topological index (HDRM*), HDR version of Modified forgotten topological index (HDRF*), and HDR version of hyper Zagreb index (HDRHM*). Then the relatively study depends on the structure-property regression analysis to test and compute the chemical applicability of these indices to predict the physicochemical properties of octane isomers. Also, we show these HDR indices have well degeneracy properties compared to other degree-based topological indices. Also, We defined and computed the Mhr-polynomial of the newly indices and applied it on COVID-19 treatments. Also, we discussed some mathematical properties of HDR indices.

Degeneracy Property of a Matrixdifferential Operator and Applications

We prove that a matrix-differential operator A in a Banach space is a Fredholm operator with zero index and construct the corresponding subspaces and projections. We find the spectrum of A. Based on properties of the operator A, we study solutions to the initial-boundary value problem for a second order partial differential equation with a small parameter e at the higher order derivatives and some parameter c at lower order terms. We clarify how the parameter c affects the behavior of the solution as e → 0.

FT-IR, Molecular Structure and Nonlinear Optical Properties of 2-(pyranoquinolin-4-yl)malononitrile (PQMN): A DFT Approach

A combined experimental and theoretical study for Fourier transform infrared spectra for 2-(pyranoquinolin-4-yl)malononitrile (PQMN) compound has been made. In advance, we investigate many physical characteristics based on DFT/B3LYP using 6-311G(d,p) basis set such as optimum structure, vibrational frequencies, thermo-chemistry, overall dipole moment, HOMO/LUMO Bandgap, nuclear repulsive energy and ionization energies, electronic affinity and chemical potential, global electrophilicity index, global hardness and finally softness (ζ). Also, we studied the non-linear optical (NLO) properties of PQMN. Results emphasize both degeneracy and diamagnetic properties of PQMN. PQMN Frontiers’ molecular orbitals (FMOs) split into two distinguished alpha (spin ↑) and beta (spin ↓) states with the same energy 3.7 eV, although its singlet spins state. Moreover, the calculated dipole moment (DM) value (13.3 Debye) for PQMN explains the mystery behind its reactive tendency with the nearby media. PQMN is a unique model for a degenerate diamagnetic semiconductor that can be easily used for optoelectronic manufactured devices such as solar cells and spintronic devices.

On the hardnesses of several quantum decoding problems

We classify the time complexities of three decoding problems for quantum stabilizer codes: quantum bounded distance decoding (QBDD), quantum maximum likelihood decoding (QMLD), and quantum minimum error probability decoding (QMEPD). For QBDD, we show that it is NP-hard based on Fujita’s result, and cover the gap of full row rank of check matrices, like what Berlekamp, McEliece, and Tilborg suggested in 1978. Then, we give some insight into the quantum decoding problems to clarify that the degeneracy property is implicitly embedded in any decoding algorithm, independent of the typical definition of degenerate codes. Then, over the depolarizing channel model, we show that QMLD and QMEPD are NP-hard. The NP-hardnesses of these decoding problems indicate that decoding general stabilizer codes is extremely difficult, strengthening the foundation of quantum code-based cryptography.

Optical servo with high design freedom using spherical-wave Bragg degeneracy in a volume holographic optical element.

A novel optical sensor is proposed and demonstrated with the use of spherical-wave Bragg degeneracy of a volume holographic optical element. Bragg degeneracy can be performed perfectly for a volume hologram written by two plane waves or spherical waves. But only spherical reference light is useful to perform severe shifting selectivity in one direction and Bragg degeneracy in another direction. The experiment corresponding to theoretical simulation was demonstrated in a volume holographic optical element, which was an optical servo for a collinear volume holographic disc. Through clever design, the displacement response of the tracking beam was observed for a magnification magnitude of 980% to the displacement of the probe beam so that the resolution requirement of the photosensor can be reduced. Besides, a high linearity of the displacement response was observed. To discover the design freedom, a theoretical study of the displacement response was done for the servo by two spherical waves. The linearity, the magnification magnitude, and the diffraction efficiency were examined and the property of the Bragg degeneracy was figured out.

On the origin of degeneracy in the genetic code.

The degeneracy of amino acid coding is one of the most crucial and enigmatic aspects of the genetic code. Different theories about the origin of the genetic code have been developed. However, to date, there is no comprehensive hypothesis on the mechanism that might have generated the degeneracy as we observe it. Here, we provide a new theory that explains the origin of the degeneracy based only on symmetry principles. The approach allows one to describe exactly the degeneracy of the early code (progenitor of the genetic code of LUCA, the last universal common ancestor) which is hypothesized to have the same degeneracy as the present vertebrate mitochondrial genetic code. The theory is based upon the tessera code, that fits as the progenitor of the early code. Moreover, we describe in detail the possible evolutionary transitions implied by our theory. The approach is supported by a unified mathematical framework that accounts for the degeneracy properties of both nuclear and mitochondrial genetic codes. Our work provides a new perspective to the understanding of the origin of the genetic code and the roles of symmetry principles in the organization of genetic information.

Onsome New Neighbourhood Degree Based Indices

Abstract In this paper, four novel topological indices named as neighbourhood version of forgotten topological index (FN ), modified neighbourhood version of Forgotten topological index (FN * ), neighbourhood version of second Zagreb index (M2 * ) and neighbourhood version of hyper Zagreb index (HMN ) are introduced. Here the relatively study depends on the structure-property regression analysis is made to test and compute the chemical applicability of these indices for the prediction of physicochemical properties of octane isomers. Also it is shown that these newly presented indices have well degeneracy property in comparison with other degree based topological indices. Some mathematical properties of these indices are also discussed here.

Remarks on global solutions to the initial-boundary value problem for quasilinear degenerate parabolic equations with a nonlinear source term

We give an existence theorem of global solution to the initial-boundary value problem for \(u_{t}-\operatorname{div}\{\sigma(|\nabla u|^2)\nabla u\}=f(u)\) under some smallness conditions on the initial data, where \(\sigma (v^2)\) is a positive function of \(v^2\ne 0\) admitting the degeneracy property \(\sigma(0)=0\). We are interested in the case where \(\sigma(v^2)\) has no exponent \(m \geq 0\) such that \(\sigma(v^2) \geq k_0|v|^m , k_0 \gt 0\). A typical example is \(\sigma(v^2)=\operatorname{log}(1+v^2)\). \(f(u)\) is a function like \(f=|u|^{\alpha} u\). A decay estimate for \(\|\nabla u(t)\|_{\infty}\) is also given.

Conventional volume holography for unconventional Airy beam shapes.

Utilizing multiplexed volume holography, a single optical element, enabling to shape structural variants of non-diffracting Airy wavefronts, from one-dimensional Airy mode to unconventional Airy modes such as vortex Airy and quad Airy modes, has been experimentally realized. Here, beam shaped angularly multiplexed volume holographic gratings (AMVHGs) are recorded in PQ: PMMA photopolymer, where five different spatial wavefronts of Airy beams have been sequentially recorded, for simultaneous reconstruction of different Airy modes, by a conventional Gaussian beam. Spatial and spectral mode selective properties of AMVHGs are demonstrated by narrow-band as well as by broadband light source. In addition, through wavelength degeneracy property, the maximum sensitivity wavelength of blue (488 nm) is used for recording in PQ: PMMA, but the AMVHGs are operated at a broad wavelength band of interest, all the way to longer wavelength in near infrared (850 nm). The K-sphere representation is used to explain the spectral properties of AMVHGs.

Concurrent Changes of Brain Functional Connectivity and Motor Variability When Adapting to Task Constraints.

In behavioral neuroscience, the adaptability of humans facing different constraints has been addressed on one side at the brain level, where a variety of functional networks dynamically support the same performance, and on the other side at the behavioral level, where fractal properties in sensorimotor variables have been considered as a hallmark of adaptability. To bridge the gap between the two levels of observation, we have jointly investigated the changes of network connectivity in the sensorimotor cortex assessed by modularity analysis and the properties of motor variability assessed by multifractal analysis during a prolonged tapping task. Four groups of participants had to produce the same tapping performance while being deprived from 0, 1, 2, or 3 sensory feedbacks simultaneously (auditory and/or visual and/or tactile). Whereas tapping performance was not statistically different across groups, the number of brain networks involved and the degree of multifractality of the inter-tap interval series were significantly correlated, increasing as a function of feedback deprivation. Our findings provide first evidence that concomitant changes in brain modularity and multifractal properties characterize adaptations underlying unchanged performance. We discuss implications of our findings with respect to the degeneracy properties of complex systems, and the entanglement of adaptability and effective adaptation.

The well-tempered cosmological constant

Self tuning is one of the few methods for dynamically cancelling a large cosmological constant and yet giving an accelerating universe. Its drawback is that it tends to screen all sources of energy density, including matter. We develop a model that tempers the self tuning so the dynamical scalar field still cancels an arbitrary cosmological constant, including the vacuum energy through any high energy phase transitions, without affecting the matter fields. The scalar-tensor gravitational action is simple, related to cubic Horndeski gravity, with a nonlinear derivative interaction plus a tadpole term. Applying shift symmetry and using the property of degeneracy of the field equations we find families of functions that admit de Sitter solutions with expansion rates that are independent of the magnitude of the cosmological constant and preserve radiation and matter dominated phases. That is, the method can deliver a standard cosmic history including current acceleration, despite the presence of a Planck scale cosmological constant.

Spatial mode multiplexing using volume holographic gratings.

We experimentally demonstrate spatial mode multiplexing of optical beams using multiplexed volume holographic gratings (MVGHs) formed in phenanthrenquinone-poly (methyl methacrylate) (PQ-PMMA) photopolymer. Multiple spatial modes of Laguerre-Gaussian (LG) beams are recorded at the same pupil area of a volume hologram resulting in MVHGs, for simultaneous reconstruction of spatial modes. In addition, a helical phase beam, a non-diffracting beam with conical phase profile, and a parabolic non-diffracting beam with cubic phase profile have also been simultaneously recorded and reconstructed from MVHGs. Utilizing Bragg wavelength degeneracy property of volume hologram these multiplexed modes are reconstructed at multiple wavelengths ranging from blue (450nm) to red (635). Due to combined effect of three-dimensional pupil, Bragg wavelength degeneracy, angular selectivity, together with spatial mode properties these, MVHGs can act as spatial mode filter with spectral filtering property. Advantages of volume holography in beam shaping are discussed. Multiple first diffraction orders with desired beam shapes obtained from the single optical element (i.e. a volume hologram with MVHGs) may find important applications in optical communication experiments, and in volume holographic imaging and microscopy. Experimental results show solid evidence that MVGHs in beam shaping provide a simple, compact, single element, and direct way to multiplex spatial modes.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

Electronic Degeneracy and Intrinsic Magnetic Properties of EpitaxialNb: SrTiO3 Thin Films Controlled by Defects.

We report thermoelectric power experiments in e-doped thin films of SrTiO3 (STO) which demonstrate that the electronic band degeneracy can be lifted through defect management during growth. We show that even small amounts of cationic vacancies, combined with epitaxial stress, produce a homogeneous tetragonal distortion of the films, resulting in a Kondo-like resistance upturn at low temperature, large anisotropic magnetoresistance, and nonlinear Hall effect. Ab initio calculations confirm a different occupation of each band depending on the degree of tetragonal distortion. The phenomenology reported in this Letter for tetragonally distorted e-doped STO thin films, is similar to that observed in LaAlO3/STO interfaces and magnetic STO quantum wells.

Global Small Solutions to Three-Dimensional Incompressible Magnetohydrodynamical System

In this paper, we consider the global wellposedness of three-dimensional incompressible magneto-hydrodynamical (MHD) system with small and smooth initial data. The main difficulty of the proof lies in establishing the global in time $L^1$ estimate for gradient of the velocity field due to the strong degeneracy and anisotropic spectral properties of the linearized system. To achieve this and to avoid the difficulty of propagating anisotropic regularity for the transport equation, we first write our system in the Lagrangian formulation. Then we employ anisotropic Littlewood--Paley analysis to establish the key $L^1$ in time estimates to the velocity and the gradient of the pressure in the Lagrangian coordinate. With those estimates, we prove the global wellposedness of the Lagrangian formulation with smooth and small initial data by using the energy method. Toward this, we will have to use the algebraic structure of the Lagrangian formulation in a rather crucial way. The global wellposedness of the original system then follows by a suitable change of variables together with a continuous argument. We should point out that compared with the linearized systems of two-dimensional MHD equations of F. Lin, L. Xu, and P. Zhang [Global Small Solutions to 2-D MHD System, arXiv:1302.5877] and that of the three-dimensional modified MHD equations of F. Lin and P. Zhang [Comm. Pure Appl. Math., 67 (2014), pp. 531--580] our linearized system here is much more degenerate and moreover, the formulation of the initial data for the Lagrangian formulation is more subtle than that of F. Lin, L. Xu, and P. Zhang.