One-dimensional Matrix Research Articles

Interacting systems and wormholes

We consider a class of tripartite systems for which two d-dimensional QFTs are cross-coupled via a third d + 1-dimensional “messenger” QFT. We analyse in detail the example of a pair of one-dimensional matrix quantum mechanics) coupled via a two­dimensional theory of the BF-type and compute its partition function and simple correlators. This construction is extendible in higher dimensions) using a Chern-Simons “messenger” theory. In all such examples, the exact partition function acquires a form, speculated to correspond to systems dual to Euclidean wormholes and the cross correlators are sufficiently soft and consistent with analogous gravitational calculations. Another variant of the tripartite system is studied, where the messenger theory is described by a non-self-interacting (matrix)-field, reaching similar conclusions. While the Euclidean theories we consider are perfectly consistent, the two possible analytic continuations into Lorentzian signature (messenger vs. boundary QFT directions) of the tripartite models, reveal physical features and “pathologies” resembling those of the expected Lorentzian gravitational backgrounds.

A μ-mode integrator for solving evolution equations in Kronecker form

In this paper, we propose a μ-mode integrator for computing the solution of stiff evolution equations. The integrator is based on a d-dimensional splitting approach and uses exact (usually precomputed) one-dimensional matrix exponentials. We show that the action of the exponentials, i.e. the corresponding batched matrix-vector products, can be implemented efficiently on modern computer systems. We further explain how μ-mode products can be used to compute spectral transforms efficiently even if no fast transform is available. We illustrate the performance of the new integrator by solving, among the others, three-dimensional linear and nonlinear Schrödinger equations, and we show that the μ-mode integrator can significantly outperform numerical methods well-established in the field. We also discuss how to efficiently implement this integrator on both multi-core CPUs and GPUs. Finally, the numerical experiments show that using GPUs results in performance improvements between a factor of 10 and 20, depending on the problem.

Electromagnetic wave transmission in hybrid fractal plasma photonic crystals through developing new kinds of productive quasi-periodic multilayers

ABSTRACT In this study, for the first time, we present a new way of producing novel quasi-periodic multilayers based on the multiplication of some primitive available sequences such as Thue–Morse, Fibonacci (of two types N and P), Cantor, and constant length square sets. We also present some pseudo-codes to create these multilayers. Using a one-dimensional transfer matrix method, we obtain the transmission coefficient for some plasma-dielectric photonic crystals. Although, employing the above-mentioned approach many new sequences may be obtained, but for conciseness purpose, we analyze the photonic band gaps of a limited number of multilayers obtained in this way. We consider the effect of the number of layers, the refractive index of the dielectric later, multiplication of different fractal sets, etc., on the electromagnetic wave transport properties.

Superexponential amplification, power blowup, and solitons sustained by non-Hermitian gauge potentials

We introduce a continuous one-dimensional non-Hermitian matrix gauge potential and study its effect on dynamics of a two-component field. The model is emulated by a system of evanescently coupled nonlinear waveguides with distributed gain and losses. The considered gauge fields lead to a variety of unusual physical phenomena in both linear and nonlinear regimes. In the linear regime, the field may undergo superexponential convective amplification. A total power of an input Gaussian beam may exhibit a finite-distance blowup, which manifests itself in absolute delocalization of the beam at a finite propagation distance, where the amplitude of the field remains finite. The defocusing Kerr nonlinearity initially enhances superexponential amplification, while at larger distances it suppresses the growth of the total power. The focusing nonlinearity at small distances slows down the power growth and eventually leads to the development of the modulational instability. Complex periodic gauge fields lead to the formation of families of stable fundamental and dipole solitons.

Measurement and theoretical analysis of sound absorption of simple cubic and hexagonal lattice granules

A structure that possesses a continuous pore space packed with a granular material exhibits acoustic characteristics based on the principle similar to that of a porous material. Such a structure is used in low-noise pavement and ballast track. Therefore, predicting the sound absorption characteristics of a clearance generated in a granular material from the particle diameter and the physical property of gas is useful for engineering. This article deals with two packing models, namely, the simple cubic lattice model and the hexagonal lattice model, to measure the sound absorption coefficient of the structure packed with a granular material whose particle diameter is a few mm. Furthermore, a simple and accurate theoretical analysis that uses a one-dimensional transfer matrix method, which does not require numerous parameters, was performed. Comparing experimental values, when the particle diameter of the granular material was 4 mm, the percentage of the boundary layer in the clearance was moderately larger than when the diameter was 8 mm; therefore, the effect of viscosity on it was larger, and its sound absorption coefficient peak was higher. Moreover, compared with the simple cubic lattice, the hexagonal lattice had a higher percentage of boundary layer in the clearance because of its smaller volume of pore space. Then, the influence of friction due to the viscosity on it was higher, and its sound absorption coefficient peak was higher. In addition, the theoretical values obtained by the proposed analysis method typically matched the experiment values.

Embedding 1D WO3 Nanotubes into 2D Ultrathin Porous g-C3N4 to Improve the Stability and Efficiency of Photocatalytic Hydrogen Production

Recently, two-dimensional (2D) g-C3N4 has attracted great interest for visible-light-driven H2 production. Thinning, doping, and reticulation have been demonstrated as effective strategies to improve the efficiency of photocatalysis, but are a challenge for structural stability. Herein, a targeted method was implemented by embedding the one-dimensional (1D) WO3 nanotubes matrix into the frameworks of 2D porous g-C3N4 to form a porous P-doped g-C3N4 nanosheets/WO3 nanotubes (PCNS/WNT) by a flexible electrostatic self-assembly process. As a visible-light-sensitive photocatalyst, the as-prepared hybrids exhibited impressive performance for hydrogen generation, which was attributed to the advantages of synergetic mechanism owing to a higher specific surface area, more reaction active sites, enhanced light absorption, and a better photogenerated carrier separation. Interestingly, the insertion of 1D WO3 nanotubes not only accelerates electrons transfer along the 1D channel but also provides robust support for 2D porous g-C3N4 architecture. As a result, the maximum photocatalytic H2 evolution rate of PCNW-50 is 547 μmol g–1 h–1, which is about four times higher than that of pure PCNS, and there is no significant reduction of H2 production after five cycles. Moreover, this 2D/1D PCNS/WNT hybrid was first reported in the area of photocatalytic hydrogen evolution and provides ideas for designing novel stable architecture of photocatalyst.

An Image Encryption Scheme Based on Lorenz Hyperchaotic System and RSA Algorithm

This research proposes a new image encryption scheme based on Lorenz hyperchaotic system and Rivest–Shamir–Adleman (RSA) algorithm. Firstly, the initial values of the Lorenz hyperchaotic system are generated by RSA algorithm, and the key stream is produced iteratively. In order to change the position and gray value of the pixel, the image data are hidden by additive mode diffusion. Secondly, the diffusion image matrix is reshaped into a one-dimensional image matrix, which is confused without repetition to hide the image data again. Then, the finite field diffusion algorithm is executed to realize the third hiding of the image information. In order to diffuse the pixel information into the entire cipher image, the additive mode diffusion algorithm needs to be looped twice. Finally, the cipher image can be obtained. The experimental results prove that the image encryption scheme proposed in this research is effective and has strong antiattack and key sensitivity. Moreover, the security of this encryption scheme relies on the RSA algorithm, which has high security.

Frequency filtering and vibrational spectrum of multiple-valley one-dimensional phononic crystals

In the present study, we have fixed the number of atoms in a one-dimensional phononic chain and changed the number of the valleys (or numbers of wells NOW) in it (by adding new terms to the system Hamiltonian) and studied the transmission properties of his system. Then, we have obtained the phononic transmission coefficient by using a one-dimensional transfer matrix method. We have also investigated the vibrational modes of the assumed system by using a direct diagonalization technique. We show that in our assumed system, there is an Omni-k bandgap within which bandgap exists for all values of the studied spring constant k. In our assumed system, we have also obtained some bi-convex lens-shaped phononic bandgaps as a function of the parameter $$V_{{{\text{conf}}}}$$ which their surface areas can be tuned by changing the number of valleys NOW. An interesting fact is that the transmission coefficient is found to be quantized versus variation of the number of wells NOW which may help experimentalists to use lower values of the material to fabricate their desired system (see the text). We observe that the transmission coefficients as a function of the NOW are some Cantor-like ones that obey self-similar bandgap structure patterns. Besides, we show that NOW and $$V_{conf}$$ are good tuning parameters that can localize the eigenmodes of the system in any part of the chain. We have provided some animation to more clearly illustrate the effect of different parameters on the transmission and vibrational properties of the system. Finally, by using a few parameters, which we have presented in this paper, we can do bandgap engineering and determine the bandgap widths, as well as their places on the frequency axis.

Electrospun Fe-Incorporated ZIF-67 Nanofibers for Effective Electrocatalytic Water Splitting.

The explorations of earth-abundant, noble metal-free, highly efficient electrocatalysts for water-splitting reactions have been considered as highly significant for imperishable energy production. Though the metal organic framework (MOF)-based materials are highly promising candidates in the area of material chemistry, the combined properties associated with MOFs and the one-dimensional (1D) fibrous matrix, which can lead to better electrocatalytic performance, have been less explored. Herein, we ascertain a fabrication method for ZIF-67 (zeolite imidazolate framework) nanofibers (NFs), Fe-ZIF NFs, and Fe-ZIF-67 NFs via the wet chemical combined electrospinning (ES) approach. The as-synthesized catalysts were utilized for the electrochemical reaction, which showed a high efficiency toward the oxygen evolution reaction (OER). Compared to other catalysts, the Fe-ZIF-67 NF catalyst showed a very less overpotential of 278 mV at a fixed current density of 10 mA cm-2. The obtained Tafel slope and Rct values are 77 mV dec-1 and 1.2 Ω, respectively. The post-X-ray photoelectron spectroscopy (XPS) analysis revealed the transformation of FeOOH during the OER study along with Co3+ states in mixed Fe-ZIF-67 NFs. In an alkaline electrolyzer, Fe-ZIF-67 NFs were utilized as the anode and a Pt wire as the cathode in 1 M KOH solution, which required a cell voltage of 1.68 V at 10 mA cm-2 current density with astonishing stability. Hence, this work should open a new path for the exploration of efficient non-noble metal catalysts for energy-related applications.

Study and estimation of sound absorption coefficient of pin holder structure

In this study, a theoretical analysis of the acoustic characteristics of a pin holder structure was conducted. In addition, the sound absorption coefficient, entering its clearance through the geometrical dimension of the clearance or the physical property of air, was calculated. The analysis model approximates the aperture of a pin holder structure as the clearance between two parallel surfaces. Thus, the propagation constant and characteristic impedance were obtained and treated as a one-dimensional transfer matrix. Subsequently, the sound absorption coefficient was calculated using the transfer matrix method and was compared with the experimental results. In the experiment, a two-microphone impedance tube was used to measure the sound absorption coefficient of the test samples. We attempted to perform a simple yet accurate estimation using these procedures. The theoretical analysis values exhibited a similar tendency to that of the experimental values.

Predicting the components and types of kerogen in shale by combining machine learning with NMR spectra

This study aims to develop a new method that combines machine learning with nuclear magnetic resonance (NMR) spectra to predict the kerogen components and types. Kerogen is the primary hydrocarbon source of shale oil/gas, and nearly half of the hydrocarbons in shale are adsorbed in kerogen. The adsorption and hydrocarbon generation capacity of kerogen is directly related to its types, molecular components, and structures. Fruitful researches studying kerogen at the molecular level have been conducted. Unfortunately, these methods are complicated, time-consuming, and labor-intensive. Our method has the advantages of high-throughput prediction, high accuracy, and time savings compared with the existing methods. Additionally, this method simplifies the operations from repetitive trial and error. This study proposes a solution to convert non-uniform two-dimensional (2D) graph into a uniform one-dimensional (1D) matrix, which makes 2D graph data available for machine learning models. An automatic labeling platform is constructed that annotated over 22,000 groups of organic matter molecules and their NMR spectra. The results show that the carbon, hydrogen, and oxygen element prediction accuracy reach 96.1%, 94.8%, and 81.7%, respectively. In addition, the accuracy of the three kerogen types is approximately 90% in total. These results reflect the excellent performance of the machine learning method. Therefore, our work provides an automated and intelligent prediction and analysis method, which is a powerful and superior tool in kerogen studies at the molecular level.

Nitrogen-doped carbon nanotubes encapsulated Bi nanobuds for lithium based high-performance energy storage devices

Bi-based electrode materials with a high theoretical capacity of 3800 mAh cm−3 and low redox potential of Bi3+/Bi for lithium ion batteries (LIBs) have attracted great attention in energy storage materials. However, the complexity of the synthetic route, structural degradation and instability of the solid electrolyte interphase (SEI) caused by the huge volume change during charge-discharge process restricts its large-scale preparation and practical application, respectively. In this paper, the nitrogen doped carbon nanotubes (N-CNTs) optimal encapsulation Bi nanobuds (Bi@N-CNT) was constructed by a facile solvent grinding method and subsequent annealing reactions that addresses these issues. The one-dimensional encapsulation matrix of N-CNTs in the composites with a high conductivity, not only prevents the exfoliation of Bi nanoparticles and accommodates the volume changes, but also constructs a stable SEI during cycling. This Bi@N-CNT anode with large specific capacity of 452.5 mAh g−1 at 0.2 A g−1 after 100 cycles, unprecedented rate capability and prolonged cyclic life span (209.6 mAh g−1 at 3 A g−1 after 1000 cycles). This work provides a scalable, simple, and efficient evolutionary method for the production of Bi@N-CNT electrode materials, this composite can be used as a potential anode for LIBs, which has a certain enlightening significance for the preparation of other alloy-type anodes.

A Study of Chosen an Optimum Type of Wavelet Filter for De-Noising an ECG signal

Among various biological signals for the diagnosing of cardiac arrhythmia, Electrocardiographic (ECG) signal is the most significant one. The interesting challenge is an accurate analysis of the noisy ECG signal. Prior to accurate analysis, these signals need for de-noising to remove these unwanted noises in the signal to get an accurate diagnosis. In order to get the best de-noising results, it should have an accurate decision about the filters that we deal with for de-noising the signals. So, in this paper we present a study for choosing the optimum wavelet filter for de-noising the electrocardiograph (ECG) signal. Signals were stored as a one-dimensional matrix and series of procedure were performed to reduce the noise. The wavelets filters were chosen that very close to the original signal after applied a random-noises to the ECG signals to get familiar with the possible noise that can the signal affected with it. Also, estimation the most standard wavelet families namely Symlets, Coiflet, and Daubechies with different methods of threshold and decomposition levels were done. The purposes of this study to conclude the convenient wavelet functions in decomposition, the de-noising and the reconstruction, the method of the threshold, and the optimal decomposition level of the wavelet.

Ultrathin Magnesium Nanosheet for Improved Hydrogen Storage with Fishbone Shaped One-Dimensional Carbon Matrix

Hydrogen is regarded as an attractive substitute for fossil fuel, but stable and safe storage of hydrogen remains a formidable challenge. In this work, a nanometer-thickness Mg nanosheet is synthes...

Eigenvalues of Ising connection matrix with long-range interaction

We examine multidimensional Ising systems on hypercube lattices and calculate analytically the eigenvalues of their connection matrices. We express the eigenvalues in terms of spin–spin​ interaction constants and the eigenvalues of the one-dimensional Ising connection matrix (the latter are well known). To do this we present the eigenvectors as Kronecker products of the eigenvectors of the one-dimensional Ising connection matrix. For periodic boundary conditions, it is possible to obtain exact results for interactions with an arbitrary large number of neighboring spins. We present exact expressions for the eigenvalues for two- and three-dimensional Ising connection matrices accounting for the first five coordination spheres (that is interactions up to next-next-next-next nearest neighbors). In the case of free-boundary systems, we show that in the two and three dimensions the exact expressions could be obtained only if we account for interactions with spins of not more than first three coordination spheres.

Deep Learning for Interictal Epileptiform Spike Detection from scalp EEG frequency sub bands.

Epilepsy diagnosis through visual examination of interictal epileptiform discharges (IEDs) in scalp electroencephalogram (EEG) signals is a challenging problem. Deep learning methods can be an automated way to perform this task. In this work, we present a new approach based on convolutional neural network (CNN) to detect IEDs from EEGs automatically. The input to CNN is a combination of raw EEG and frequency sub-bands, namely delta, theta, alpha and, beta arranged as a vector for one-dimensional (1D) CNN or matrix for two-dimensional (2D) CNN. The proposed method is evaluated on 554 scalp EEGs. The database consists of 18,164 IEDs marked by two neurologists. Five-fold cross-validation was performed to assess the IED detectors. The resulting 1D CNN based IED detector with multiple sub-bands achieved a false positive rate per minute of 0.23 and a precision of 0.79 at 90% sensitivity. Further, the proposed system is evaluated on datasets from three other clinics, and the features extracted from CNN outputs could significantly discriminate (p-values <; 0.05) the EEGs with and without IEDs. We have proposed an optimized method with better performance than the literature that could aid clinicians to diagnose epilepsy expeditiously, and thereby devise proper treatment.

Пространственно-фазовая фокусировка излучателей матричного имитатора на две точки приема

This paper discusses the issues of constructing the configuration of a coherent matrix simulator for modeling echo signals of a two-position system. The condition is formulated in the form of a system of equations that the emitted signals are in-phase at both points of reception. A matrix satisfying this condition provides a simulation of a target in the same position for two spaced antennas. To ensure in-phase operation, it is proposed to use the possibilities of placing the radiators and controlling the initial phases of the signals. Relations are obtained for calculating the coordinates of the 2-point configuration and for calculating the phase addition value. Based on these relations, an algorithm for the synthesis of an extended one-dimensional matrix with the required angular size is developed. It is shown that the points of such a matrix can be located on one straight line. The obtained algorithm was used to synthesize a configuration of seven emitters for the given parameters of the two-position system. Using numerical experiments, the adequacy of the model was verified. Different positions of the point target were set, and a monopulse direction finder model was used to find its direction. The results of numerical experiments confirm the reliability of the theoretical results. They can be used in mathematical and simulation modeling of reflections from real radar targets for two-position systems.

Transfer-matrix theory of surface spin-echo experiments with molecules

${}^3$He beam spin-echo experiments have been used to study surface morphology, molecular and atomic surface diffusion, phonon dispersions, phason dispersions and phase transitions of ionic liquids. However, the interactions between ${}^3$He atoms and surfaces or their adsorbates are typically isotropic and weak. To overcome these limitations, one can use molecules instead of ${}^3$He in surface spin-echo experiments. The molecular degrees of freedom, such as rotation, may be exploited to provide additional insight into surfaces and the behaviour of their adsorbates. Indeed, a recent experiment has shown that $\textit{ortho}$-hydrogen can be used as a probe that is sensitive to the orientation of a Cu(115) surface [Godsi et al., Nat. Comm. $\textbf{8}$, 15357 (2017)]. However, the additional degrees of freedom offered by molecules also pose a theoretical challenge: a large manifold of molecular states and magnetic field-induced couplings between internal states. Here, we present a fully quantum mechanical approach to model molecular surface spin-echo experiments and connect the experimental signal to the elements of the time-independent molecule-surface scattering matrix. We present a one-dimensional transfer matrix method that includes the molecular hyperfine degrees of freedom and accounts for the spatial separation of the molecular wavepackets due to the magnetic control fields. We apply the method to the case of $\textit{ortho}$-hydrogen, show that the calculated experimental signal is sensitive to the scattering matrix elements, and perform a preliminary comparison to experiment. This work sets the stage for Bayesian optimization to determine the scattering matrix elements from experimental measurements and for a framework that describes molecular surface spin-echo experiments to study dynamic surfaces.

Critical dimension and negative specific heat in one-dimensional large- N reduced models

We investigate critical phenomena of the Yang-Mills (YM) type one-dimensional matrix model that is a large-$N$ reduction (or dimensional reduction) of the $D+1$ dimensional $U(N)$ pure YM theory (bosonic BFSS model). This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory. We study the matrix model at a three-loop calculation via the "principle of minimum sensitivity" and find that there is a critical dimension $D=35.5$: At $D \le 35$, the transition is of first order, while it is of second order at $D\ge 36$. Furthermore, we evaluate several observables in our method, and they nicely reproduce the existing Monte Carlo results. Through the gauge/gravity correspondence, the transition is expected to be related to a Gregory-Laflamme transition in gravity, and we argue that the existence of the critical dimension is qualitatively consistent with it. Besides, in the first order transition case, a stable phase having negative specific heat appears in the microcanonical ensemble, which is similar to Schwarzschild black holes. We study some properties of this phase.

Topological vacuum structure of the Schwinger model with matrix product states

We numerically study the single-flavor Schwinger model with a topological $\theta$-term, which is practically inaccessible by standard lattice Monte Carlo simulations due to the sign problem. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial $\theta$-dependence of several lattice and continuum quantities in the Hamiltonian formulation. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle $\theta$, thus respecting CP invariance, while lattice artifacts still depend on $\theta$. We also confirm that negative masses can be mapped to positive masses by shifting $\theta\rightarrow \theta +\pi$ due to the axial anomaly in the continuum, while lattice artifacts non-trivially distort this mapping. This mass regime is particularly interesting for the (3+1)-dimensional QCD analog of the Schwinger model, the sign problem of which requires the development and testing of new numerical techniques beyond the conventional Monte Carlo approach.