Arbitrary Form Research Articles

Upper bounds for the rank of powers of quadrics

We establish an upper bound for the rank of every power of an arbitrary quadratic form. Specifically, for any s∈N, we prove that the s-th power of a quadratic form of rank n grows as ns. Furthermore, we demonstrate that its rank is subgeneric for all n>(2s−1)2.

A New Method for Creating Structured High‐Performance Current Collectors for Electrochemical Applications

A significant challenge in many electrochemical systems is finding a stable, high‐performing current collector material that is mechanically robust, adaptable in form factor, and free of precious metals. Titanium electrodes are robust in many of these regards but exhibit poor charge transfer performance due to self‐passivation. Herein, a new materials processing paradigm based on the titanium/titanium nitride (Ti/TiN) system which allows for robust, stable, and low‐resistance current collectors of arbitrary form factor is presented. Specifically, a gas‐nitriding process for 3D‐printed titanium electrodes that results in a 20‐fold improvement of charge transfer characteristics relative to the untreated material is outlined. The ability to utilize 3D‐structured current collectors with a net 40‐fold improvement in performance over nonstructured electrodes is further demonstrated. This novel approach to creating electrochemical current collectors requires minimal laboratory resources and can be widely adapted for a variety of applications, including desalination, electrolysis, energy storage, and basic research. The work described herein provides both a means for accelerating research and opens the door to hierarchical tuneability for enhanced performance.

Pythagoreanism and Modern Models of Cosmology

Turning to the accumulated philosophical knowledge, the scientist almost always discovers that there are ideas in it which are far ahead of their time, but which can help in solving scientific problems of quite another historical epoch. In this respect one of the most revealing examples are associated with the discovery of heliocentrism and the General Theory of Relativity. Philosophical ideas and principles immanent in one or another particular science and serving for the solution of some problem of it form the very philosophical foundations of the given science. These, in turn, are by no means identical with the whole body of knowledge which philosophy creates. By reflecting on the foundations of science and turning to the analysis of its arbitrary forms – namely cosmology – philosophical reflection elaborates ideas and principles that can play an essential role in a certain stage of scientific inquiry.

Optical solitons, qualitative analysis, and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation

In this paper, we study the highly dispersive nonlinear perturbation Schrödinger equation, which has arbitrary form of Kudryashov's with sextic‐power law refractive index and generalized nonlocal laws. For the equation has highly dispersive nonlinear terms and higher order derivatives, it cannot be integrated directly, so we build an integrable factor equation for the approximated equation and apply the trial equation method and the complete discrimination system for polynomial method to create new soliton solutions. On the other hand, we use the bifurcation theory to qualitatively analyze the equation and find the model has periodic solutions, bell‐shaped soliton solutions, and solitary wave solutions via phase diagrams. The topological stability of the solutions with respect to the parameters is explored in order to better understand the effect of parameters perturbations on the stability of the model's solutions. Furthermore, we analyze the modulation instability and give the corresponding linear criterion. After accounting for external perturbation terms, we analyze the chaotic behaviors of the equation through the largest Lyapunov exponents and phase diagrams.

Nonlinear incompressible shear wave models in hyperelasticity and viscoelasticity frameworks, with applications to Love waves

General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves propagating on an interface between materials with different mechanical properties. The model is valid for a broad class of hyper-viscoelastic materials. For the Murnaghan constitutive model, shear wave equations contain cubic and quintic differential polynomial terms, including viscoelasticity contributions in terms of dispersion terms that include mixed derivatives uxxt of the material displacement. Full (2+1)-dimensional numerical simulations of waves propagating in the bulk of a two-layered solid are undertaken and analysed with respect to the source position and mechanical properties of the layers. Interfacial nonlinear Love waves and free upper surface shear waves are tracked; it is demonstrated that in the fully nonlinear case, the variable wave speed of interface and surface waves generally satisfies the linear Love wave existence condition c1<v<c2, while tending to the larger material wave speed c1 or c2 for large times.

Supramolecular Luminescent Copper-Nanocluster-Based Dough with Excellent Electrical Conductivity Sensing Properties.

In recent years, the rapid advancement of flexible conductive materials has significantly increased the demand for dough materials that offer high flexibility and conductivity for diverse applications. Here, we developed a flexible, stretchable, and self-healing dough utilizing hydrogen-bonding interactions between glutathione-stabilized copper nanoclusters (GSH-Cu NCs) and poly(acrylic acid) (PAA). The dough materials can be kneaded, readily reshaped, and further processed to create bulk materials of arbitrary form factors. The incorporation of PAA not only preserved the vibrant blue emission of GSH-Cu NCs but also enhanced their electrical conductivity and stretchability. The dough can be stretched up to 25 times its initial length and achieves complete self-healing in a short time. Moreover, the dough can automatically repair physical damage and return to its initial conductivity levels after healing. Surprisingly, the electrical conductivity of the dough can reach as high as 2.97 S/m, which is relatively superior compared to that of conventional conductive materials. This study presents a dough that serves as a highly sensitive strain sensor, capable of effectively monitoring human movement across a broad range of strains.

Perspective – Leveraging the Versatility of DNA Origami and Electrochemistry for New Sensing Modalities

Abstract Electrochemical biosensors are uniquely positioned to offer real-time in vivo molecular sensing due to their robustness to both biofluids and contaminants found in biofluids, and their adaptability for the detection of different analytes by their use of oligonucleotides or proteins as binding moiety. DNA Origami, the folding of a long DNA scaffold by hundreds of shorter oligonucleotide “staple” strands, allows the construction of nanoscale molecular objects of essentially arbitrary form, flexibility and functionality. We describe work at the intersection of these two fields and their – hopefully – bright future together.

Determination of hydrostatic pressure on the plane surface of an arbitrary non-simmetrical form by the three-command method K123

Competitive struggle in the conditions of wide access to unlimited amounts of information and computerization of all branches of production and services imposes strict requirements on specialized knowledge, practical skills and general mathematical culture of future engineers. The online program of modern multivariate engineering calculation of the problem of determining the force of hydrostatic pressure on an element of a flat asymmetric surface with a curvilinear face is presented - https://www.k123.org.ua/jeh5.html. Algorithms are implemented according to the author's method of three commands K123 (c) Yu.D. Kopanytsia (hereinafter the K123 method). A client-server solution based on CGI technology with a web form for inputting source data has been implemented. The results of the online calculation were performed according to the new analytical dependencies obtained on the basis of the author's method K123. In parallel, the numerical algorithms of the author's method of three K123 commands and the conclusions of the corresponding calculations in tabular form were implemented. Realized generation of graphics by the server program based on the coordinates of the points obtained by iterative calculations according to the algorithms of the numerical implementation of the K123 method. The relative error of iterative calculations and the estimation of the accuracy of the result are automatically determined based on the proposed exact analytical dependencies.

Investigations on Cylindrical Surrounding Double-Gate (CSDG) MOSFET using AlxGa1-xAs/InP: Pt with La2O3 oxide layer for fabrication.

The Cylindrical Surrounding Double-Gate MOSFET has been designed using Aluminium Gallium Arsenide in its arbitrary alloy form alongside Indium Phosphide with Lanthanum Dioxide as a high-ƙ dielectric material. The heterostructure based on the AlxGa1-xAs/InP: Pt has been used in the design and implementation of the MOSFET for RF applications. Platinum serves as the gate material, which has higher electronic immunity toward the Short Channel Effect and highlights semiconductor properties. The charge buildup is the main concern in the field of MOSFET design when two different materials are considered for fabrication. The usage of 2 Dimensional Electron Gas has been outstanding in recent years to help the electron buildup and charge carrier accumulation in the MOSFETs regime. Device simulation used for the smart integral systems is an electronic simulator that uses the physical robustness and the mathematical modeling of semiconductor heterostructures. In this research work, the fabrication method of Cylindrical Surrounding Double Gate MOSFET has been discussed and realized. The scaling down of the devices is essential to reduce the area of the chip and heat generation. By using these cylindrical structures, the area of contact with the circuit platform is reduced since the cylinder can be laid down horizontally. The coulomb scattering rate is observed to be 18.3 % lower than the drain terminal when compared to the source terminal. Also, at x = 0.125 nm, the rate is 23.9 %, which makes it the lowest along the length of the channel; at x = 1 nm, the rate is 1.4 % lesser than that of the drain terminal. A 1.4 A/mm2 high current density had been achieved in the channel of the device, which is significantly larger than comparable transistors. The conventional transistor occupies a larger area than the proposed cylindrical structures transistor and is also efficient in RF applications.

Data-driven contract design

We propose a prior-free model of incentive contracting in which the principal's beliefs about the agent's production technology are characterized by revealed preference data. The principal and the agent are each financially risk neutral and the agent's preferences are understood to be quasilinear in effort. Prior to contracting with the agent, the principal observes the output produced by a population of identical agents in best response to finitely many exogenously-specified contracts. She views any technology that rationalizes this data as plausible and evaluates contracts according to their guaranteed expected payoff against the set of all such technologies. This paper does four things. First, we characterize the set of technologies that are consistent with the revealed preference data. Second, we show that robustly optimal contracts are either empirical contracts or equity bonus contracts that supplement mixtures of contracts from the data with equity payments. Third, we provide conditions under which these optimal contracts append equity payments to only a single contract from the data. Fourth, and finally, we show that all of our results generalize without complication to a setting in which there might be arbitrary forms of unobserved heterogeneity within the population of agents.

Greedy Sidon sets for linear forms

The greedy Sidon set, also known as the Mian-Chowla sequence, is the lexicographically first set in N that does not contain x1,x2,y1,y2 with x1+x2=y1+y2. Its growth and structure have remained enigmatic for 80 years. In this work, we study a generalization from the form x1+x2 to arbitrary linear forms c1x1+…+chxh; these are called Sidon sets for linear forms. We explicitly describe the elements of the greedy Sidon sets for linear forms when ci=ni−1 for some n≥2, and also when h=2,c1=2,c2≥4, the “structured” domain. We also contrast the “enigmatic” domain when h=2,c1=2,c2=3 with the “structured” domain, and give upper bounds on the growth rates in both cases.

3D printing of customized Li-S microbatteries

Microbatteries serve as essential energy supply components in microelectronic, wearable and implantable devices. Despite recent efforts, developing lithium metal microbatteries with high energy densities and mechanical flexibility in structural design is still challenging, because of the poor interfacial stability and poor processability of lithium foil. Herein, we developed lithium-sulfur (Li-S) microbatteries with customized configurations using 3D printing techniques, which consist of a printable Li anode hosted within a graphene aerogel framework and a printable S cathode based on a carbon nanocages framework, featuring abundant porous structures and large specific surface areas. Consequently, the 3D-printed Li anode achieves over 900 hours of cycling with low overpotentials at an ultrahigh current density of 10 mA cm−2, and the 3D-printed S cathode delivers an ultrahigh capacity of 21.9 mAh cm−2 at the high thickness of 2.3 mm. Furthermore, the 3D-printed Li-S cell delivers an ultrahigh areal energy density of 48.4 mWh cm−2 at a high power density of 3.5 mW cm−2. The application potential of the 3D-printed customized Li-S microbatteries with arbitrary form factors is demonstrated by LED lighting and powering wearable sensor integration system, paving the way for their applications in miniaturized devices.

Temporal scaling theory for bursty time series with clusters of arbitrarily many events.

Long-term temporal correlations in time series in a form of an event sequence have been characterized using an autocorrelation function that often shows a power-law decaying behavior. Such scaling behavior has been mainly accounted for by the heavy-tailed distribution of interevent times, i.e., the time interval between two consecutive events. Yet, little is known about how correlations between consecutive interevent times systematically affect the decaying behavior of the autocorrelation function. Empirical distributions of the burst size, which is the number of events in a cluster of events occurring in a short time window, often show heavy tails, implying that arbitrarily many consecutive interevent times may be correlated with each other. In the present study, we propose a model for generating a time series with arbitrary functional forms of interevent time and burst size distributions. Then, we analytically derive the autocorrelation function for the model time series. In particular, by assuming that the interevent time and burst size are power-law distributed, we derive scaling relations between power-law exponents of the autocorrelation function decay, interevent time distribution, and burst size distribution. These analytical results are confirmed by numerical simulations. Our approach helps to rigorously and analytically understand the effects of correlations between arbitrarily many consecutive interevent times on the decaying behavior of the autocorrelation function.

Generalizing the moments method for primary neutron spectra

Motivated by recent experimental results Hartouni et al. (2023); Mannion et al. (2023) which identified the presence of non-Maxwellian ion velocity distributions in ICF plasmas, we revisit the moments method for analysing the shapes of primary neutron spectra emitted by plasmas undergoing thermonuclear burn. We assume that the ion distribution functions are of an arbitrary form and develop a set of “generalized” moments, that are ordered in terms of increasing powers of centre of mass velocity, but for which the effects of shifts of centre of mass velocity (equivalent to fluid velocity in the case of Maxwellian ion distributions) are suppressed. This set of generalized moments provides the most sensitive measure of relative velocity contributions to the shape of the neutron spectrum (an effect that has been colloquially referred to as “viso”). We also demonstrate that pairs of antipodal neutron spectral detectors are most suitable for measuring these contributions.

Generalizing electroosmotic-flow predictions over charge-modulated periodic topographies: tuneable far-field effects

The classical Helmholtz–Smoluchowski (HS) model of electroosmosis holds for homogeneously charged interfaces in contact with a fluid layer bearing an equal and opposite net charge. However, inhomogeneities in the surface charge and topography are inevitable, either as practical materials and fabrication artefacts, or at times as deliberately introduced modulations for flow control. In an effort to arrive at an analytically tractable theoretical framework for addressing the underlying electro-mechanical coupling, here, we generalize the traditional HS theory to an extent where both the surface charge and topographies may bear arbitrary and independent periodic forms. Using a spectral-asymptotic approach, we further arrive at closed-form expressions for describing the resulting electroosmotic pumping for topographic features with small characteristic amplitude to pattern period ratio, as relevant for most practical scenarios. We subsequently execute full-scale numerical simulations without any restrictions on the surface charge and topography variations to assess the efficacy of the theoretical framework. The corresponding test beds include distinctive signature patterns – for example, a square-wave surface charge distribution on trapezoidal pit topographies. Our results reveal that the charge–topography interplay induces an anisotropic flow drift, deviating from the classical HS paradigm. This, in turn, provides new quantitative insights into highly selective electroosmotic flow control via judicious design of the charge and topographical patterns, resulting in controllable accentuation, attenuation, nullification, deflection and even complete reversal of the flow. Our analysis further establishes a provision of estimating the zeta potentials of naturally ‘contaminated’ surfaces, as well as explaining the electrophoresis of large inhomogeneous particles; a paradigm that remained to be explored thus far.

Isotropy indices of Pfister multiples in characteristic 2

Let F be a field of characteristic 2, π an n-fold bilinear Pfister form over F and φ an arbitrary quadratic form over F. In this note, we investigate Witt index, defect, total isotropy index and higher isotropy indices of φ and π⊗φ and prove relations among the indices of these two forms over certain field extensions.

Dark energy and dark matter interaction: A nonlinear dynamical system study

This paper presents a methodical dynamical analysis of the Big Bang model, taking into account dark matter and an arbitrary form of dark energy. Nevertheless, why dynamic analysis? The primary advantage of the dynamical analysis approach is that it obviates the necessity to precisely solve the system for every individual dependent variable. Instead, it enables the prediction of the overall evolutions. In this regard, there are some powerful tools of non-dynamical systems (theorems, perturbation, etc.) which can help us a lot. The model under consideration is a nonlinear system with two dimensions (2D). In order to investigate this, we employ a sophisticated form of nonlinear dynamical systems theory in our research. We have delved into the full potential of nonlinear dynamical system theory known until now in our work. This analysis has produced very interesting solutions, which are in quite a contrast with the linear analysis approach. The stability of the system is considered at length, and the corresponding evolutions of the universe are also discussed consequently. A handful number of figures are given to visualize the behavior of the evolutions. The plots that are presented here are vector field plots and a new plotting technique initiated by us and used in our earlier papers. Interestingly, our work indicates the universe might resemble “phantom” evolution. Also, among the fixed points of our model, one is able to escape the singular situation called “Big Rip”.

Nonstationary random vibration analysis of hysteretic systems with fractional derivatives by FFT-based frequency domain method

Nonstationary random vibration problems of nonlinear fractional systems are challenging and drawing increasing attention. This study presents an efficient numerical method for the random vibration analysis of large-scale nonlinear fractional systems subjected to fully nonstationary excitations. Firstly, the fast Fourier transform (FFT)-based frequency domain method originally proposed for the nonstationary random vibration analysis of linear integer-order systems is extended to linear fractional systems, in which the explicit expression of dynamic responses of fractional systems is derived based on the load superposition principle and Newmark method. Secondly, an equivalent linearization analysis framework is constructed to solve the nonstationary responses of hysteretic systems with fractional derivatives, in which the nonstationary response analyses of equivalent linear systems are accomplished by the FFT-based frequency domain method. The presented method can account for nonstationary excitations with arbitrary forms of evolutionary power spectrum, even of the non-separable one. Two numerical examples are used to confirm its superior performance in terms of accuracy and computational efficiency.

Active Fault-Locating Scheme for Hybrid Distribution Line Based on Mutation of Aerial-Mode Injected Pulse

Due to the overlap of initial traveling wave signals, the traveling wave propagation process in hybrid distribution lines is complicated to analyze. The most significant challenge posed by the traditional passive traveling wave-locating method for hybrid distribution lines lies in identifying the fault section and distinguishing the reflected wave from the fault point or the hybrid connection points. Based on this approach, with the application of the aerial-mode component of the pulse signal generated at the fault point, a fault-section-identification and fault-locating scheme for hybrid distribution feeders with active pulse injection is proposed. When power in a line is cut after a single-to-line ground (SLG) fault occurs, the same pulse is injected into the three phases from the neutral point of the coupling capacitor bank to construct the zero-mode component, which propagates to the SLG fault three-phase asymmetrical point, producing an aerial-mode component that is reflected back to the first end of the line. With the application of the arrival time of an aerial-mode wavefront, it is simple to locate the SLG fault for arbitrary forms of hybrid lines. The simulation results confirm the feasibility of the fault-locating scheme under different feeders, different fault locations, and fault resistances. The results of the experiments confirm the high practical value of the proposed method.

Exploring Arbitrariness Objections to Time Biases

AbstractThere are two kinds of time bias: near bias and future bias. While philosophers typically hold that near bias is rationally impermissible, many hold that future bias is rationally permissible. Call this normative hybridism. According to arbitrariness objections, certain patterns of preference are rationally impermissible because they are arbitrary. While arbitrariness objections have been leveled against both near bias and future bias, the kind of arbitrariness in question has been different. In this article we investigate whether there are forms of arbitrariness that are common to both kinds of preferences and, hence, whether there are versions of the arbitrariness objection that are objections to both near bias and future bias. If there are, then this might go some way toward undermining normative hybridism and to defending thoroughgoing time-neutralism.