Complete Theory Research Articles

The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process

This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and irregular rhythms, not separating them, but complementing them within the framework of a single integrated model. The class of cyclically correlated random processes includes the subclass of cyclostationary (periodically) correlated random processes, which enable the use of a set of powerful methods of analysis and the forecasting of cyclic signals with a stable rhythm. Mathematical structures that model the cyclic, phase and rhythmic structures of a cyclically correlated random process are presented. The sufficient and necessary conditions that the structural function and the rhythm function of the cyclically correlated random process must satisfy have been established. The advantages of the cyclically correlated random process in comparison with other mathematical models of cyclic signals with a variable rhythm are given. The obtained results contribute to the emergence of a more complete and rigorous theory of this class of random processes and increase the validity of the methods of their analysis and computer simulation.

Precise Evolutionary Asteroseismology of High-Amplitude δ Scuti Star AE Ursae Majoris

Stellar structure and evolution theory is one of the bases in modern astronomy. Stellar inner structures and their evolutionary states can be precisely tested by asteroseismology, since the inner information is brought to the stellar surface by the global oscillating waves and becomes observable. For stellar evolutionary speed (i.e., how long timescale does a star stay at a special evolution phase?), because of the insurmountable gap between the timescales of the evolutionary history of human civilization and a star, it can only be roughly tested by ensemble of stars in different evolutionary stages in most cases, and all the snapshots of these stars make up our global view of stellar evolution. The effect of stellar evolution on the structure and the corresponding global size of a pulsating star will lead to tiny period variations of its pulsation modes, which are the most valuable indicators of its evolutionary state and can be used to test the stellar evolution theory by a single star rather than ensemble of stars. Here, we report a High-Amplitude δ Scuti star AE Ursae Majoris, which is located in the post main-sequence (MS) evolutionary stage and its observed linear period variation rate can be practically ascribed to its evolutionary effect. The result tests the stellar evolution theory from the pre-MS to post-MS with an unprecedented precision by a single star, and the framework can be extended to other type of pulsating stars to perform precise evolutionary asteroseismology, which aims to test the current stellar evolution theory in different evolutionary stages, discover the discrepancies between the theory and observations, and ultimately build a complete and precise stellar evolution theory to backtrack the history of each of these stars.

Spectrally accurate numerical quadrature formulas for a class of periodic Hadamard Finite Part integrals by regularization

We consider the numerical computation of Hadamard Finite Part (HFP) integralsKm(t;u)=⨎0TSm(π(x−t)T)u(x)dx,0<t<T,m∈{1,2,…}, where u(x) is T-periodic and sufficiently differentiable andS2r−1(y)=cos⁡ysin2r−1⁡y,S2r(y)=1sin2r⁡y,r=1,2,3,…. For each m, we regularize the HFP integral Km(t;u) and show thatKm(t;u)=K0(t;Um)≡∫0T(log⁡|sin⁡π(x−t)T|)Um(x)dx,Um(x) being some linear combination of the first m derivatives of u(x). We then propose to approximate Km(t;u) by the quadrature formula Qm,n(t;u)≡Km(t;ϕn), where ϕn(x) is the nth-order balanced trigonometric polynomial that interpolates u(x) on [0,T] at the 2n equidistant points xn,k=kT2n, k=0,1,…,2n−1. The implementation of Qm,n(t;u) is simple, the only input needed for this being the 2n function values u(xn,k), k=0,1,…,2n−1. Using Fourier analysis techniques, we develop a complete convergence theory for Qm,n(t;u) as n→∞ and prove that it enjoys spectral convergence when u∈C∞(R). We illustrate the effectiveness of Qm,n(t;u) with numerical examples for m=0,1,…,5.We also show that the HFP integral ⨎0Tf(x,t)dx of any T-periodic integrand f(x,t) that has mth order poles at x=t+kT, k=0,±1,±2,…, but is sufficiently differentiable in x on R∖{t±kT}k=0∞, can be expressed in terms of the Ks(t;u(⋅,t)), where u(x,t) is a T-periodic and sufficiently differentiable function in x on R that can be computed from f(x,t). Therefore, ⨎0Tf(x,t)dx can be computed efficiently using our new numerical quadrature formulas Qs,n(t;u(⋅,t)) on the individual Ks(t;u(⋅,t)). Again, only 2n function evaluations, namely, u(xn,k,t), k=0,1,…,2n−1, are needed for the whole process.

Integrating out beyond tree level and relativistic superfluids

We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the U(1) Goldstone low-energy effective theory that describes the spontaneously broken phase of a ϕ4 theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) ϕ4. We perform the same analysis for a renormalizable scalar SO(N) theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original SO(N) symmetry.

Research on Lane Changing Game and Behavioral Decision Making Based on Driving Styles and Micro-Interaction Behaviors.

Autonomous driving technology plays an essential role in reducing road traffic accidents and ensuring more convenience while driving, so it has been widely studied in industrial and academic communities. The lane-changing decision-making process is challenging but critical for ensuring autonomous vehicles’ (AVs) safe and smooth maneuvering. This paper presents a closed-loop lane-changing behavioral decision-making framework suitable for AVs in fully autonomous driving environments to achieve both safety and high efficiency. The framework is based on a complete information non-cooperative game theory. Moreover, we attempt to introduce human driver-specific driving styles (reflected by aggressiveness types) and micro-interaction behaviors for both sides of the game in this model, enabling users to understand, adapt, and utilize intelligent lane-changing techniques. Additionally, a model predictive control controller based on the host-vehicle (HV) driving risk field (DRF) is proposed. The controller’s optimizer is used to find the optimal path with the lowest driving risk by using its optimizer and simultaneously adjusting its control variables to track the path. The method can synchronize path planning and motion control and provide real-time vehicle state feedback to the decision-making module. Simulations in several typical traffic scenarios demonstrate the effectiveness of the proposed method.

Multiconfiguration Pair-Density Functional Theory for Chromium(IV) Molecular Qubits.

Pseudotetrahedral organometallic complexes containing chromium(IV) and aryl ligands have been experimentally identified as promising molecular qubit candidates. Here we present a computational protocol based on multiconfiguration pair-density functional theory for computing singlet–triplet gaps and zero-field splitting (ZFS) parameters in Cr(IV) aryl complexes. We find that two multireference methods, multistate complete active space second-order perturbation theory (MS-CASPT2) and hybrid multistate pair-density functional theory (HMS-PDFT), perform better than Kohn–Sham density functional theory for singlet–triplet gaps. Despite the very small values of the ZFS parameters, both multireference methods performed qualitatively well. MS-CASPT2 and HMS-PDFT performed particularly well for predicting the trend in the ratio of the rhombic and axial ZFS parameters, |E/D|. We have also investigated the dependence and sensitivity of the calculated ZFS parameters on the active space and the molecular geometry. The methodologies outlined here can guide future prediction of ZFS parameters in molecular qubit candidates.

Ramanujan Fourier Mode Decomposition and Its Application in Gear Fault Diagnosis

As an important part of rotating machinery, gear is easy to appear some unexpected fault states, and its fault diagnosis is very important. Fourier decomposition method (FDM) is a common method for gear fault diagnosis, but the noise robustness, period recognition, and extraction capabilities of FDM are unsatisfactory. Based on this, in this article, Ramanujan Fourier mode decomposition (RFMD) method is proposed. The RFMD not only has a complete mathematical theory foundation but also has an excellent ability to identify and extract periodic components. Emulational and experimental results of planetary gearbox show that the RFMD method has good noise robustness and can accurately extract gear fault characteristic information. Thus, it is an effective gear fault diagnosis method.

Stratagems and the Byzantine culture of war: the theory of military trickery and ethics in Byzantium (c. 900–1204)

Abstract Although there has been significant scholarly attention on just war (jus ad bellum) in Byzantium and an increasing interest in the study of the Byzantine culture of war, military trickery and jus in bello (just conduct of war) remain largely unexplored by Byzantinists. This paper aims to fill this gap by studying the theory of military trickery and ethics in Byzantium, c. 900 -1204. It explores and analyses this aspect of jus in bello in Byzantium by employing methods and concepts from Byzantine history, war studies and military ethics. The paper begins by examining the impact of dominant literary traditions (Classical and Biblical) on Byzantine perceptions of military trickery, and then explores the reception and development of Classical and Biblical notions of military trickery and ethics by different sub-cultures in Byzantium (e. g., theologians, jurists, tacticians, historians, orators, poets). The author then attempts to frame a more complete theory of Byzantine military trickery and ethics, and to reflect on the relationship between jus ad bellum and jus in bello in Byzantium.

Multireference Study of Optically Addressable Vanadium-Based Molecular Qubit Candidates.

Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound's viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here, we study a previously identified optically addressable molecular qubit, (C6F5)3trenVCNtBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods: complete active space second-order perturbation theory (CASPT2), multiconfiguration pair-density functional theory (MC-PDFT), and hybrid MC-PDFT (HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V3+ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.

Idealizations and ideal policing

Political philosophy often focuses on “major institutions” that make up the “basic structure” of society. These include political, economic, and social institutions. In this paper I argue first that policing plays a substantial role in generating the kinds of inequalities and problems that are concerns of social or structural justice, and therefore that police agencies qualify as a major institution. When we abandon full compliance or similar idealizations, it is clear that policing is not a concern secondary to, e.g., the electoral system or the scheme of property rights in a society. Nor, I argue, does maintaining full compliance or moral character idealizations obviate an active enforcement role. Eliminating that role from an idealized model society requires engaging in a methodologically and substantively unattractive amount of abstraction. The result is that an active enforcement role is at the core of a complete theory of justice rather than something that is significant only “downstream” from more fundamental issues.

Flavor hierarchies, flavor anomalies, and Higgs mass from a warped extra dimension

The recent B-meson anomalies are coherently explained at the TeV scale by 4321 gauge models with hierarchical couplings reminiscent of the Standard Model Yukawas. We show that such models arise as the low-energy limit of a complete theory of flavor, based on a warped fifth dimension where each Standard Model family is quasi-localized on a different brane. The Higgs is identified as a pseudo-Nambu-Goldstone boson emerging from the same dynamics responsible for 4321 symmetry breaking. This novel construction unifies quarks and leptons in a flavor non-universal manner, provides a natural description of flavor hierarchies, and addresses the electroweak hierarchy problem.

Extension of natural reaction orbital approach to multiconfigurational wavefunctions.

Recently, we proposed a new orbital analysis method, natural reaction orbital (NRO), which automatically extracts orbital pairs that characterize electron transfer in reaction processes by singular value decomposition of the first-order orbital response matrix to the nuclear coordinate displacements [Ebisawa et al., Phys. Chem. Chem. Phys. 24, 3532 (2022)]. NRO analysis along the intrinsic reaction coordinate (IRC) for several typical chemical reactions demonstrated that electron transfer occurs mainly in the vicinity of transition states and in regions where the energy profile along the IRC shows shoulder features, allowing the reaction mechanism to be explained in terms of electron motion. However, its application has been limited to single configuration theories such as Hartree-Fock theory and density functional theory. In this work, the concept of NRO is extended to multiconfigurational wavefunctions and formulated as the multiconfiguration NRO (MC-NRO). The MC-NRO method is applicable to various types of electronic structure theories, including multiconfigurational theory and linear response theory, and is expected to be a practical tool for extracting the essential qualitative features of a broad range of chemical reactions, including covalent bond dissociation and chemical reactions in electronically excited states. In this paper, we calculate the IRC for five basic chemical reaction processes at the level of the complete active space self-consistent field theory and discuss the phenomenon of electron transfer by performing MC-NRO analysis along each IRC. Finally, issues and future prospects of the MC-NRO method are discussed.

Resolving Ultrafast Photoinitiated Dynamics of the Hachimoji 5-aza-7-deazaguanine Nucleobase: Impact of Synthetically Expanding the Genetic Alphabet†.

The guanine derivative, 5-aza-7-deazaguanine (5N7C G) has recently been proposed as one of four unnatural bases, termed Hachimoji (8-letter) to expand the genetic code. We apply steady-state and time-resolved spectroscopy to investigate its electronic relaxation mechanism and probe the effect of atom substitution on the relaxation mechanism in polar protic and polar aprotic solvents. Mapping of the excited state potential energy surfaces is performed, from which the critical points are optimized by using the state-of-art extended multi-state complete active space second-order perturbation theory. It is demonstrated that excitation to the lowest energy 1 ππ* state of 5N7C G results in complex dynamics leading to ca. 10- to 30-fold slower relaxation (depending on solvent) compared with guanine. A significant conformational change occurs at the S1 minimum, resulting in a 10-fold greater fluorescence quantum yield compared with guanine. The fluorescence quantum yield and S1 decay lifetime increase going from water to acetonitrile to propanol. The solvent-dependent results are supported by the quantum chemical calculations showing an increase in the energy barrier between the S1 minimum and the S1 /S0 conical intersection going from water to propanol. The longer lifetimes might make 5N7C G more photochemically active to adjacent nucleobases than guanine or other nucleobases within DNA.

Generalized partially coherent power-exponent-phase vortex beams

We propose a generalized partially coherent power-exponent-phase vortex beam, and study its generation and propagation characteristics in space-frequency domain. A complete transmission theory suitable for all generalized power-exponent-phase vortex beams is established and then demonstrated by experiments. The results show that generalized partially coherent power-exponent-phase vortex beams have their own characteristics in fan-shaped intensity distribution, intensity distribution of main lobes and side lobes and phase singularities. By combining theory and experiments, we summarize these characteristics, and put forward some potential application prospects.

Radiative effects in the scalar sector of vector leptoquark models

Gauge models with massive vector leptoquarks at the TeV scale provide a successful framework for addressing the B-physics anomalies. Among them, the 4321 model has been considered as the low-energy limit of some complete theories of flavor. In this work, we study the renormalization group evolution of this model, laying particular emphasis on the scalar sector. We find that, despite the asymptotic freedom of the gauge couplings, Landau poles can arise at relatively low scales due to the fast running of quartic couplings. Moreover, we discuss the possibility of radiative electroweak symmetry breaking and characterize the fine-tuning associated with the hierarchy between the electroweak scale and the additional TeV-scale scalars. Finally, the idea of scalar fields unification is explored, motivated by ultraviolet embeddings of the 4321 model.

Laminar flow in channels with porous walls: advancing the existence, uniqueness and approximation of solutions via fixed point approaches

The purpose of this work is to develop a more complete theory regarding solutions to the problem of laminar flow in channels with porous walls. We establish new knowledge regarding the qualitative and quantitative properties of solutions to a fourth order boundary value problem under consideration. In contrast to the previous literature, our strategy involves establishing new a priori bounds on solutions and draws on contractive mapping principles. This enables a deeper understanding of the problem by strategically addressing the questions of existence, uniqueness and approximation of solutions under one integrated framework, rather than applying somewhat disjointed approaches. Through this strategy, we advance current knowledge by extending the range of values of the Reynolds number under which the problem will admit a unique solution; and we furnish a sequence of functions whose limit converges to this solution, enabling an iterative approximation to any theoretical degree of accuracy.

Constraints on multifield inflation from the BOSS galaxy survey

We use redshift-space galaxy clustering data from the BOSS survey to constrain local primordial non-Gaussianity (LPNG). This is of particular importance due to the consistency relations, which imply that a detection of LPNG would rule out all single-field inflationary models. Our constraints are based on the consistently analyzed redshift-space galaxy power spectra and bispectra, extracted from the public BOSS data with optimal window-free estimators. We use a complete perturbation theory model including all one-loop power spectrum corrections generated by LPNG. Our constraint on the amplitude of the local non-Gaussian shape is $f_{\rm NL}^{\rm local}=-33\pm 28$ at 68\%\,CL, yielding no evidence for primordial non-Gaussianity. The addition of the bispectrum tightens the $f_{\rm NL}^{\rm local}$ constraints from BOSS by $20\%$, and allows breaking of degeneracies with non-Gaussian galaxy bias. These results set the stage for the analysis of future surveys, whose larger volumes will yield significantly tighter constraints on LPNG.

Spiral-Transform-Based Fractal Sorting Matrix for Chaotic Image Encryption

Chaotic image encryption is widely used in the field of information security. This paper proposes a novel chaotic image encryption method with spiral-transform-based fractal sorting matrix (STFSM). First of all, the theory of STFSM with good scrambling effect is introduced, which has good irregularity and iterative. Then, the iterative algorithm and calculation example of STFSM are introduced. STFSM can be used as the map of spatial location transformations to implement the design of image encryption. Based on the complete STFSM theory and iterative algorithm, a chaotic image cryptosystem based on STFSM is proposed to achieve a good image encryption process. To test the security of the proposed algorithm, security tests and analyses such as entropy analysis, correlation analysis, resistance to differential attacks analysis, and robustness analysis are used for the proposed algorithm. The experimental analysis illustrates that the algorithm has a better encryption effect, whether using conventional tests or the attacks simulations described in this paper and can also effectively resist the attacks.

Dynamics of eddying abyssal mixing layers over sloping rough topography

Abstract ABSTRACT: The abyssal overturning circulation is thought to be primarily driven by small-scale turbulent mixing. Diagnosed watermass transformations are dominated by rough topography “hotspots”, where the bottom-enhancement of mixing causes the diffusive buoyancy flux to diverge, driving widespread downwelling in the interior—only to be overwhelmed by an even stronger up-welling in a thin Bottom Boundary Layer (BBL). These watermass transformations are significantly underestimated by one-dimensional (1D) sloping boundary layer solutions, suggesting the importance of three-dimensional physics. Here, we use a hierarchy of models to generalize this 1D boundary layer approach to three-dimensional eddying flows over realistically rough topography. When applied to the Mid-Atlantic Ridge in the Brazil Basin, the idealized simulation results are roughly consistent with available observations. Integral buoyancy budgets isolate the physical processes that contribute to realistically strong BBL upwelling. The downwards diffusion of buoyancy is primarily balanced by upwelling along the sloping canyon sidewalls and the surrounding abyssal hills. These flows are strengthened by the restratifying effects of submesoscale baroclinic eddies and by the blocking of along-ridge thermal wind within the canyon. Major topographic sills block along-thalweg flows from restratifying the canyon trough, resulting in the continual erosion of the trough’s stratification. We propose simple modifications to the 1D boundary layer model which approximate each of these three-dimensional effects. These results provide local dynamical insights into mixing-driven abyssal overturning, but a complete theory will also require the non-local coupling to the basin-scale circulation.

M-Theory and F-Theory over Theoretical Analysis on Cosmic Strings and Calabi-Yau Manifolds Subject to Conifold Singularity with Randall-Sundrum Model

String theory always comes with heavy mathematical rigor as it questions the most significant and impossible attempt to make a scale-invariant phenomenology between general relativity and quantum theory. Thus, steps have been taken to simplify the theory a bit thereby making it accessible to general yet enthusiastic readers of physics. However, as there is numerous mathematics involved in the modeling of this theory, thus, any chance to make a purely non-mathematical approach towards strings would prove vacuous and intimidating making the pathway of this marvelous theory chocked with unnecessary assumptions resulting in false analogies (or hopes) relating to this theory. Thus, where it’s almost impossible to proceed without any equations, we have given a few just to wipe out some logical confusion arising to the first readers of strings. Few necessary diagrams are included along with intense theory and least mathematics for making this significant approach of theoretical physicists accessible to general learners or readers.&#x0D; Topics: Bosonic string theory, supersymmetric string theory, M – theory, F – theory, dualities and interconnectedness, viability, Randall – Sundrum model for tackling the hierarchy problem of particle physics, conifold singularities, Branes, Bulks, Extremal black holes, Ekpyrotic cosmology, topological aspects of Calabi – Yau (CY) manifolds, A and B models, Mirror Symmetries; AdS/CFT, cosmic strings, all in a way accessible to every reader.&#x0D; Methods: Theoretical analogies, deductions, principles behind the origin, development along with the probable conclusion of this theory, the roots of its origin, the necessary difficulty for detecting those strings, and approaches done by theorists to work out the pathway of achieving Einstein’s dream of unification irrespective of several hindrances.&#x0D; Results: String theory itself is not a complete theory. Rather it’s in the process of further development through the increment of time resulting in more applications of mathematics by developing or incorporating them in due needs. Thus, without stating any concrete results, the theory has been tackled in this paper with a viable hypothesis based on the current understanding, and previous attempts are stated to have been made for its success.