One-dimensional Objects Research Articles

Hadron-quark hybrid model, modular transformation, and Roberge-Weiss transition

In the framework of modular transformations, we reformulate the recently proposed hadron-quark hybrid model when the imaginary baryonic chemical potential is introduced. In this case, the number density of the hybrid model is obtained by the modular transformation of the complex number densities of the baryons (antibaryons) and the quarks (antiquarks). We can regard these number densities as the basis in the complex plane. As a result, we can consider the torus, which is characterized by the basis. Since the complex structure of the torus is invariant under the modular transformation, we can extract the topological property of the hadron-quark system using the untransformed baryon (antibaryon) and the quark (antiquark) number densities. We apply this model to analyze the Roberge-Weiss transition. It is shown that the torus vanishes at the baryonic chemical potential where the Roberge-Weiss transition appears because the number density of baryons (antibaryons) is not linearly independent of the number density of quarks (antiquarks). When the temperature T is lower than the Roberge-Weiss transition temperature TRW, the torus shrinks smoothly to the one-dimensional object at the Roberge-Weiss transition point, but the discontinuity does not appear. On the other hand, the discontinuity of the geometrical object appears when T>TRW. We also calculate the modulus of the torus and transform it into the fundamental region. The transformed moduli are symmetric below TRW, but the symmetry is broken above TRW. Published by the American Physical Society 2025

Phase Retrieval of One-Dimensional Objects by the Multiple-Plane Gerchberg–Saxton Algorithm Implemented into a Digital Signal Processor

In the current study, we address the phase retrieval of one-dimensional phase objects from near-field diffraction patterns using the multiple-plane Gerchberg–Saxton algorithm, which is still widely used for phase retrieval. The algorithm was implemented in a low-cost digital signal processor capable of fast Fourier transform using Q15 arithmetic, which is used by the previously mentioned algorithm. We demonstrate similarity between one-dimensional phase objects, i.e., vectors cut out of a phase map of the tertiary spherical aberration retrieved by the multiple-plane Gerchberg–Saxton algorithm, and these vectors are measured with a non-contact profiler. The tertiary spherical aberration was induced by a phase plate fabricated using grayscale lithography. After subtracting the vectors retrieved by the algorithm from those measured with the profiler, the root mean square error decreased, while a corresponding increase in the Strehl ratio was observed. A single vector of size 64 pixels was retrieved in about 2 min. The results suggest that digital signal processors that are capable of one-dimensional FFT and fixed-point arithmetic in Q15 format can successfully retrieve the phase of one-dimensional objects, and they can be used for applications that do not require real-time operation, i.e., analyzing the quality of cylindrical micro-optics.

Decomposition squared

In this paper, we test and extend a proposal of Gu, Pei, and Zhang for an application of decomposition to three-dimensional theories with one-form symmetries and to quantum K theory. The theories themselves do not decompose, but, OPEs of parallel one-dimensional objects (such as Wilson lines) and dimensional reductions to two dimensions do decompose, sometimes in two independent ways. We apply this to extend conjectures for quantum K theory rings of gerbes (realized by three-dimensional gauge theories with one-form symmetries) via both orbifold partition functions and gauged linear sigma models.

SPEAKING BODIES, VISIBLE VOICES: NARRATIVE TENSION IN COPPOLA’S APOCALYPSE NOW: REDUX (2001)

Francis Ford Coppola’s Apocalypse Now: Redux (2001), a 2001 re-release of his 1979 Vietnam War epic, sparked significant discussions among both academic scholars and mainstream media. The extended version, which features almost an hour-long addition of new scenes, challenged the question of the film’s continued relevance within the evolving Hollywood industry. While the original version may have highlighted the horror and dehumanization of the Vietnam War, it was also criticized for depicting women as one-dimensional sexual objects and effectively silencing their voices. However, by utilizing Verstraten’s notion of filmic narrative, Mulvey’s visual pleasure, and Stark’s narrative voicelessness, this research aims to show how narrative tension is displayed in Apocalypse Now: Redux and how it highlights the representation of the female characters’ subjectivity. We argue that the Redux version offers a notable difference from the stereotypical portrayal of women in war film. By incorporating the newly added scenes, Apocalypse Now: Redux provides the female characters with more agency and individuality, allowing them to move beyond the limitation of being mere decorations.

Dynamic modeling of a sliding ring on an elastic rod with incremental potential formulation

Abstract Mechanical interactions between rigid rings and flexible cables find broad application in both daily life (hanging clothes) and engineering system (closing a tether-net). A reduced-order method for the dynamic analysis of sliding rings on a deformable one-dimensional (1D) rod-like object is proposed. In contrast to the conventional approach of discretising joint rings into multiple nodes and edges for contact detection and numerical simulation, a single point is used to reduce the order of the model. To ensure that the sliding ring and flexible rod do not deviate from their desired positions, a new barrier function is formulated using the incremental potential theory. Subsequently, the interaction between tangent frictional forces is obtained through a delayed dissipative approach. The proposed barrier functional and the associated frictional functional are C2 continuous, hence the nonlinear elastodynamic system can be solved variationally by an implicit time-stepping scheme. The numerical framework is initially applied to simple examples where the analytical solutions are available for validation. Then, multiple complex practical engineering examples are considered to showcase the effectiveness of the proposed method. The simplified ring-to-rod interaction model has the capacity to enhance the realism of visual effects in image animations, while simultaneously facilitating the optimisation of designs for space debris removal systems.

Design of Optimal Control Systems in the Frequency Domain by the Functional of the Generalized Work

The paper considers the problem of analytical design of optimal controllers (ADOC) for one-dimensional linear stationary objects according to the functional of generalized work (FGW) A. A. Krasovsky. The use of FGW in comparison with the quadratic performance functional greatly simplifies the calculation of the optimal controller — the calculation of its matrix of coefficients mainly consists in solving the linear matrix Lyapunov equation, which, in contrast to the nonlinear matrix Riccati equation, fundamentally reduces the amount of calculations. In addition, the use of FGW provides the best stability margins of the designed system in terms of amplitude and phase. This work is devoted to the development of a method for solving the ADOC problem A. A. Krasovsky in the frequency (complex) domain, which reduces the determination of the transfer function coefficients of the optimal controller for an object of order n to the solution of the corresponding system of n linear algebraic equations. In this regard, the proposed method for solving the ADOC problem by A. A. Krasovsky differs by a much smaller amount of calculations in comparison with the standard method, in which the Lyapunov equation is solved with the desired matrix of dimensions n * n. The proposed method for the synthesis of optimal control systems, which has an analytical nature, became the basis for solving the inverse problem ADOC A. A. Krasovsky, which consists in determining the values of the weight coefficients of the FGW, which provide the given primary quality indicators of the synthesized control system. Using its relations, a relatively simple method for calculating the FGW coefficients based on the given values of the error coefficients for the designed dynamic system has been developed.

Effective brane field theory with higher-form symmetry

We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

Метод проверки робастного качества управления для линейных одномерных дискретных систем управления

The article deals with one-dimensional linear control objects in discrete time. It is assumed that the operators of the control object have structural and parametric inaccuracies in the description. In this paper, a criterion for the robust quality of control is obtained for a system consisting of a discrete control object with structural perturbations and a modal controller. Based on this criterion, a numerical method for checking the robust quality of control has been developed. The effectiveness of the method is illustrated by an example.

Deep Photometry of Suspected Gravitational Lensing Events: Potential Detection of a Cosmic String

Cosmic strings (CS) are one-dimensional cosmological-size objects predicted in realistic models of the early Universe. Analysis of the cosmic microwave background (CMB) anisotropy data from the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck surveys revealed several CS candidates. One of the candidates, CSc-1, was found to be most reliable because of the statistically significant chains of gravitational lensing (GL) candidates in its field. We observed the brightest of the objects in the CSc-1 field, a galaxy pair SDSSJ110429.61+233150.3. The significant correlation between the spectra of the two components indicates the possible GL nature of the pair. Our simulations of observational data in the CSc-1 field shows that a large number of pairs can be explained by the complex geometry of the CS. Simulations of the SDSSJ110429 galaxy pair has shown that the observed angle between the components of the pair can be explained if the CS is strongly inclined and, possibly, bent in the image plane. In our preliminary data, we also detected the sign of the sharp isophotal edge in one image, which along with CMB and spectral data strongly suggests the possibility of a CS detection.

Programming of one-dimansional and two-dimensional tokens for tokenization of land plots

The use of blockchain tools that allows spliting virtual objects into parts is considered. Examples of practical use of the developed algorithms are presented. The concept of one-dimensional and two-dimensional tokens representing one-dimensional and flat objects is proposed. Algorithms for the implementation of one-dimensional tokens are developed, and the peculiarities of their practical application are considered. A designed smart contract allows to conduct a basic list of operations with one-dimensional tokens. Algorithms, providing implementation of two-dimensional tokens, are proposed. Peculiarities of presenting territories of virtual worlds and land plots are suggested. A comparative analysis of the use of NFT and two-dimensional tokens for presenting the Earth surface areas is performed. Methods that ensure ownership of tokens at different levels are proposed.

One-dimensional packaging with method of modified ant colony

The study explores the use of the ant algorithm for solving one-dimensional packing problems. It discusses the structure of the decision search graph, the search process on the graph, methods of pheromone deposition and evaporation. The study employs a cyclic method of ant systems. A new strategy for finding effective solutions is proposed based on modification and hybridization of the canonical representations of the particle swarm algorithm. The paradigm of a swarm of transforming chromosomes is described, which provides the ability to represent solutions in the affine space of chromosomes with integer parameter values. The mechanisms of chromosome transformation in the affine space to increase the weight of affine bonds are considered. Experimental research was conducted on an IBM PC, showing improved results compared to existing algorithms. The proposed approach can be useful for solving packaging problems and optimizing the distribution of one-dimensional objects.

Optimization of source parameters in dynamic network structure objects

The optimization of parameters for concentrated sources that influence the operation of a dynamic network structure is the focus of this study. The network structure comprises numerous one-dimensional objects, each governed by a system of ordinary differential equations with nonlocal boundary conditions to describe their states. Sources affect individual points within these subobjects, as well as their connection points. The optimization process aims to determine the optimal locations and power levels of these sources, based on predefined target functionality criteria. We derive the necessary optimality conditions for the concentrated sources' parameters and present the results of numerical experiments using a test problem as an illustrative example.

The 5th Dimension and its Implications for the String Theory, Conservation of Energy and Heisenberg Uncertainty Principle

In 1919, the mathematician Theodor Kaluza began to play around with Albert Einstein’s formulas for gravity. Out of curiosity, he reworked the equations to see how they‘d look in five, rather than four, dimensions. The exercise yielded an extra set of equations, which were the same as James Clerk Maxwell’s equations for the electromagnetic field. His idea of a fifth dimension had produced a mathematical unification of gravity and electromagnetism. Since Kaluza’s calculations yielded an extra set of equations with Einstein’s formulas for gravity, it’s logical to assume that extending the number of known dimensions to five might also extend E = mc2. This article also visits conservation of mass and energy / mass-energy equivalence, Electromagnetism, Dark Matter, Dark Energy, the Matrix, Antigravitons, Incompleteness Theorems, New Irrationals, Calculus, Celluloid Motion, and Vector-Tensor-Scalar Geometry. And as the text accompanying Figure 5 says, “The counterclockwise rotation does not have to encompass 360 degrees. It can be divided into single degrees – and even arcseconds which are 3,600 times smaller than a degree. Each arcsecond (or tiny part of it) could correspond to a separate dimension and the total dimensions might make up a temporal multiverse that’s reminiscent of string theory, the cosmological framework that says particles are composed of one-dimensional objects called strings (a group of binary digits is called a single-dimensional bit string).” Finally, Heisenberg’s Principle of Indeterminacy - in which the position and the velocity of a particle cannot both be measured exactly, at the same time, even in theory - is revised. Quantum uncertainty is changed into quantum certainty by software containing a new type of irrational number – actually, irrational equations - that’s based on mathematics’ Matrix and topology’s Mobius strip, as well as being interdimensional. Ludwig Wittgenstein, an Austrian-British philosopher, once stated, "The limits of my language mean the limits of my world." Wittgenstein proposed that our understanding of the world is shaped by the language we use to describe it. This concept extends to mathematics, which can be seen as a specialized language. So if a person has no doubt that 1 + 1 = 2, he or she can never arrive at a truly Unified Theory in which only one thing exists. The maths accepted in 2023 is indispensable in enabling advancements in technology and science that have transformed our lives but is incapable of fully describing Unification. Scientific history has shown that it can go partway. Scientists consequently assume it will eventually go all the way.

АНАЛІЗ ПРУЖНИХ ХВИЛЕУТВОРЕНЬ У КАНАТАХ ВАНТАЖОПІДЙОМНИХ КРАНІВ

In the article the boundary value problem on the elastic longitudinal waves motion in the load lifting cranes and mine mechanisms variable length ropes is considered. Solutions of the Cauchy problem, which describe longitudinal oscillations propagation in the ropes (flexible suspensions) as in areas with moving boarders, are found. Displacements and stresses dynamic fields in variable length steel ropes of the specified load lifting mechanisms are investigated. Usually the ropes are balanced, and the main rope carries concentrated stress which before the systems movement was at the main ropes lower end. Dynamic forces in perfectly elastic variable length steel ropes estimation is shown, that only when lifting ropes without end loads under non-integrated boundary conditions, their efforts do not increase. However, practical experience shows that this phenomenon is not observed at moderate lifting speeds due to the fact that along with the dynamic forces amplitudes increase. Due to the decrease in length there is a simultaneous decrease in the amplitudes of their oscillations. The object of analysis refers to a wide range of variable length oscillations one-dimensional objects. A classical mathematical model to describe oscillations and waveforms is used. When studying wave fields in areas with moving boundaries the reflection of pulses from such boundaries is established. Elastic type waveforms in variable length rods (rope models) taking into account the fact that these rods have circular cross section of variable (length of rope/rod) area (rods are cylindrical, rotational paraboloids form, conical rods) is considered. Method based on the possibility of constructing wave equation from waves reflected from fixed and moving given boundaries of a semi-infinite domain solutions is applied.

Selection of Weight Coefficients of Quadratic Quality Functional in Solving ADOC Problem in the Letov—Kalman Formulation

For linear stationary one-dimensional control objects, the inverse problem of analytical design of optimal controller (ADOC) is considered, which consists in determining the weight coefficients of the quadratic functional of the optimality of the control process, providing a closed control system with the set values of primary quality indicators (static error, transient time and overshoot). It is analyzed in relation to both the ADOC problem in the Letov-Kalman formulation. A method of its solution is proposed based on the transformation of the ADOR problem to a canonical form in which the control object is described by a matrix differential equation in the Frobenius form, and the quality functional is defined as an integral of the sum of the products of the canonical phase coordinates of the object with the corresponding weight coefficients, as well as the square of the control signal. It is shown that the solution of the inverse canonical ADOC Letov-Kalman problem is determined by the values of only three non-zero weighting coefficients of the criterion, and one of them has a single value. The values of the other two coefficients are proposed to be found in the process of modeling the synthesized optimal control system from the conditions of ensuring for it the values of primary quality indicators no more than the specified ones. The results obtained, presented in the form of Theorems 1 and 2, are extended to the synthesis of astatic control systems, in which an additional integrator is connected to the plant output to obtain astaticism. Since such an "extended" control object is described using a state vector that has the first two phase coordinates of the canonical form, the synthesis of the optimal system is carried out without converting the object description to the canonical form of the phase variable and vice versa. The construction of an astatic control system is illustrated by an example.

Physical modeling and geometric shape simulation for one-dimensional flexible objects with cylindrical surface constraints

This study develops forces equilibrium differential equations for the geometric modeling of 1D flexible objects with surface constraints. These second-order equations are an extension of the Cosserat elastic rod theory and include both bending and torsion. Variables were established for the centerline and attitude in the Cartesian coordinate system of the cross section. This paper specifically investigates the case of a 1D flexible object constrained by a cylindrical surface. To solve this problem, a novel hybrid semi-analytical numerical method is proposed. In this process, a Hamiltonian function and an initial integral operator are introduced in a cylindrical coordinate system. The analytical solution, decoupled in polar coordinates, is then derived. The improved finite difference method was then used to obtain three cylindrical coordinates, which ensured numerical stability and efficiency. The results of a geometric shape simulation with differing boundary conditions demonstrate that this proposed method is capable of real-time modeling. As such, this technique could be a promising new tool for use in graphics simulations of elongated structures, such as DNA molecules, drill pipes, and submarine cables.

Accelerating the Heat Diffusion: Fast Thermal Relaxation of a Microcantilever

In most systems, thermal diffusion is intrinsically slow with respect to mechanical relaxation. We devise here a generic approach to accelerate the relaxation of the temperature field of a one-dimensional object, in order to beat the mechanical time scales. This approach is applied to a micrometer-sized silicon cantilever, locally heated by a laser beam. A tailored driving protocol for the laser power is derived to quickly reach the thermal stationary state. The model is implemented experimentally yielding a significant acceleration of the thermal relaxation, up to a factor 30. An excellent agreement with the theoretical predictions is reported. This strategy allows a thermal steady state to be reached significantly faster than the natural mechanical relaxation.

Mesh-independent multidimensional coupling of surface and subsurface water flow models

Abstract We present a new approach for multidimensional surface–subsurface flow coupling. The method does not require mesh-to-canal refinement or alignment and is based on numerical characteristics of the intersection of one-dimensional hydraulic object beds and the surface faces of the 3D tetrahedral mesh. The method is validated using widely recognized tilted v-catchment with subsurface and Borden catchment benchmarks.

Ultrafast Strong-Field Electron Emission and Collective Effects at a One-Dimensional Nanostructure

Enhanced near-fields at metallic nanostructures enable the generation of ultrafast nanometric electron pulses and the investigation of fundamental ultrafast dynamics in electron emission. Here we show strong-field induced photoemission from a nanometer-sharp tungsten-covered silicon nanoblade and report the systematic measurement of intensity-dependent electron energy spectra and yields. The observed plateau and cutoff features in the electron spectra indicate the presence of elastic electron rescattering in the enhanced near-fields at the surface of the one-dimensional nanostructure. For the first time, we can hence observe strong-field features from a one-dimensional object, as opposed to zero-dimensional needle tips employed so far. A comparison with results from classical and quantum simulations reveals that the extended geometry of the nanoblades and a cascaded near-field enhancement due to surface roughness leads to a broad energy distribution and high electron energies. A systematic analysis of the electron yield demonstrates nonlinear photoemission at moderate laser intensities and a clear transition to a regime with linear intensity dependence. This distinct feature is interpreted as the onset of space-charge trapping. The presented one-dimensional nanostructure enables us to generate above keV electrons without noticeable target damage and more than 13000 electrons per laser pulse, which is of utmost interest for novel classes of ultrafast photocathodes.

A method for finding a least-cost corridor on an ordinal-scaled raster cost surface

ABSTRACT The least-cost path problem is a widely studied problems in geographic information science. In raster space, the problem is to find a path that accumulates the least amount of cost between two locations based on the assumptions that the path is a one-dimensional object (represented by a string of cells) and that the cost (per unit length) is measured on a quantitative scale. Efficient methods are available for solution of this problem when at least one of these assumptions is upheld. This is not the case when the path has a width and is a two-dimensional object called a corridor (represented by a swath of cells) and the cost (per unit area) is measured on an ordinal scale. In this paper, we propose one additional model that characterizes a least-cost corridor on an ordinal-scaled raster cost surface – or a least ordinal-scaled cost corridor for short – and show that it can be transformed into an instance of a multiobjective optimization problem known as the preferred path problem with a lexicographic preference relation and solved accordingly. The model is tested through computational experiments with artificial landscape data as well as real-world data. Results show that least ordinal-scaled cost corridors are guaranteed to contain smaller areas of higher cost than conventional least-cost corridors at the expense of more elongated and winding forms. The least ordinal-scaled cost corridor problem has computational complexity of O(n 2.5) in the worst case, resulting in a longer computational time than least-cost corridors. However, this difference is smaller in practice.