Relative Equilibrium Research Articles

On the computation of the gradient in implicit neural networks

AbstractImplicit neural networks and the related deep equilibrium models are investigated. To train these networks, the gradient of the corresponding loss function should be computed. Bypassing the implicit function theorem, we develop an explicit representation of this quantity, which leads to an easily accessible computational algorithm. The theoretical findings are also supported by numerical simulations.

Assessment of cephalometric parameters and correlation with the severity of the obstructive sleep apnea syndrome

Abstract Background In individuals diagnosed with obstructive sleep apnea syndrome (OSAS), variations in craniofacial structure have been inconsistently documented, showing differing degrees of alteration between obese and nonobese patients. In addition, sleep disturbance has also been shown to induce disequilibrium in this population of patients. This pilot observational study aimed to assess craniofacial values in obese and nonobese subpopulations of patients with OSAS and their correlation and association with the severity of OSAS. We also assessed whether OSAS patients are characterized by an impaired equilibrium in relation to and associated with the severity of OSAS. Methods We included all consecutive adult patients with OSAS. Through cephalometry, we assessed the upper (UPa-UPp) and lower (LPa-LPp) pharynx diameters, superior anterior facial height (Sor-ANS), anterior facial height (ANS-Me), anterior vertical dimension (Sor-Me), posterior facial height (S-Go) and craniovertebral angle (CVA). Furthermore, we analyzed postural equilibrium through a stabilometric examination. Results Forty consecutive OSAS patients (45% female with a mean age of 56 ± 8.2 years) were included. The subgroup of nonobese patients had a reduced UPa-UPp (p = 0.02). Cephalometric measurements were correlated with the severity of OSAS in nonobese patients, whereas only Sor-ANS was correlated with the severity of OSAS in the obese subpopulation. In the overall population, altered craniofacial values are associated with severe OSAS. Although there are differences in equilibrium between obese and nonobese OSAS patients, the stabilometric measurements were not correlated or associated with OSAS severity. Conclusion Altered craniofacial values and compromised equilibrium in OSAS patients are linked to OSAS severity. Therefore, the management of OSAS should be tailored not only to weight management but also to craniofacial and postural rehabilitation to enhance patient outcomes.

Theoretical investigation on action mechanism and mollifying efficacy of propellant stabilizers.

This project performed quantum chemical computation, through kinetic and thermodynamic analyses to compare relative reactivity, reaction rate, and equilibrium composition from the possible pathways in connection with stabilizer-nitrodioxide reactions to determine the stability of the materials for practical application. Corresponding achievements have promoted the use of N-methyl-p-nitroaniline (MNA) and dinitrophenyl malonamide series (M3, M4, and M5) stabilizers as high priorities for selection. The Gaussian 09 program (G09) (Frisch et al 2009) and density functional theory (DFT) calculations with the B3LYP/6-31G(d,p) function were performed to obtain related geometric and thermodynamic energy data for the molecular systems in this study. The synchronous transit-guided quasi-Newton method (STQN) (Peng and Schlegel Isr J Chem 33:49, 1993) was applied through the QST3 procedure to identify single imaginary frequency-valued transition-state species. The related reaction rate constant (k) and pre-exponential factor (A) were obtained, based on transition state theory (Su 2008), using Eqs. 11 and 12.

On the motion stabilization of a three-link robotic manipulator with incomplete measurement

Abstract. This paper considers a mathematical model of a manipulator which consists of a vertical column, two links, connected to it in series, and a gripper with a load. The column resting on a fixed base can rotate around its vertical axis. The links are connected by cylindrical hinges allowing them to rotate in the same vertical plane. The column and the links are modeled as rigid bodies with the links having unequal principal moments of inertia. The position of the manipulator in space is determined by three rotation angles of the column and the links. The manipulator can have several types of steady-state program movements. When gravitational torques are compensated by control torques applied in the cylindrical hinges, the manipulator has a program equilibrium position. The manipulator can also have a program motion when the column rotates at a given constant angular velocity, and the links have given relative equilibrium positions in their plane. The stabilization problem of manipulator motion is investigated by means of control torques with feedback when only the rotation angles of the column and links are measured. The problem posed is solved in the form of a nonlinear proportional-integral controller taking into account the cylindrical phase space of the manipulator's mathematical model. The solution includes construction of a Lyapunov functional with a semi-definite derivative and application of the corresponding theorems on the asymptotic stability of non-autonomous functional differential retarded-type equations. The obtained conditions for the program motion stabilization are robust with respect to the mass-inertial parameters of the manipulator. The numerical simulation results demonstrate global attraction to its given position in cylindrical phase space.

Asymptotic Antipodal Solutions as the Limit of Elliptic Relative Equilibria for the Two- and n-Body Problems in the Two-Dimensional Conformal Sphere

We consider the two- and n-body problems on the two-dimensional conformal sphere MR2, with a radius R>0. We employ an alternative potential free of singularities at antipodal points. We study the limit of relative equilibria under the SO(2) symmetry; we examine the specific conditions under which a pair of positive-mass particles, situated at antipodal points, can maintain a state of relative equilibrium as they traverse along a geodesic. It is identified that, under an appropriate radius–mass relationship, these particles experience an unrestricted and free movement in alignment with the geodesic of the canonical Killing vector field in MR2. An even number of bodies with pairwise conjugated positions, arranged in a regular n-gon, all with the same mass m, move freely on a geodesic with suitable velocities, where this geodesic motion behaves like a relative equilibrium. Also, a center of mass formula is included. A relation is found for the relative equilibrium in the two-body problem in the sphere similar to the Snell law.

On the linear stability of the Lamb–Chaplygin dipole

The Lamb–Chaplygin dipole (Lamb, Hydrodynamics, 2nd edn, 1895, Cambridge University Press; Lamb, Hydrodynamics, 3rd edn, 1906, Cambridge University Press; Chaplygin, Trudy Otd. Fiz. Nauk Imper. Mosk. Obshch. Lyub. Estest., vol. 11, 1903, pp. 11–14) is one of the few closed-form relative equilibrium solutions of the two-dimensional (2-D) Euler equation characterized by a continuous vorticity distribution. We consider the problem of its linear stability with respect to 2-D circulation-preserving perturbations. It is demonstrated that this flow is linearly unstable, although the nature of this instability is subtle and cannot be fully understood without accounting for infinite-dimensional aspects of the problem. To elucidate this, we first derive a convenient form of the linearized Euler equation defined within the vortex core which accounts for the potential flow outside the core while making it possible to track deformations of the vortical region. The linear stability of the flow is then determined by the spectrum of the corresponding operator. Asymptotic analysis of the associated eigenvalue problem shows the existence of approximate eigenfunctions in the form of short-wavelength oscillations localized near the boundary of the vortex and these findings are confirmed by the numerical solution of the eigenvalue problem. However, the time integration of the 2-D Euler system reveals the existence of only one linearly unstable eigenmode and since the corresponding eigenvalue is embedded in the essential spectrum of the operator, this unstable eigenmode is also shown to be a distribution characterized by short-wavelength oscillations rather than a smooth function. These findings are consistent with the general results known about the stability of equilibria in 2-D Euler flows and have been verified by performing computations with different numerical resolutions and arithmetic precisions.

Cost-effectiveness analysis of amivantamab plus chemotherapy versus chemotherapy alone in NSCLC with EGFR Exon 20 insertions.

Amivantamab plus chemotherapy has been proved to be an efficient treatment strategy for non-small-cell lung cancer (NSCLC) with epidermal growth factor receptor (EGFR) exon 20 insertions. The aim of this study was to conduct the cost-effectiveness analysis of amivantamab-chemotherapy compared with chemotherapy alone in NSCLC harboring EGFR exon 20 insertion mutations. We constructed a Markov model based on the data derived from the PAPILLON trial. We evaluated the cost, quality-adjusted life years (QALYs), and incremental cost-effectiveness ratio (ICER). One-way and probabilistic sensitivity analyses were used to evaluate the influence of different parameters on this model. Compared with chemotherapy alone, amivantamab combined with chemotherapy treatment gained an incremental effectiveness of 0.473 QALYs and an incremental cost of $361,950.952, which resulted in an ICER of $765,224/QALY. The ICER was much higher than the willingness-to-pay threshold of 15,0000/QALY. One-way sensitivity analysis revealed that amivantamab cost was the leading influential factor in the model. Compared with chemotherapy alone, amivantamab plus chemotherapy is not a cost-effective first-line treatment choice for NSCLC patients with EGFR exon 20 insertions. The costly price of amivantamab is one of the major reasons for the high cost of this combined treatment strategy. Therefore, it is imperative to take into account the high cost of amivantamab in the subsequent clinical application and strive to attain a relative equilibrium between its significant clinical benefit and economic encumbrance.

Effect of Microclimate on the Mass Emergence of Hypothenemus hampei in Coffee Grown under Shade of Trees and in Full Sun Exposure.

The rainfall regime has a significant impact on the microclimate and mass emergence of the coffee berry borer, Hypothenemus hampei (Coleoptera: Curculionidae) (CBB). Little is known, however, about the shade tree-microclimate-CBB mass emergence interaction. The objective of the present study was to compare the effect of microclimate on the mass emergence of CBB in a full sun-exposed plot with a plot shaded by trees. The experiment was conducted on a Robusta coffee farm in southern Chiapas, Mexico. In each plot, 18 traps baited with an alcohol mixture were installed to capture flying females, collecting caught individuals every hour from 8:00 to 18:00 h. A meteorological station recorded several microclimatic variables on 13 weekly sampling dates from February to May 2022. Significantly more CBB females were captured in the shaded plot. The largest number of CBB captures was recorded between 14:00 and 16:00 h for the shade plot and between 15:00 and 17:00 h for the sun-exposed plot. The mass emergence of CBB showed a positive association with precipitation, dew point, and wind speed samples and a negative association with maximum air temperature, average relative humidity, ultraviolet radiation, wind speed, and equilibrium moisture content. Our observations show that the relationship between shade trees, microclimate, and mass emergence of CBB is complex and that its study helps us to gain deeper insight into CBB bioecology and advance control techniques against this important pest.

Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints

In this paper, a detailed and comprehensive linear stability analysis of a rolling toroidal wheel is performed. The wheel is modeled as a rigid toroid-shaped body rolling without slipping on a horizontal surface. The nonlinear equations of motion constitute a Differential-Algebraic Equations system, given by the dynamic equilibrium equations augmented with the nonholonomic constraints, which arise from the no-slip condition. The circular steady motion and the linearized equations of motion along this relative equilibrium are obtained, for both the solid and hollow tori. The expressions of the linearized equations and the corresponding eigenvalues are derived analytically as a function of the torus aspect ratio. The variation of the stability boundary with the torus aspect ratio is shown. A comparison of the results obtained in the solid and hollow scenarios is included, and all the results are validated with the rolling hoop, which corresponds to a degenerate torus with zero aspect ratio. In the particular case of the steady straight-line rolling and spinning about a vertical diameter, which constitute limit motions of the circular steady motion, the critical rotational and angular speeds required for stabilization are obtained.

Experimental analysis of submerged vanes' configuration for mitigating local scour at piers in a sharp bend: Influence of quantity, length, and orientation

This research study focuses on the examination of the effects of submerged vanes on the variations of bend topography, particularly in the proximity of a bridge pier, using a laboratory model. The experimental setup consisted of a 180-degree bend with a rectangular cross section, wherein a cylindrical pier with a diameter of 5 cm was positioned at the center of a flume. Plexiglas vanes were strategically installed upstream of the bridge pier. The study aimed to measure the maximum depth of local scour during the period of relative equilibrium. Parametric studies were conducted to investigate the influence of various factors, including the number of vanes, different vane lengths, and vane angles. The resulting scour profiles were compared to assess the effectiveness of the different configurations. The experimental findings demonstrated that the maximum reduction in scour depth around the bridge pier was observed when three submerged vanes, with a length 1.5 times the diameter of the pier, were placed at an angle of 15° relative to the tangent at the mid-section of the bend. This configuration resulted in an approximate reduction of scour depth by 30 percent compared to other cases examined in the study.

Finiteness of stationary configurations of the planar four-vortex problem

For the planar four-vortex problem, we show that there are finitely many stationary configurations consisting of equilibria, rigidly translating configurations, relative equilibria (uniformly rotating configurations) and collapse configurations. We also provide upper bounds for these classes of stationary configurations.

A Note on Stability of a Dopant for Perovskite Solar Cells: Dimerization of 2,2′-bis(trifluoromethyl)-[1,1′-biphenyl]-4,4′-diamine Iodine

The note continues with the density-functional theory (DFT) quantum-chemical understanding of perovskite solar cells at molecular level. In particular, 2,2′-bis(trifluoromethyl)-[1,1′-biphenyl]-4,4′-diamine iodine (or BFBAI2, stoichiometry C14H12F6I2N2) is further calculated—the species is known to improve the power conversion efficiency and device stability. The thermodynamic-stability calculations are performed at the M06-2X/3-21G level with anharmonic vibrational analysis (including vibrational-rotational coupling) for construction of the vibrational-rotational partition functions. The dimerization is shown to be an essential feature of BFBAI2 (it is based on the formation of two hydrogen bonds). The BFBAI2 dimerization is described in the terms of the standard Gibbs energy and the related dimerization equilibrium constant. Comparisons are made with the water dimer, commonly used as a model system for hydrogen-bond formation. The equilibrium constants for the water dimerization are consistently lower than for the dimerization of BFBAI2 - as the presence of two hydrogen bonds in the BFBAI2 dimer contributes to the larger stabilization. The dimerization of BFBAI2 upon higher surface coverages represents an additional factor for the layer stabilization as there is decrease in the standard Gibbs energy at moderate temperatures. The dimerization also brings additional features for modulation of surface conditions.

Asymptotic relative equilibrium in the n-body problem: Relativistic application in the Poincaré upper half-plane

In this paper, we study the [Formula: see text]-body problem in the Poincaré upper half-plane [Formula: see text], where the radius [Formula: see text] of the Poincaré disk is fixed. We introduce a new potential to derive the condition for hyperbolic relative equilibria on [Formula: see text]. We analyze the relative equilibrium of positive masses moving along geodesics under the [Formula: see text] group. This result is utilized to establish the existence of relative equilibria for the [Formula: see text]-body problem on [Formula: see text] for [Formula: see text] and [Formula: see text]. We revisit previously known results and uncover new qualitative findings on relative equilibria that are not evident in an extrinsic context. Additionally, we provide a simple expression for the center of mass of a system of point particles on a two-dimensional surface with negative constant Gaussian curvature.

Transformations of Glycerol into High-Value-Added Chemical Products: Ketalization and Esterification Reactions

Biomass allows us to obtain energy and high-value-added compounds through the use of different physical and chemical processes. The glycerol obtained as a by-product in the synthesis of biodiesel is considered a biomass compound that has the potential to be used as a raw material to obtain different chemical products for industry. The development and growth of the biodiesel industry allows for the projection of glycerol biorefineries around these plants that efficiently and sustainably integrate the biodiesel production process together with the glycerol transformation processes. This work presents a review of the ketalization and esterification of glycerol to obtain solketal and acetylglycerols, which are considered products of high added value for the chemical and fuel industry. First, the general aspects and mechanisms of both reactions are presented, as well as the related chemical equilibrium concepts. Subsequently, the catalysts employed are described, classifying them according to their catalytic nature (zeolites, carbons, exchange resins, etc.). The reaction conditions used are also described, and the best results for each catalytic system are presented. In addition, stability studies and the main deactivation mechanisms are discussed. Finally, the work presents the kinetic models that have been formulated to date for some of these systems. It is expected that this review work will serve as a tool for the advancement of studies on the ketalization and esterification reactions that allow for the projection of biorefineries based on glycerol as a raw material.

Linear Stability of an Elliptic Relative Equilibrium in the Spatial $$n$$-Body Problem via Index Theory

Linear Stability of an Elliptic Relative Equilibrium in the Spatial $$n$$-Body Problem via Index Theory

Exploring the free-energy landscape of a rotating superfluid.

The equilibrium state of a superfluid in a rotating cylindrical vessel is a vortex crystal-an array of vortex lines, which is stationary in the rotating frame. Experimental realizations of this behavior typically show a sequence of transient states before the free-energy-minimizing configuration is reached. Motivated by these observations, we construct a new method for a systematic exploration of the free-energy landscape via gradient-based optimization of a scalar loss function. Our approach is inspired by the pioneering numerical work of Campbell and Ziff [Phys. Rev. B. 20, 1886 (1979)] and makes use of automatic differentiation, which crucially allows us to include entire solution trajectories in the loss. We first use the method to converge thousands of low free-energy relative equilibria in the unbounded domain for vortex numbers in the range 10≤N≤30, which reveals an extremely dense set of mostly saddle-like solutions. As part of this search, we discover new continuous families of relative equilibria, which are often global minimizers of free energy. These continuous families all consist of crystals arranged in a double-ring configuration, and we assess which state from the family is most likely to be observed experimentally by computing energy-minimizing pathways from nearby local minima-identifying a common entry point into the family. The continuous families become discrete sets of equal-energy solutions when the wall is introduced in the problem. Finally, we develop an approach to compute homoclinic orbits and use it to examine the dynamics in the vicinity of the minimizing state by converging connections for low-energy saddles.

북한 쌀 시장의 지역 간 통합과 거래 구조

Since the 2000s, North Korea has been shifting away from a socialist planned economy towards a mixed plan-market system, marking a significant transformation in its economic approach. This research concentrates on scrutinizing the North Korean consumer goods market, with a specific focus on rice. The study encompasses nine cities (five/four in Western/Eastern region), covering the period from January 2012 to December 2021. The paper adopts a theoretical framework rooted in the efficient market hypothesis, using statistical analysis to examine absolute and relative prices. Notably, it identifies nearly perfect price parity in two pairs of cities (F-H, West and D-G, East). The relative price analysis shows that all pairs are in relative equilibrium, indicating that market integration has been established across regions. These findings offer statistical evidence of the coexistence of planned and market-based elements in the North Korean rice distribution system. In addition to price analysis, this paper delves into the North Korean rice trading network and associated transaction costs in selected regions. Consequently, this study holds substantial academic distinction, offering valuable insights into North Korea's essential goods distribution system.

ПРОЦЕССУАЛЬНОЕ ФОРМИРОВАНИЕ НОРМЫ В СИСТЕМЕ ОБЩЕСТВЕННЫХ ОТНОШЕНИЙ

The article deals with the problem of social normality, which is actualized in the conditions of a communicative and information society. It is quite justifi ed that in modern realities, the study of the role of the norm in human behavioral strategies is the most relevant. This article is based on the assumption that the norm cannot be reduced to a set of rules of behavior as an external regulator of human activity. In the traditions of psychoanalysis and the phenomenological school, it is proposed to consider the norm in the unity of intentionality and rationality. In a comparative analysis of the conclusions of psychological and sociological sciences, it is determined that the norm is a mechanism for motivating activity. The possibility of the evolution of the norm from recognition as an external stimulus to a factor of internal action is revealed. The approaches to the norm as a form of state equilibrium of public relations are analyzed. Particular attention is paid to the state of the norm as a combination of hypothetical punishment and the degree of inner sensitivity of a person to the norm. An attempt was made to analyze the thesis about the unconditional nature of some, in particular, using the example of morality. In this regard, a critical section of modern classifi cations of normative components is given. The theoretical consequences of singling out regulation as an independent part of standards were traced. The psychic nature of social normality has been proven. It is shown that the norm can be considered as a mechanism of human changes. The importance of taking into account the norm in the processes of pleasure-without pleasure is noted.

Finite Froude and Rossby numbers counter-rotating vortex pairs

We investigate the nonlinear evolution of pairs of three-dimensional, equal-sized and opposite-signed vortices at finite Froude and Rossby numbers. The two vortices may be offset in the vertical direction. The initial conditions stem from relative equilibria obtained numerically in the quasi-geostrophic regime, for vanishing Froude and Rossby numbers. We first address the linear stability of the quasi-geostrophic opposite-signed pairs of vortices, and show that for all vertical offsets, the vortices are sensitive to an instability when close enough together. In the nonlinear regime, the instability may lead to the partial destruction of the vortices. We then address the nonlinear interaction of the vortices for various values of the Rossby number. We show that as the Rossby number increases, destructive interactions, where the vortices break into pieces, may occur for a larger separation between the vortices, compared to the quasi-geostrophic case. We also show that for well-separated vortices, the interaction is non-destructive, and ageostrophic effects lead to the deviation of the trajectory of the pair of vortices, as the anticyclonic vortex dominates the interaction. Finally, we show that the flow remains remarkably close to a balanced state, emitting only waves containing negligible energy, even when the interaction leads to the destruction of the vortices.

Risks and uncertainties in carbon capture, transport, and storage projects: A comprehensive review

The rapid escalation of climate change and global warming underscores the critical role of CO2 emissions, necessitating effective mitigation strategies. Carbon Capture and Storage (CCS) has emerged as a promising way to address this challenge. It is estimated that CCS could account for 25–67% of emissions reductions in heavy industries. Nonetheless, the realization of large-scale CCS deployment demands a meticulous evaluation of associated risks (e.g., pure and speculative) and uncertainties (e.g., aleatoric, epistemic and Knightian) across the entire process. This review paper provides a comprehensive analysis of the risks and uncertainties (R&U), both technical (e.g., oprational and site chractrization) and non-technical (e.g., financial, political and social) inherent in CCS initiatives. Drawing from a diverse array of recent literature sources—including more than 400 CCS-related articles, books, theses, and reports—the analysis spans the period from 2015 to 2023. The methodology adheres rigorously to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, ensuring methodical precision and coherence. Our analysis indicates that approximately 47% of studies found from 2015 focused on technical R&U in CCS, while the remaining 53% addressed non-technical R&U. This distribution demonstrates a relative equilibrium in the research landscape as depicted in the literature. This review by considering R&U within the CCS landscape can provide crucial insights for engineers and researchers in decarbonization. It serves as a vital guide for navigating intricate challenges in CCS projects. Moreover, administrators and developers can use this knowledge to enhance technological security and cost-efficiency. Ultimately, this paper identifies practical strategies and methodologies that enhance the feasibility of CCS, offering concrete recommendations and suggestions to elevate the success potential of CCS endeavors.