Newtonian Equations Research Articles

Elastic waves scattering by the schoty in microscopic system 2D

We investigate the scattering phenomenon at the non-uniform crystalline surface. Localized modes emerge in its vicinity due to the inhomogeneity-induced breakdown of translation symmetry. The phonon scattering mechanisms at the inhomogeneity are investigated by means of the Newton equation and matching approach. Numerical findings are presented across a wide range of scattering energies, together with the estimation of the transmission and reflection probabilities and the elastic wave average transmittance across the defect. This shows how the softening, homogeneity, and hardening characteristics of the perturbed defect vary in their scattering spectra. Fano resonances in the spectra are caused by the coherent coupling between the localized modes created by the defect and the propagating mode of the ideal waveguide. For a variety of values of the elastic constants in the bulk and inhomogeneous domain, a comprehensive explanation is given. The features of the system model and the stimulating dimensionless frequencies are used to calculate the conductance of the system.

Generalized uncertainty principle from the regularized self-energy

We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality. The particle mass M is no longer concentrated into a point but is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle, which is interpreted as a regularized self-energy. We extend our results and find corrections to the relativistic particles using the Klein–Gordon, Proca and Dirac equations. An important finding is that we extract a form of the generalized uncertainty principle (GUP) from the corrected energy. This form of the GUP is shown to depend on the nature of particles; namely, for bosons (spin 0 and spin 1) we obtain a quadratic form of the GUP, while for fermions (spin 1/2) we obtain a linear form. The correlation we find between spin and GUP may offer insights for investigating quantum gravity.

A Survey of Dynamical and Gravitational Lensing Tests in Scale Invariance: The Fall of Dark Matter?

We first briefly review the adventure of scale invariance in physics, from Galileo Galilei, Weyl, Einstein, and Feynman to the revival by Dirac (1973) and Canuto et al. (1977). In the way that the geometry of space–time can be described by the coefficients gμν, a gauging condition given by a scale factor λ(xμ) is needed to express the scaling. In general relativity (GR), λ=1. The “Large Number Hypothesis” was taken by Dirac and by Canuto et al. to fix λ. The condition that the macroscopic empty space is scale-invariant was further preferred (Maeder 2017a), the resulting gauge is also supported by an action principle. Cosmological equations and a modified Newton equation were then derived. In short, except in extremely low density regions, the scale-invariant effects are largely dominated by Newtonian effects. However, their cumulative effects may still play a significant role in cosmic evolution. The theory contains no “adjustment parameter”. In this work, we gather concrete observational evidence that scale-invariant effects are present and measurable in astronomical objects spanning a vast range of masses (0.5 M⊙< M <1014M⊙) and an equally impressive range of spatial scales (0.01 pc < r < 1 Gpc). Scale invariance accounts for the observed excess in velocity in galaxy clusters with respect to the visible mass, the relatively flat/small slope of rotation curves in local galaxies, the observed steep rotation curves of high-redshift galaxies, and the excess of velocity in wide binary stars with separations above 3000 kau found in Gaia DR3. Last but not least, we investigate the effect of scale invariance on gravitational lensing. We show that scale invariance does not affect the geodesics of light rays as they pass in the vicinity of a massive galaxy. However, scale-invariant effects do change the inferred mass-to-light ratio of lens galaxies as compared to GR. As a result, the discrepancies seen in GR between the total lensing mass of galaxies and their stellar mass from photometry may be accounted for. This holds true both for lenses at high redshift like JWST-ER1 and at low redshift like in the SLACS sample. Of note is that none of the above observational tests require dark matter or any adjustable parameter to tweak the theory at any given mass or spatial scale.

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The problem of displacive phase transitions (by which crystals pass on heating from a less symmetric to a more symmetric form) is investigated through numerical integration of the Newton equations of motion for a realistic model, in the paradigmatic case of quartz. Usually such transitions are discussed in terms of the positions of the atoms, while the role of normal modes is emphasized here. The key preliminary property established, in agreement with the indications given by Landau in his thermodynamic-like approach, is that four well definite modes are sufficient to describe the transition, the remaining modes just acting as a noise. The main result is then that such four modes constitute a closed Hamiltonian subsystem presenting an effective potential parametrically dependent on specific energy. The effective potential is actually computed, through (appropriately defined) time-averages of the accelerations of the relevant modes, and is found to describe, as energy is varied, a pitchfork bifurcation, once more confirming in dynamical terms the Landau result. The effective potential also allows one to advance a possible explanation of the “soft mode” phenomenon, namely the occuring, in the Raman spectrum, of a peak whose frequency depends on temperature and vanishes at the transition.

Numerical analysis of gas-solid flow erosion in different geometries as alternatives to a standard pipe elbow

This study was conducted with the aim of replacing different geometric fittings instead of the standard 90° elbow and trying to change the flow pattern to reduce erosion damage. Among fittings, the elbows are at a more serious risk. Numerical investigation of the present erosion with the novelty of research on non-spherical particles and changes in the impact angle of particles along with fluid flow using eight new proposed fittings, including two miter fittings, three blinded fittings, one reducer elbow fitting, and two spherical elbows fittings in comparison with the standard 90° elbow was controlled. The numerical simulation of the gas-solid two-phase flow of non-spherical particles was studied using the Euler-Lagrange approach. To carry out the study numerical, first, the gas flow was modeled by the Navier-Stokes equations and the turbulent Reynolds stress model, and then the solid particles were injected using Newton's equation. Finally, the erosion was calculated using Grant and Tabakoff model of the restitution of particles of after hitting the wall and the erosion model of Oka. The amount of erosion caused by changes in the flow pattern was investigated to evaluate the performance of the new proposed fittings. Numerical results for the most critical mode (Vin = 27 m/s and DP = 300 μm) showed that the new proposed fittings increase the erosion resistance by 22.5 % to 39.6 % compared to the standard 90° elbow. Also, in this research, the effect of different parameters including flow velocity, particle diameter size, particle input rate, and particle rotation on erosion were investigated.

Trade Effects of Non-Tariff Barriers in Tanzania: A Case of the Dar es Salaam-Namanga Busy Border Trade Post

The main objective of this study is to examine and quantify the effects of Non-Tariff Barriers (NTBs) on cargo trade movement in Tanzania, focusing on the Dar es Salaam-Namanga Border Post. Specifically, the study aims to identify the main administrative or technical requirements along this trade route (both old and new), analyze the regularity of these requirements based on respondents’ feedback, and provide recommendations for mitigating NTBs. The study utilized an empirical survey design, collecting mostly qualitative data on border trade performance and perceived non-tariff barriers. The research was guided by economic theory and targeted formal and informal cross-border traders, transport companies, truck drivers, weighbridge attendants, and customs and revenue authorities. Data was collected through desk research, interviews, questionnaires, and stakeholder consultations. The Dar es Salaam-Namanga route was chosen for its importance as the busiest commercial corridor in the East African Community (EAC). The study employed both probability and non-probability sampling techniques, restricted to the Arusha-Namanga roadway. Four data collection methods were used: desk research, interviews, questionnaires, and stakeholder consultations. The data were analyzed using thematic analysis for qualitative information, and an econometric model based on Newton's gravitational equation (a modified gravity model) was used to quantify trade effects. Statistical Package for Social Sciences (SPSS) was employed for stepwise multiple linear regression analysis. The model's predictive power was tested using an F-test, and it was verified to meet assumptions of linearity, homoscedasticity, and multicollinearity. The results revealed that roadblocks, customs clearance, permits, and road infrastructure significantly affected trade performance. Unethical practices at weighbridges, frequent police checks, and customs procedures lead to monetary losses and time delays for cross-border traders. Bribery, police checks, and unloading processes during inspections were identified as factors contributing to the perception of NTBs as costly and time-consuming. On a positive note, improved road conditions have reduced transportation costs by lowering vehicle repair expenses and decreasing travel time. The study concludes that there is a need for regional cooperation within the EAC to eliminate existing NTBs. It recommends streamlining administrative procedures and working hours at border points, and implementing monitoring systems to ensure the effective removal of unnecessary barriers to trade. These measures are essential to improving trade efficiency and promoting the goals of the re-established East African Community.

Discrete Schrödinger–Newton equations with power nonlinearity

We study Schrödinger–Newton equations with general power nonlinearity on the lattice Z d . After the proof of well-posedness of the Cauchy problem, our interest is focused on the existence of stable standing (stationary) solutions. Employing variational methods we prove the existence of a ground state solution solving the associated stationary system. Orbital stability as well as exponential localization of the ground state is verified. Finally, we discuss the existence of excitation thresholds for ground state solutions in dependence of the conserved mass ( l 2 -norm).

Flow induced vibration with forced convection of a stationary and oscillating filleted bluff bodies in a staggered position

Flow induced vibration (FIV) and forced convection heat transfer from staggered cylinders are numerically investigated with Re = 150 and Pr = 0.7. Cylinders are arranged in a staggered manner with three different stagger angles (α) = 15°, 30°, and 45°. The upstream cylinder (UC) is kept fixed while the downstream cylinder (DC) is mounted. The cross section of the bluff body is altered by parameter (r*) = 0 (square cylinder), 0.5, 0.75, and 1 (circular cylinder). For every stagger angle and r*, the reduced velocity is varied from 2 to 10. The mass ratio (m*) of the DC is kept at 10 and damping constant set to zero for maximum vibrational amplitude. The incompressible Navier–Stokes equations are coupled with Newton's equation for the mass-damper system of the vibrating cylinder. Flow induced vibration was studied with the help of frequency characteristics, dynamics response of cylinders, and instantaneous phase plots of lift and amplitude. Generally, in the case of square cylinders a delayed response can be observed as compared to other configurations. For α=15°, the DC is fully submerged into the wake of static UC. P + S (P: pair; S: singlet)-type vortices can be observed for r* = 0. For other configurations of filleted cylinders, such as r* = 0.5, 0.75, and 1 at Ur=4, 2 parallel row formation is formed due to negative sign vortices while the other one was a combination of positive and negative vortices in pseudo-P formation. At higher Ur=6 and 8, coalesced and irregular wakes can be noticed. As the stagger angle is increased to higher than 30°, the wake of both cylinders becomes more pronounced. Due to the change in stagger angle, fs (vortex shedding frequency) of UC and DC forces decouples. 2P-type vortex shedding can be observed at Ur=4 for r* = 0.75 and 1. Pairs of vortices are coupled from each cylinder in a row where negative vortices coalesce while losing energy. For lower r* = 0 and 0.5, there is a tendency for three row formation. Further increase in angle pushed the DC completely out of the wake of the UC although vortices from both cylinders are still found to interact and exhibit three row formation and 2P-type vortex shedding. Heat transfer from the DC is highly dependent on the stagger angle. For r* = 1 and 0.5 at Ur=2, the change in Nuavg is 15% and 14.7%, respectively, when the angle changed from 15° to 45°. Heat transfer from any FIV system can be directly influenced by dynamic response, position, shape, and flow topology. The generated results are provide insight for understanding the vibrational modes and heat transfer from two bluff bodies involving fluid–structure interactions.

Integrating Newton's equations of motion in the reciprocal space.

We here present the normal dynamics technique, which recasts the Newton's equations of motion in terms of phonon normal modes by exploiting a proper sampling of the reciprocal space. After introducing the theoretical background, we discuss how the reciprocal space sampling enables us to (i) obtain a computational speedup by selecting which and how many wave vectors of the Brillouin zone will be considered and (ii) account for distortions realized across large atomic distances without the use of large simulation cells. We implemented the approach into an open-source code, which we used to present three case studies: in the first one, we elucidate the general strategy for the sampling of the reciprocal space; in the second one, we illustrate the potential of the approach by studying the stabilization effect of temperature in α-uranium; and in the last one, we investigate the characterization of Raman spectra at different temperatures in MoS2/MX2 transition metal dichalcogenide heterostructures. Finally, we discuss how the procedure is general and can be used to simulate periodic, semiperiodic, and finite systems such as crystals, slabs, nanoclusters, or molecules.

Maximal acceleration in Rainbow gravity

In this paper, we derive maximal acceleration of a massive particle in Rainbow gravity. Using eight-dimensional phase-space metric compatible with Rainbow gravity, we obtain the maximal acceleration, valid up to first order in the Rainbow gravity parameter η. Using the positivity condition on maximal acceleration, we find that the upper bound on the Rainbow gravity parameter is of the order of for positron and for a black hole. After obtaining the expression for maximal acceleration for different choices of Rainbow functions, we derive corresponding modifications to Unruh temperature. Comparing with the observational value of the Unruh temperature, we find the upper bound on η as for positron radiation. We then derive geodesic equations for different choices of Rainbow functions and also obtain the Newtonian limit of these geodesic equations. We find that the changes in the value of maximum acceleration, maximum temperature and Newtonian force equation are dependent on the choices of Rainbow functions.

Molecular Dynamic Simulations for Biopolymers with Biomedical Applications.

Computational modeling (CM) is a versatile scientific methodology used to examine the properties and behavior of complex systems, such as polymeric materials for biomedical bioengineering. CM has emerged as a primary tool for predicting, setting up, and interpreting experimental results. Integrating in silico and in vitro experiments accelerates scientific advancements, yielding quicker results at a reduced cost. While CM is a mature discipline, its use in biomedical engineering for biopolymer materials has only recently gained prominence. In biopolymer biomedical engineering, CM focuses on three key research areas: (A) Computer-aided design (CAD/CAM) utilizes specialized software to design and model biopolymers for various biomedical applications. This technology allows researchers to create precise three-dimensional models of biopolymers, taking into account their chemical, structural, and functional properties. These models can be used to enhance the structure of biopolymers and improve their effectiveness in specific medical applications. (B) Finite element analysis, a computational technique used to analyze and solve problems in engineering and physics. This approach divides the physical domain into small finite elements with simple geometric shapes. This computational technique enables the study and understanding of the mechanical and structural behavior of biopolymers in biomedical environments. (C) Molecular dynamics (MD) simulations involve using advanced computational techniques to study the behavior of biopolymers at the molecular and atomic levels. These simulations are fundamental for better understanding biological processes at the molecular level. Studying the wide-ranging uses of MD simulations in biopolymers involves examining the structural, functional, and evolutionary aspects of biomolecular systems over time. MD simulations solve Newton's equations of motion for all-atom systems, producing spatial trajectories for each atom. This provides valuable insights into properties such as water absorption on biopolymer surfaces and interactions with solid surfaces, which are crucial for assessing biomaterials. This review provides a comprehensive overview of the various applications of MD simulations in biopolymers. Additionally, it highlights the flexibility, robustness, and synergistic relationship between in silico and experimental techniques.

Phenomenological Analogy between Gross-Pitaevskii Theory for Bose-Einstein Condensate and Newton Equation for Classical Mechanics

In this work we found an interesting analogy between Gross-Pitaevskii theory for Bose-Einstein condensate at zero temperature and Newton equation of classical particle in the classical physics. Although this analogy is a pure phenomenology, it brings a new perspective to physics in general, in particular to quantum physics, as well as to many-body physics.

Numerical modeling of hydrodynamics of spouted bed in solid fuel boiler

The issues of numerical modeling of hydrodynamics of a spouted fuel bed in the furnace of a solid-fuel boiler are considered. At present, solid-fuel boilers are widely used in the power industry of the Russian Federation, with the share of coal-fired generation to remain significant in the projected terms. Therefore, the study of the efficiency of thermal and hydrodynamic processes that ensure the implementation of clean coal technologies is a relevant task both today and in the long term. The article presents the following main stages of numerical modelling of the hydrodynamics of the spouted bed: problem formulation with selection of boundary and initial conditions, methods of solving the Navier-Stokes and continuity equations for the air flow, Newton's equations and diffusion equations for particles. The k-omega turbulence model was used in the calculations that is described by means of two partial differential equations for the variables k (kinetic energy of turbulence) and omega (specific dissipation rate). A comparative analysis of environmental advantages and disadvantages of existing methods of combustion of low-grade coal in schemes with in-cycle gasification (ICG) is carried out. Advantages and difficulties of switching to structures with CFB in the spouted bed mode are shown. Numerical modeling of the cold spouted bed created by means of particle injection is performed, a set of initial settings and boundary conditions is presented, the adequacy of the obtained results is verified by hydrodynamic characteristics of the isothermal process. The obtained results allow us to proceed to the next stages with non-isothermal models, with heat exchange and combustion reactions in the spouted bed of coal taken into account. The following refinement of the physical model will allow to achieve more accurate and reliable results and to ensure their correct scaling.

Propagation of dark solitons of DNLS equations along a large-scale background

We study dynamics of dark solitons in the theory of the derivative nonlinear Schrödinger equations by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes’ remark that relationships for harmonic linear waves and small-amplitude soliton tails satisfy the same linearized equations, so the corresponding solutions can be converted one into the other by replacement of the packet’s wave number k by iκ, κ being the soliton’s inverse half-width, we find the Hamiltonian and the canonical momentum of the soliton’s motion. The Hamilton equations are reduced to the Newton equation whose solutions for some typical situations are compared with exact numerical solutions of the Kaup-Newell DNLS equation.

Analysis of the flow and thermal-fluid–solid coupling of crude oil in circular pipe caused by variable pressure gradient

Abstract Globally, enhanced oil recovery (EOR) has become a pressing issue as the demand for crude oil continues to increase. This study investigates the flow and thermal-fluid–solid coupling of crude oil in a rod pump during hot water recovery and obtains the maximum recovery of crude oil in a vertical pipeline through numerical analysis. The pressure gradient in the pump barrel was first developed and deduced based on the ideal gas state equation and Bernoulli’s equation. According to the rheological experiment results, it was proven that the light crude oil conforms to the Newtonian constitutive equation. Subsequently, the momentum equation of crude oil flowing in the pipeline and fluid–solid coupling heat transfer equations were established and solved using the finite difference method. The effects of the thermal recovery temperature T w , wall thickness c, and stroke time n of the rod pump on flow Q are discussed. In particular, the flow Q within 1 min first increases and then slows down with the increase in stroke time n and reaches its maximum value at n = 7 r/min. Furthermore, flow Q decreases with an increase in c but increases as T w increases; c = 1.2 cm, T w = 363 K is the best oil recovery scheme.

Quantum recurrences in the kicked top

The emergence of classical chaos from an underlying quantum mechanics remains a challenging question due to the differences between dynamics driven by Schrödinger's equation versus Newton's equations. We present an infinite family of purely quantum recurrences that are not present in the classical limit of a chaotic system. They take the form of stroboscopic unitary evolutions in the quantum kicked top that act as the identity after a finite number of kicks. These state-independent recurrences are present in all finite dimensions and depend on the strength of the chaoticity parameter of the top. We further discuss the relationship of these periodicities to the quantum kicked rotor dynamics and the phenomenon of quantum antiresonance. Published by the American Physical Society 2024

Newtonian gravitational waves from a continuum

Gravitational waves are being shown to derive directly from Newtonian dynamics for a continuous mass distribution, e.g. compressible fluids or equivalent. It is shown that the equations governing a continuous mass distribution, i.e. the inviscid Navier–Stokes equations for a general variable gravitational field g ( t , x ) , are equivalent to a form identical to the Maxwell equations from electromagnetism, subject to a specified condition. The consequence of this equivalence is the creation of gravity waves that propagate at a finite speed. The latter implies that Newtonian gravitation as presented in this paper is not ‘spooky action at a distance’ but rather is similar to electromagnetic waves propagating at finite speed, despite the apparent form appearing in the integrated field formula. In addition, this proves that, in analogy to the Maxwell equations, the Newtonian gravitation equations are Lorentz invariant for waves propagating at the speed of light. Since gravitational waves were so far derived only from Einstein’s general relativity theory, it becomes appealing to check if there is a connection between the Newtonian waves presented in this paper and the general relativity type of waves at least in a certain limit of overlapping validity, i.e. as a flat-space approximation. The latter is left for follow-up research.

Agglomeration behaviors of different types of complex TiN inclusions in high titanium wear resistant steel

Large-sized titanium-containing inclusion clusters seriously affect the continuous casting and performance of high titanium wear-resistant steel. In the current work, thermodynamic calculations were firstly conducted to predict the formation of various complex TiN inclusions, viz, TiOx-TiN, Al2O3–TiN and LaAlO3–TiN. Based on that, laboratory-scale experiments were designed to prepare samples containing a single type of complex TiN inclusions. The agglomeration characterizes of different complex inclusions were compared by combing in-situ observation based on confocal laser scanning microscopy and Newtonian motion equation. Furthermore, the Kralchevsky-Paunov model was used to study the influences of density and size on the agglomeration behavior of complex TiN inclusions. The result shows that the attractive force between TiOx-TiN complex inclusions increases from 1.93 × 10−18 to 4.34 × 10−17 N, while it was 3.41 × 10−17 to 5.12 × 10−16 N for Al2O3–TiN complex inclusions and 6.42 × 10−18 to 1.14 × 10−16 N for LaAlO3–TiN inclusions. Based on the experimental results and theoretical calculation, the agglomeration tendency of Al2O3–TiN is the strongest due to the considered size and compared to the TiOx-TiN inclusions, the stronger agglomeration tendency of LaAlO3–TiN ones can be attributed to their higher density.

Development of equation of motion deciphering locomotion including omega turns of Caenorhabditis elegans.

Locomotion is a fundamental behavior of Caenorhabditis elegans (C. elegans). Previous works on kinetic simulations of animals helped researchers understand the physical mechanisms of locomotion and the muscle-controlling principles of neuronal circuits as an actuator part. It has yet to be understood how C. elegans utilizes the frictional forces caused by the tension of its muscles to perform sequenced locomotive behaviors. Here, we present a two-dimensional rigid body chain model for the locomotion of C. elegans by developing Newtonian equations of motion for each body segment of C. elegans. Having accounted for friction-coefficients of the surrounding environment, elastic constants of C. elegans, and its kymogram from experiments, our kinetic model (ElegansBot) reproduced various locomotion of C. elegans such as, but not limited to, forward-backward-(omega turn)-forward locomotion constituting escaping behavior and delta-turn navigation. Additionally, ElegansBot precisely quantified the forces acting on each body segment of C. elegans to allow investigation of the force distribution. This model will facilitate our understanding of the detailed mechanism of various locomotive behaviors at any given friction-coefficients of the surrounding environment. Furthermore, as the model ensures the performance of realistic behavior, it can be used to research actuator-controller interaction between muscles and neuronal circuits.

Development of equation of motion deciphering locomotion including omega turns of Caenorhabditis elegans

Locomotion is a fundamental behavior of Caenorhabditis elegans (C. elegans). Previous works on kinetic simulations of animals helped researchers understand the physical mechanisms of locomotion and the muscle-controlling principles of neuronal circuits as an actuator part. It has yet to be understood how C. elegans utilizes the frictional forces caused by the tension of its muscles to perform sequenced locomotive behaviors. Here, we present a two-dimensional rigid body chain model for the locomotion of C. elegans by developing Newtonian equations of motion for each body segment of C. elegans. Having accounted for friction-coefficients of the surrounding environment, elastic constants of C. elegans, and its kymogram from experiments, our kinetic model (ElegansBot) reproduced various locomotion of C. elegans such as, but not limited to, forward-backward-(omega turn)-forward locomotion constituting escaping behavior and delta-turn navigation. Additionally, ElegansBot precisely quantified the forces acting on each body segment of C. elegans to allow investigation of the force distribution. This model will facilitate our understanding of the detailed mechanism of various locomotive behaviors at any given friction-coefficients of the surrounding environment. Furthermore, as the model ensures the performance of realistic behavior, it can be used to research actuator-controller interaction between muscles and neuronal circuits.