Higher Time Derivatives Research Articles

Binary Dynamics through the Fifth Power of Spin at O(G^{2}).

We use a previously developed scattering-amplitudes-based framework for determining two-body Hamiltonians for generic binary systems with arbitrary spin S. By construction this formalism bypasses difficulties with unphysical singularities or higher-time derivatives. This framework has been previously used to obtain the exact velocity dependence of the O(G^{2}) quadratic-in-spin two-body Hamiltonian. We first evaluate the S^{3} scattering angle and two-body Hamiltonian at this order in G, including not only all operators corresponding to the usual worldline operators, but also an additional set due to an interesting subtlety. We then evaluate S^{4} and S^{5} contributions at O(G^{2}) which we confirm by comparing against aligned-spin results. We conjecture that a certain shift symmetry together with a constraint on the high-energy growth of the scattering amplitude specify the Wilson coefficients for the Kerr black hole to all orders in the spin and confirm that they reproduce the previously obtained results through S^{4}.

Sub-optimal Solution of the Inverse Kinematic Task of Redundant Robots without Using Lagrange Multipliers

In the paper a novel approach is suggested for solving the inverse kinematic task of redundant open kinematic chains. Traditional approaches as the Moore-Penrose generalized inverse-based solutions minimize the sum of squares of the timederivative of the joint coordinates under the constraint that contains the task itself. In the vicinity of kinematic singularities where these solutions are possible the hard constraint terms produce high time-derivatives that can be reduced by the use of a deformation proposed by Levenberg and Marquardt. The novel approach uses the basic scheme of the Receding Horizon Controllers in which the Lagrange multipliers are eliminated by direct application of the kinematic model over the horizon in the role of the ”control force”, and no reduced gradient has to be computed. This fact considerably decreases the complexity of the solution. If the cost function contains penalty for high joint coordinate time-derivatives the kinematic singularities are ab ovo better handled. Simulation examples made for a 7 degree of freedom robot arm demonstrate the operation of the novel approach. The computational need of the method is still considerable but it can be further decreased by the application of complementary tricks.

Fermat’s principle and the effect of jerk on light motion near the Sun

In classical mechanics, in the case of gravitational and electromagnetic interactions, the force on a particle is usually proportional to its acceleration: The force acts locally on the particle. However, there are situations possible-if the particle moves through a suitable medium, for example, in which the force depends also on the first-time derivative of its acceleration, the jerk, and on its second-time derivative, the snap, and possibly also on higher-time derivatives. Such forces are called nonlocal, and this work investigates such nonlocal forces, mainly those depending on the jerk. In particular, we implement jerk and acceleration in geodesics by means of the nonlocal-in-time kinetic energy approach to spacetime physics. We describe a framework that can be used to estimate the quantum nonlocal time parameter by studying the deflection of light around the Sun. Comparing our results with long baseline interferometry (VLBI) observations, we concluded that the nonlocal time parameter [Formula: see text] s.

Ostrogradsky instability can be overcome by quantum physics

In theories with higher time derivatives, the Hamiltonian analysis of Ostrogradsky predicts an instability. However, this Hamiltonian treatment does not correspond the way that these theories are treated in quantum field theory, and the instability may be avoided in at least some cases. We present a very simple model which illustrates these features.

Statistics on Omega Band Properties and Related Geomagnetic Variations

AbstractUsing the list of the omega structures based on the Magnetometers‐Ionospheric Radars‐All‐sky Cameras Large Experiment network (Partamies et al., 2017, https://doi.org/10.5194/angeo-35-1069-2017), we obtained a number of important statistical characteristics describing the surface magnetic field. Based on 438 events, typical magnetic variations associated with the passage of the single omega were obtained. The typical variation, obtained using superposed epoch analysis, is associated with a local bending of the westward electrojet and statistically confirms the distribution of equivalent ionospheric currents obtained in earlier observations of single omegas. It was found that during low and moderate geomagnetic activity, the appearance of the omega structures in the dark morning magnetic local time (MLT) sector results in two times higher than average dB/dt on the ground surface. Also, the velocity, direction of movement, and area of omega structures were calculated. It is shown that faster and bigger omegas produce larger time derivatives of the ground magnetic field. Furthermore, we demonstrate that in the 03–08 MLT sector, superposed magnetic variations for the arbitrary events of very high time derivatives |dB/dt| > 10 nT/s, reveal magnetic signatures similar to omegas. Our findings, together with the results described by Apatenkov et al. (2020, https://doi.org/10.1029/2019gl086677), emphasize the important role of omega structures in the formation of large geomagnetically induced currents.

On the Planning and Construction of Railway Curved Track

Increasing demand for railway vehicle speed has pushed the railway track designers to develop high-quality track. An important measure of track quality is the character of the transition curve track connecting different intersecting straight tracks. A good transition curve track must be able to negotiate the intermittent stresses and dynamic effects caused by changes in lateral acceleration at high speed. This paper presents the constructional methods for planning transition curves considering the dynamics of movement. These methods consider the non-compensated lateral acceleration, deviation in lateral acceleration and its higher time derivatives. This paper discusses the laying methods of circular, vertical and transition curves. Key aspects in laying a curved track e.g. widening of gauge on curves are discussed in this paper. This paper also suggests a transition curve which is effective not only from a dynamic point of view considering lateral acceleration and its higher time derivative but also consider the geometric conditions along with the required deflection angle.

Numerical solution of Showalter–Sidorov and Cauchy problems of ion–acoustic waves propagation mathematical model

The paper deals with the problem of numerical investigation of semilinear mathematical model of ion-acoustic waves propagation in plasma. The research is based on the previous study of solvability of the Cauchy problem for an abstract semilinear Sobolev type equation of higher order. The theory of relatively polynomially bounded operator pencils, the theory of differentiable Banach manifolds, and the phase space method are used for analytical study of the model. Projectors splitting spaces into direct sums of subspaces are constructed. Given equation is reduced to a system of two equations. One of them determines the phase space of the initial equation, and its solution is a function with values from the eigenspace of the operator at the highest time derivative. The solution of the second equation is the function with values from the image of the projector. Moreover, in the second section, the sufficient conditions for the solvability of the abstract problem under study are presented. These results are applied to the mathematical model of ion-acoustic waves in plasma which is based on the fourth-order equation with a singular operator at the highest time derivative. Reducing the matematical model to an abstract problem, we obtain sufficient conditions for the existence of unique solution. The results of analytical investigation of the Showalter – Sidorov problem which is more natural for Sobolev type equations are also presented in this section. The Galerkin method is used for numerical study of the model. An algorithm for the numerical solution of the Showalter – Sidorov problem for the model of ion-acoustic waves in plasma is described in the last section.

A novel model of nonlocal thermoelasticity with time derivatives of higher order

The objective of this work is to introduce a new system of differential equations describing the nonlocal thermoelasticity theory with higher time derivatives and two‐phase lags. In order to obtain this model, we used the nonlocal continuum theory proposed by Eringen and the methodology of the Taylor series expansion of higher‐order time derivatives. Some generalized thermoelasticity theories follow as limited cases. This model is used to study the thermoelastic interaction in a nonlocal medium. The medium is exposed to an applied magnetic field and a periodic time heat source with a constant strength. Some comparisons have been displayed in figures to estimate the influences of the nonlocal parameter and magnetic field as well as the parameters of higher‐order on all the field quantities.

Quantum Correction for Newton’s Law of Motion

A description of the motion in noninertial reference frames by means of the inclusion of high time derivatives is studied. Incompleteness of the description of physical reality is a problem of any theory, both in quantum mechanics and classical physics. The “stability principle” is put forward. We also provide macroscopic examples of noninertial mechanics and verify the use of high-order derivatives as nonlocal hidden variables on the basis of the equivalence principle when acceleration is equal to the gravitational field. Acceleration in this case is a function of high derivatives with respect to time. The definition of dark metrics for matter and energy is presented to replace the standard notions of dark matter and dark energy. In the Conclusion section, problem symmetry is noted for noninertial mechanics.

Experimental investigation of perpetual points in mechanical systems

In dissipative dynamical systems, equilibrium (stationary) points have a dominant organizing effect on transient motion in phase space, especially in nonlinear systems. These time-independent solutions are readily defined in the context of ordinary differential equations, that is, they occur when all the time derivatives are simultaneously zero. However, there has been some recent interest in perpetual points: points at which the higher time derivatives are zero, but not necessarily the first. Previous work has focused on analytic work (including simulation) and some experimental studies of electric circuits. This paper focuses attention on the occurrence of these points in a simple mechanical system, including experimental verification. Thus, points of zero acceleration can be found in which the corresponding velocity is a maximum or minimum, but not zero. Specifically, the rigid-arm pendulum is used to generate data for which acceleration (and its derivative) can be evaluated. In this paper an experimental (mechanical) setup is described, specifically designed to investigate perpetual points, including a description of the data analysis approaches developed to identify their location.

Problem with Integral Conditions in the Time Variable for a Sobolev-Type System of Equations with Constant Coefficients

In a domain obtained as a Cartesian product of an interval [0,T] and the space ℝ p , p ∈ ℕ, for a system of equations (with constant coefficients) unsolved with respect to the highest time derivative, we study the problem with integral conditions in the time variable for a class of functions almost periodic in the space variables. A criterion of uniqueness and sufficient conditions for the existence of solution of this problem in different functional spaces are established. We use the metric approach to solve the problem of small denominators encountered in the construction of the solution.

Quantum gravity and renormalization

The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

Математические модели нелинейных продольно-поперечных колебаний объектов с движущимися границами

Произведены нелинейные постановки задач, описывающих продольно-поперечные колебания объектов с движущимися границами. Полученные математические модели состоят из системы двух нелинейных дифференциальных уравнений в частных производных с наибольшей производной по времени второго порядка и по пространственной переменной - четвeртого порядка. Нелинейные условия на движущейся границе имеют максимальную производную по времени второго порядка и по пространственной переменной третьего порядка. Учтены геометрическая нелинейность, вязкоупругость, изгибная жeсткость колеблющегося объекта, а также упругость подложки, на которой расположен объект. Получены граничные условия в случае наличия энергетического обмена между частями объекта слева и справа от движущейся границы. Движущаяся граница имеет присоединeнную массу. Учтeн упругий характер присоединения границы. С помощью полученной математической модели описываются продольно-поперечные колебания большой интенсивности объектов с движущимися границами. При получении математических моделей использован вариационный принцип Гамильтона.

Higher time derivatives in effective equations of canonical quantum systems

Quantum-corrected equations of motion generically contain higher time derivatives, computed here in the setting of canonically quantized systems. The main example in which detailed derivations are presented is a general anharmonic oscillator, but conclusions can be drawn also for systems in quantum gravity and cosmology.

Higher-time derivative of in-depth temperature sensors for aerospace heat transfer

This paper presents a novel sensor that delivers higher-time derivatives of temperature in combination with a thermocouple calibration curve. This highly attractive quantity has been demonstrate to be of critical importance for acquiring both stable and accurate surface and in-depth heat fluxes, predicting sudden changes in surface heat fluxes without inverse analysis, and predicting the future temperature in a thermal control environment. This paper outlines the motivation for developing such a sensor, presents the salient and poignant features of the initial design and processes required for arriving at the sensor while incurring minimal component delay times. Finally, preliminary predictions are presented using an experimental thermocouple drop facility that allows for comparison with an analytic model. The presented results are highly encouraging for stability, accuracy and repeatability.

<i>In Situ</i> Higher-Time Derivative of Temperature Sensors for Aerospace Heat Transfer

This paper presents a novel sensor that delivers, in combination with a thermocouple calibration curve, higher-time derivatives of temperature. This paper provides motivation for developing such a sensor, presents the salient and poignant features of the initial design and processes required for arriving at the sensor while incurring minimal component delay times (lag time), and displays preliminary predictions using an experimental thermocouple drop facility that allows for comparison with an analytic model. The presented results are highly encouraging for stability, accuracy and repeatability.

Boundary-value problem for equations with variable coefficients unsolvable with respect to the higher time derivative

In a cylindrical domain, we study the unique solvability of a boundary-value problem with data given on the whole boundary of the domain for a certain class of linear equations with partial higher-order derivatives that are unsolvable with respect to the higher time derivative with variable coefficients depending on spatial coordinates. The obtained results are transferred to the case where the equation is perturbed by a nonlinear term in the linear part.

The higher time derivatives of the generalized liapunov function

Using the generalized N-body expression for a Liapunov functional developed by Prigogine and coworkers, a condition is obtained whereby the successive time derivatives of this function alternate in sign for weakly coupled systems. This generalized Liapunov function contains contributions from the diagonal as well as off-diagonal (correlation) components of the density matrix. The alternating sign condition is applied (and seen to hold true) for the cases of elastic phonon scattering in a lattice, three-phonon scattering (the anharmonic lattice), and the quantum electron gas. It is also proved simply for the Friedrichs model.

Weighted power counting and Lorentz violating gauge theories. I: General properties

We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at large momenta, but no higher time derivatives. We show that the regularity of the gauge-field propagator privileges a particular spacetime breaking, the one into space and time. We then concentrate on the simplest class of models, study four dimensional examples and discuss a number of issues that arise in our approach, such as the low-energy recovery of Lorentz invariance.

Weighted scale invariant quantum field theories

We study a class of Lorentz violating quantum field theories that contain higher space derivatives, but no higher time derivatives, and become renormalizable in the large N expansion. The fixed points of their renormalization-group flows provide examples of exactly "weighted scale invariant" theories, which are noticeable Lorentz violating generalizations of conformal field theories. We classify the scalar and fermion models that are causal, stable and unitary. Solutions exist also in four and higher dimensions, even and odd. In some explicit four dimensional examples, we compute the correlation functions to the leading order in 1/N and the critical exponents to the subleading order. We construct also RG flows interpolating between pairs of fixed points.