Velocity Transformation Research Articles

New derivation of space-time linear transformation between inertial frames based on the principle of relativity

In deriving that the space-time transformation between two inertial frames is linear, one commonly relies on the premises that any inertial frame has physical properties invariant under space-time translations. We present a different derivation of linearity which is based on the principle of relativity. In fact, we show that it is possible to circumvent the discussion of linearity in deriving the space-time transformation between inertial frames. Following the principle of relativity, it is inevitable that the only transformation compatible with the principle of relativity is the Generalized Lorentz Transformation (GLT which is linear). Distinct from other derivations, we prove the existence of a universal speed limit by examining the continuity and monotonicity of the velocity transformation function. In our derivation, we do not explicitly employ the translational invariance of inertial frames as the logical starting point. Neither do we invoke the constant speed of light as a fundamental postulate. The new derivation highlights the pivotal role of the principle of relativity in logically establishing the theory of special relativity.

An improved torque sensorless speed control method for electric assisted bicycle with consideration of coordinate conversion

In this paper, we propose an improved torque sensorless speed control method for electric assisted bicycle, this method considers the coordinate conversion. A low-pass filter is designed in disturbance observer to estimate and compensate the variable disturbance during cycling. A DC motor provides assisted power driving, the assistance method is based on the real-time wheel angular velocity and coordinate system transformation. The effect of observer is proved, and the proposed method guarantees stability under disturbances. It is also compared to the existing methods and their performances are illustrated through simulations. The proposed method improves the performance both in rapidity and stability.

Continuous wavelet transformation of seismic data for feature extraction

Continuous wavelet transformation (CWT) as a new mathematical tool has provided deep insights for the identification of localized anomalous zone in the time series data set. In this study, a three-layer geological model is investigated by CWT to locate seismic reflections temporally and spatially. This model consists of three layers, where the third layers of the anticline structure are assumed to act as a pure sandstone hydrocarbon reservoir with 10% porosity. The equation of Gassmann has been implemented for the pore fluid substitution in the reservoir. Synthetic seismic data are generated for the three-layer geological model. Due to the presence of noise, it is always difficult to interpret seismic data. But, CWT has the ability of noise reduction, improving the visualization of a data set and locating the anomalies in terms of scalogram and 3D CWT coefficients. Synthetic seismic data of the geological structure are transformed by CWT. The successful transformation of P-wave velocity, synthetic seismic data and acoustic impedance inversion provided evidence to distinguish different interfaces accurately. CWT has successfully located seismic reflections by localizing high-energy spectrum within the cone of influence. Three high-energy spectrums have been identified at 0.8 s, 1 s and 1.07 s, and it exactly matches the seismic data and three-layer geological model.

Two-phase flow simulation of breaking solitary waves over surface-piercing and submerged conical structures

A two-phase flow model is employed to study three-dimensional (3D) breaking of solitary waves over surface-piercing and submerged conical structures. Details of the wave pre-breaking, overturning, and post-breaking processes are included. The governing equations are discretized by the finite volume method and the PISO algorithm is utilized for the pressure-velocity coupling. The air–water interface is captured using a volume of fluid approach and the Cartesian cut-cell method is implemented to deal with the complex topography of the conical structures. The method is validated first using available experimental data of a solitary wave propagating over a surface-piercing conical island and good agreement between the experiment and simulation data is obtained. The model is then applied to study 3D breaking waves over a submerged conical structure, with 3D wave profiles and surface velocities being presented and discussed. The detailed 3D velocity fields, energy dissipation and transformation during the wave breaking process are presented.

Numerical investigation of spatial-developing turbulent heat transfer in forced convections at different supercritical pressures

Direct numerical simulations have been adopted to study the turbulent heat transfer in forced convections of supercritical water at two different supercritical pressures P=23 MPa and P=25 MPa in a heated pipe with constant wall heat flux and a bulk Reynolds number of Re0=5400. The present study aims to reveal the mechanisms of turbulent heat transfer of superciritical fluids at different pressures in a spatial-developing flow. The results show that at the smaller pressure ratio Pr=P/Pc, where Pc is the critical pressure, the property variations become more drastic, and both the skin friction coefficient and Nusselt number become smaller. The decompositions of skin friction and Nusselt number show that it is mainly due to the large turbulence reduction along the streamwise direction. The analyses of turbulent kinetic energy (TKE), the turbulent shear stress, and the production of TKE confirm this point. Moreover, it was found that the thermophysical property fluctuations are very large and significantly influence the turbulent statistics in the supercritical fluid flows. Due to the large property fluctuations, it was found that the density-fluctuation-related terms are significant and their values are actually comparable to the mean-density-related terms. Due to their negative contributions to turbulent shear stress and turbulent heat flux, the turbulence and heat transfer are severely attenuated by the large thermophysical property fluctuations. For near-wall scaling in spatial-developing flows at supercritical pressures, the semi-local velocity transformation with a semi-local coordinate shows a better agreement in the logarithmic region. However, a clear deviation still exists, especially for mean temperature because all the transformations only incorporate the local mean property variations and cannot consider their fluctuations.

Composition of velocities and momentum transformations in a scator-deformed Lorentz metric

The transformations of coordinates, velocities and momenta between inertial frames are described via real scator algebra. This algebra imposes a hyperbolic metric that is identical to the Lorentz metric in $$1+1$$ dimensions but becomes deformed in higher dimensions. Differences in the transformations of transverse quantities arise due to this departure in two and three spatial dimensions. The structure admits velocities arbitrarily close to c in orthogonal directions, but nonetheless, the scator velocity magnitude is always subluminal. The transformation between frames is described by an isometric scator product mapping. The product operation satisfies commutative group properties in a restricted subspace. Due to these properties, a sequence of Lorentz boosts can be synthesized as a single Lorentz boost without involving a rotation. A consequence of this algebraic structure is that the scator composition of velocities does not produce a Thomas rotation. The scenarios where this deformed metric could play a relevant role have not been yet assessed.

Mean velocity and temperature scaling for near-wall turbulence with heat transfer at supercritical pressure

Compared with conventional gaseous and liquid fluids, fluids operating at supercritical pressure undergo drastic variations in thermophysical properties within a small temperature range across the pseudo-critical point. Therefore, the effect of these variations on flow and heat transfer must be studied. This paper presents direct numerical simulations (DNSs) of the turbulent heat transfer of CO2 at supercritical pressure in a fully developed channel flow between two isothermal walls. The thermophysical property tables generated from the REFPROF 9.1 database were used in this DNS. The velocity and temperature scaling and the analogy between momentum and scalar transport are comprehensively explored by using stress balance and semi-local methods. The results show that at small temperature differences, the velocity transformation developed by Trettel and Larsson [“Mean velocity scaling for compressible wall turbulence with heat transfer,” Phys. Fluids 28, 026102 (2016)] with a semi-local coordinate provides a good description of the near-wall turbulence of supercritical fluids. Upon including how large specific-heat variations affect temperature transformation, the logarithmic region of the cooled wall becomes consistent, as does the heated wall in a certain temperature range. In addition, in near-wall turbulence with small temperature differences at supercritical pressure, momentum transport is highly analogous to scalar transport.

Wake events during early three-dimensional transition of a circular cylinder placed in shear flow

Three-dimensional (3D) direct numerical simulations are carried out for shear flows past a circular cylinder in the early 2D (two-dimensional)–3D transition regime. The effect of incoming shear is buried in a source term employing a velocity transformation. Wake transition events are inspected for both planar and span-wise shear flows. Parallel, time-mean-symmetric shedding for planar shear and oblique vortex shedding for span-wise shear are observed with a near wake roll-up vortical structure. Vortex splits and dislocations are found without any order in time for moderate shear, while they give way to visibly higher levels of instabilities at higher shear rates. Mode “B” instabilities are noted for planar shear, while opposite streamwise vortices align in parallel horizontal layers for span-wise shear. Local Strouhal frequency (Stz) drops inside a span-wise cell for span-wise shear with finite jumps across cell boundaries. Wavelet multiresolution analysis indicates a strong flushing effect, triggered by vortex dislocations, which gives rise to a new frequency event. The dominant span-wise mode indicates periodic forcing of mode “A” instabilities at a rate close to the inverse of local Strouhal number. In contrast, the streamwise velocity modes result in a global span-wise similarity. Intrinsic secondary instabilities play a vital role in span-wise shear cases. The addition of planar shear makes the downstream defect layer nearly span-wise-invariant. However, the velocity defect is entirely controlled by the span-wise shear. The momentum thickness exhibits streamwise growth, similar to the Blasius profile. The shape factor of such profiles indicates a delay in laminar–turbulent transition for span-wise shear.

The Clock Riddle and Einstein’s Third Postulate of Special Relativity

The present work calls attention to an undeclared assumption made by Einstein in his landmark paper [Ann. Physik 322 (10), 891 (1905)] in which he introduced the Special Theory of Relativity (STR). The emphasis in textbooks and periodicals is always on his two postulates of relativity [the Relativity Principle (RP) and the constancy of the speed of light in free space]. Yet, the well-known results of his theory such as Fitzgerald-Lorentz length contraction (FLC) and the symmetry of time dilation (two clocks in motion each running slower than the other) are based exclusively on this third postulate. It is shown that an alternative assumption of clock-rate proportionality (Newtonian Simultaneity) is also consistent with Einstein’s first two postulates and with the Relativistic Velocity Transformation (RVT), but that it leads to a fundamentally different space-time transformation than the Lorentz Transformation (LT) of STR. It is referred to as the Newton-Voigt Transformation (NVT). Its predictions regarding length and time measurements by moving observers differ sharply from those of the LT. A “clock riddle,” distinct from the well-known “clock paradox,” is presented to underscore the differences between these two versions of the relativistic space-time transformation. It is shown that the NVT is consistent with remote simultaneity and the impossibility of time inversion, and therefore does not rule out the existence of faster-than-c particles under the condition that they have null proper mass

PRE STACK DEPTH MIGRATION UNTUK KOREKSI EFEK PULL UP DENGAN MENGGUNAKAN METODE HORIZON BASED DEPTH TOMOGRAPHY PADA LAPANGAN ‘A1 DAN A2’

In the case of seismic data processing with sandstone lithology such as shale and carbonate often get the result of data processing which have pull up effect especially on the time domain migration result. Pre stack depth migration is a processing based on focusing the amplitude according to the actual depth by using the input interval velocity. Migration is performed using kirchhoff pre stack depth migration algorithm. Pre stack depth migration is done with modeling of horizontal based depth tomography method. This method uses residual moveout correction applied along the horizon-picking line. This research uses two field data that is A1 and A2 Field. A1field has characteristics of carbonate rock that produce pull up shaped similar to carbonate layer. A2 field has a pull-up effect that is not very clear but has build up because of the layer above it. Stages performed starting from the processing of pre stack time migration in the form of velocity picking, generate rms velocity and migration time domain. The pre stack depth migration process begins with a velocity transformation with the dix transformation equation to generate interval velocity, migrate Pre stack depth migration, perform horizon interpretations and perform velocity modeling using the horizon based depth tomography method. The iteration is done 4 times and resulted in the final section of pre stack depth migration which has been corrected by pull up effect.

Linear Regression under Special Relativity

This study investigated the problem posed by using ordinary least squares (OLS) to estimate parameters of simple linear regression under a specific context of special relativity, where an independent variable is restricted to an open interval, (-c, c). It is found that the OLS estimate for the slope coefficient is not invariant under Lorentz velocity transformation. Accordingly, an alternative estimator for the parameters of linear regression under special relativity is proposed. This estimator can be considered a generalization of the OLS estimator under special relativity; when c approaches to infinity, the proposed estimator and its variance converges to the OLS estimator and its variance, respectively. The variance of the proposed estimator is larger than that of the OLS estimator, which implies that hypothesis testing using the OLS estimator and its variance may result in a liberal test under special relativity.

Barrier-Lyapunov Function based Dynamic Surface Control of Quad-Rotorcraft

Abstract A novel framework is proposed in this paper for control of a quad-rotorcraft where hierarchical design is constructed via barrier Lyapunov function (BLF) combined with dynamic surface control (DSC). DSC solves the requirement of higher order differentiability of reference pose and avoiding the complexity that arises due to the “explosion of terms” coming out from repeated derivatives of reference attitude and desired thrust vector. BLF satisfies attitude constraint in real-time and thereby ensures non-singularity of velocity transformation leading to feasible control design. Stability analysis shows that all the signals in the closed-loop system are uniformly ultimately bounded and tracking error converges asymptotically. The performance of the BLF-based DSC is illustrated with a suitable example.

Trajectory tracking control algorithm in terms of quasi-velocities for a class of vehicles

This paper studies the problem of trajectory tracking control for a class of vehicles (underwater vehicles, some horizontally moving vehicles, indoor airships). The control development is based on some velocity transformation arising from the inertia matrix decomposition, Lyapunov’s direct method and a non-adaptive nonlinear tracking controller in terms of the Generalized Velocity Components (GVC). In the nonlinear controller the control gains are strictly related to the vehicle dynamics (especially dynamical couplings). The general algorithm is presented for a 6 DOF vehicle. In the simulation two trajectories were tested. Moreover, one robustness test was done (corresponding to robustness issue considered in this work). The simulation results obtained for a full airship model show that the proposed control scheme guarantees satisfactory performance.

Impedance inversion of pre-stack seismic data in the depth domain

The extensive application of pre-stack depth migration has produced huge volumes of seismic data, which allows for the possibility of developing seismic inversions of reservoir properties from seismic data in the depth domain. It is difficult to estimate seismic wavelets directly from seismic data due to the nonstationarity of the data in the depth domain. We conduct a velocity transformation of seismic data to make the seismic data stationary and then apply the ridge regression method to estimate a constant seismic wavelet. The estimated constant seismic wavelet is constructed as a set of space-variant seismic wavelets dominated by velocities at different spatial locations. Incorporating the weighted superposition principle, a synthetic seismogram is generated by directly employing the space-variant seismic wavelets in the depth domain. An inversion workflow based on the model-driven method is developed in the depth domain by incorporating the nonlinear conjugate gradient algorithm, which avoids additional data conversions between the time and depth domains. The impedance inversions of the synthetic and field seismic data in the depth domain show good results, which demonstrates that seismic inversion in the depth domain is feasible. The approach provides an alternative for forward numerical analyses and elastic property inversions of depth-domain seismic data. It is advantageous for further studies concerning the stability, accuracy, and efficiency of seismic inversions in the depth domain.

Tree-topology-oriented modeling for the real-time simulation of sedan vehicle dynamics using independent coordinates and the rod-removal technique

Multibody dynamics of vehicle systems can be simulated in real time using semi-recursive-based formulations and their various versions, which are normally described in terms of relative coordinates. To efficiently and accurately simulate closed-loop vehicle multibody systems, a semi-recursive formulation must be optimally combined with a numerical integration algorithm. Although a significant number of contributions has been reported in this field, there is still a need to improve accuracy and computational efficiency of real-time or faster-than-real-time simulation. This paper focuses on the loop-closure techniques that can be used when modeling vehicle systems. Consequently, a canonical tree topology is introduced to take advantage of recursive kinematics and dynamics. To this end, real-time vehicle simulations are performed based on a semi-recursive formulation and a tree-topology-oriented modeling method. The applied semi-recursive formulation makes use of double velocity transformation and independent coordinates. The introduced canonical tree topology is generated via joint-cut and rod-removal techniques. The structures of the canonical tree topologies are studied in terms of bodies, joints, constraint equations and branches. How they affect solution accuracy and computational efficiency is investigated in detail. For numerical examples, a 15-degree-of-freedom sedan vehicle model is analyzed and simulated using the semi-recursive formulation and a 4th-order Runge–Kutta algorithm in various system-tree topology cases. The results highlight the efficiency gain of the tree-topology-oriented modeling method.

Simulating anisotropic flows with isotropic lattice models via coordinate and velocity transformation

We propose a rectangular lattice Boltzmann model for anisotropic flows based on coordinate and velocity transformation. Unlike other existing rectangular models which tuned the lattice Boltzmann algorithm to fit the rectangular or cuboid lattice grids, here we apply the general lattice Boltzmann method to solve the transformed system over regular square lattice grids. The method is tested with simulations of representative anisotropic flows, including flows in narrow straight and wavy channels, the Taylor–Green vortex flow, and the flow through an elliptical particle array. These simulations show that in general our method produces satisfactory results; however, the aspect ratio [Formula: see text] is limited to relatively large values ([Formula: see text]). The effects of [Formula: see text] on simulation accuracy and stability have been carefully examined, and a possible remedy to improve these concerns has been proposed. The method and analysis could be useful for future development of more robust and practical anisotropic lattice Boltzmann models for realistic simulations.

Micro-PIV and numerical study on influence of vortex on flow and heat transfer performance in micro arrays

In this paper, Micro-Particle Image Velocimetry (Micro-PIV) system has been used to visualize the flow properties of deionized water flowing across circular, ellipse and diamond micro pin-fin arrays with Reynolds number situated between 100 and 400. While Fluent 15.0 is used to simulate the velocity distribution, streamline patterns and temperature distribution around micro pin-fin arrays. Micro-PIV results and simulation outcomes have been compared to investigate the flow and heat transfer characteristics of micro pin-fin arrays. Among three types of pin-fins, backflow occurs firstly at the tail of circular pin-fins and wake vortices form gradually, then the structure of the vortex gradually lengthens. The velocity and pressure transformation along the single pin-fin is a decompression acceleration region at first and turns into a pressurization deceleration from the middle to the tail of pin-fin. The area of higher temperature region of vortices at the back of circular pin-fin is the largest, which results in better heat transfer performance.

Inverse modeling approach for transformation of propeller shaft angular deformation and velocity to propeller torque load

In full-scale trials or model-scale tests, the propeller torque load is typically measured indirectly on the propeller shaft. Due to structural flexibility and mass of the propeller and propeller shaft, the measured propeller shaft torque response includes a time delay and amplitude difference compare to the propeller load. These differences are usually small during propeller operation, but may be significant during transient states (i. e. starting of the engine, rough sea, or operation in ice-covered waters). In this paper, an inverse model is used to calculate propeller load based on the propeller shaft response. The results indicate that the inverse model can be less complex than the complete propulsion machinery model and consider only the propeller and propeller shaft. Several modeling approaches are tested based on four proposed measuring setups and three forms of system discretization. Out of five inverse modeling approaches, two approaches showed the ability to transform measured propeller shaft angular deformation and velocity responses, colored with noise, into the corresponding rule-based propeller torque load with acceptable accuracy. Furthermore, the robustness of the inverse approaches to the random ice-propeller interaction, sampling frequency, measuring location along the propeller shaft and starting time (before and during ice-propeller interaction), is discussed.

A striatal interneuron circuit for continuous target pursuit

Most adaptive behaviors require precise tracking of targets in space. In pursuit behavior with a moving target, mice use distance to target to guide their own movement continuously. Here, we show that in the sensorimotor striatum, parvalbumin-positive fast-spiking interneurons (FSIs) can represent the distance between self and target during pursuit behavior, while striatal projection neurons (SPNs), which receive FSI projections, can represent self-velocity. FSIs are shown to regulate velocity-related SPN activity during pursuit, so that movement velocity is continuously modulated by distance to target. Moreover, bidirectional manipulation of FSI activity can selectively disrupt performance by increasing or decreasing the self-target distance. Our results reveal a key role of the FSI-SPN interneuron circuit in pursuit behavior and elucidate how this circuit implements distance to velocity transformation required for the critical underlying computation.

The transformation of the affine velocityand its application to a rotating disc

The aim of the article is to find a transformation that links the local affine velocity of a non-rigid body in the laboratory inertial reference frame $ S $ with the centro-affine velocity of motion of this body in the accompanying accelerated frame $ k $. This paper is based on the kinematics of a continuous medium and the generalized Lorentz transformation. In this paper we show the 3D transformation of velocity linking the reference system $ S $ and the reference system $ k $, which moves without rotation. Wherein the motion of various points of the rigid system $ k $ is inhomogeneous. Using these formulas, we obtain the desired direct and inverse transformation of the local affine velocity. Important special cases of this transformation are considered. They are the motion of particles in a uniform force field and the precession of Thomas. As an example of using the transformation of affine velocity in $ S $, accelerated rotation of the disk was considered and the local angular velocity and the magnitude of the deformation of its points were calculated. Wherein, the calculated stretching coefficient is consistent with the known one, and the formula found for the angular velocity is more general than the earlier result obtained for uniform rotation of the disk.