Instantaneous Part Research Articles

New avenue for accurate analytical waveforms and fluxes for eccentric compact binaries

We introduce a new paradigm for constructing accurate analytic waveforms (and fluxes) for eccentric compact binaries. Our recipe builds on the standard Post-Newtonian (PN) approach but (i) retains implicit time-derivatives of the phase space variables in the instantaneous part of the noncircular waveform, and then (ii) suitably factorizes and resums this partly PN-implicit waveform using effective-one-body (EOB) procedures. We test our prescription against the exact results obtained by solving the Teukolsky equation with a test-mass source orbiting a Kerr black hole, and compare the use of the exact vs PN equations of motion for the time derivatives computation. Focusing only on the quadrupole contribution, we find that the use of the exact equations of motion yields an analytical/numerical agreement of the (averaged) angular momentum fluxes that is improved by $40\%$ with respect to previous work, with $4.5\%$ fractional difference for eccentricity $e=0.9$ and black hole dimensionless spin $-0.9\leq \hat{a}\leq +0.9$. We also find a remarkable convergence trend between Newtonian, 1PN and 2PN results. Our approach carries over to the comparable mass case using the resummed EOB equations of motion and paves the way to faithful EOB-based waveform model for long-inspiral eccentric binaries for current and future gravitational wave detectors.

Modelling the Delayed Nonlinear Fiber Response in Coherent Optical Communications

Fiber nonlinearities, that lead to nonlinear signal interference (NLI), are typically regarded as an instantaneous material response with respect to the optical field. However, in addition to an instantaneous part, the nonlinear fiber response consists of a delayed contribution, referred to as the Raman response. The imaginary part of its Fourier transform, referred to as the Raman gain spectrum, leads to inter-channel stimulated Raman scattering (ISRS). ISRS is a nonlinear effect that redistributes optical power from high to lower frequencies during propagation. However, as the nonlinear fiber response is causal, the Raman spectrum obeys the Kramers-Kronig relations resulting in the real part of the complex valued Raman spectrum. While the impact of the imaginary part (i.e. ISRS) is well studied, the direct implications of its associated real part on the NLI are unexplored. In this work, a theory is proposed to analytically quantify the impact of the real Raman spectrum on the nonlinear interference power. Starting from a generalized Manakov equation, an extension of the ISRS Gaussian Noise (GN) model is derived to include the real Raman spectrum and, thus, to account for the complete nonlinear Raman response. Accurate integral expressions are derived and approximations in closed-form are proposed. Different formulations for the case of single -and dual polarized signals are derived and novel analytical approximations of the real Raman spectrum are proposed. Moreover, it is analytically shown that the real Raman spectrum scales the strength of the instantaneous nonlinear distortions depending on the frequency separation of the interacting frequencies. A simple functional form is derived to assess the scaling of the NLI strength. The proposed theory is validated by numerical simulations over C-and C+L band, using experimentally measured fiber data.

Study on Rotary Bending Forming Process of Torsional Damper Shell Pulley

To study the integral forming process of torsion damper shell pulley with characteristic structure is of great significance for producing and developing of the rotational part such as shell pulley. A processing way was proposed by combining plate bending forming and roller structure design, to integral forming torsion damper shell pulley. A model for two-step bending forming was establishedvia finite element method. Under the radial feeding of roller, the outer edge of plate was subjected to compress thickening and secondary thickened after bending, and effective stress and metal flow in the deformation zone were analyzed by using marking point. Combining with the structural characteristics of shell pulley, a design criterion "rotating thickening, gathering thickening" of roller was proposed. The metal flow in deformation zone was effectively controlled through the characteristic structure of roller, thereby the specific region to forming multi-wedge toothwas obtained. The quantitative analysis of the instantaneous part section in the forming process, combining with the design criteria of roller structure and material flow rate, radius and arc angle of roller were determined. With the objective forming parameters, the comparison between the simulation results and the experimental are basically coincided, the ribs were fully formed and the specific regions was thickened to minimum value, which verified the feasibility of sheet-bulk metal rotary bending forming theory and the design criterion of roller structure.

Schwinger-Dyson equations in Coulomb gauge consistent with numerical simulation

In the present work we undertake a study of the Schwinger-Dyson equation (SDE) in the Euclidean formulation of local quantum gauge field theory, with Coulomb gauge condition $\partial_i A_i = 0$. We continue a previous study which kept only instantaneous terms in the SDE that are proportional to $\delta(t)$ in order to calculate the instantaneous part of the time component of the gluon propagator $D_{A_0 A_0}(t, R)$. We compare the results of that study with a numerical simulation of lattice gauge theory and find that the infrared critical exponents and related quantities agree to within 1\% to 3\%. This raises the question, "Why is the agreement so good, despite the systematic neglect of non-instantaneous terms?" We discovered the happy circumstance that all the non-instantaneous terms are in fact zero. They are forbidden by the symmetry of the local action in Coulomb gauge under time-dependent gauge transformations $g(t)$. This remnant gauge symmetry is not fixed by the Coulomb gauge condition. The numerical result of the present calculation is the same as in the previous study; the novelty is that we now demonstrate that all the non-instantaneous terms in the SDE vanish. We derive some elementary properties of propagators which are a consequence of the remnant gauge symmetry. In particular the time component of the gluon propagator is found to be purely instantaneous $D_{A_0 A_0}(t, R) = \delta(t) V(R)$, where $V(R)$ is the color-Coulomb potential. Our results support the simple physical scenario in which confinement is the result of a linearly rising color-Coulomb potential, $V(R) \sim \sigma R$ at large $R$.

Froude-Krylov forces from exact pressure integrations on adaptive panel meshes in a time domain partially nonlinear model for ship motions

A partially nonlinear time domain model for predicting ship motions is presented with Froude-Krylov forces being calculated on the exact instantaneous wet part of the floating body. An adaptive mesh technique following a quad-tree subdivision and cutting scheme is applied, in order to track the free-surface of the undisturbed wave, and its intersection with the hull, to generate instantaneous wet meshes. Analytical exact pressure integration expressions are evaluated on the, thus formed, wet panel mesh, regarding the undisturbed wave and hydrostatic pressures, which allow for considerably coarse meshes without any loss of accuracy. Diffraction and radiation forces are kept linear with the latter being introduced using linear unit impulse response functions. The body is impeded from drifting by artificial kinematic restrains in non-restoring modes.Roll decay motions of a military vessel's hull, and under head, beam and quartering waves are numerically predicted and compared with published experimental ones, for zero advance speed. The capabilities and limitations of the proposed method, taking into account the specific simulation setup applied, are addressed. An overall agreement with the experiments is witnessed, with the method showing a considerable improvement of numerical predictions of the ship motions in beam and quartering waves in comparison with those by a linear method.

A unified micromechanics-based damage model for instantaneous and time-dependent behaviors of brittle rocks

This paper presents a unified micromechanics-based damage model for instantaneous and time-dependent inelastic behaviors of brittle rocks subjected to compressive stresses. The constitutive model is formulated in a combined homogenization/thermodynamics framework. The inelastic deformation is induced by frictional sliding along closed cracks, and strongly coupled with damage evolution by crack growth. Material degradation is described by a scalar-valued internal damage variable that is decomposed into two parts: an instantaneous part induced by applied stresses and a time-dependent part by subcritical cracking due to stress corrosion. Based on the system free energy determined with the Mori–Tanaka homogenization scheme, we propose a Coulomb-type friction criterion, which serves simultaneously as the yielding function and plastic potential, implying the use of an associated flow rule. An instantaneous damage criterion based on the conjugated force associated with the damage variable and a time-dependent damage criterion in terms of progressive evolution of microstructure are introduced. For the latter, an efficient computational algorithm is explored to solve numerically the strain history-dependent integration. As the first phase of validation, the proposed model is finally applied to simulate two typical brittle rocks, Dagangshan diabase and Xiangjiaba sandstone.

Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms

We compute the instantaneous contributions to the spherical harmonic modes of gravitational waveforms from compact binary systems in general orbits up to the third post-Newtonian order. We further extend these results for compact binaries in quasi-elliptical orbits using the 3PN quasi-Keplerian representation of the conserved dynamics of compact binaries in eccentric orbits. Using the multipolar post-Minkowskian formalism, starting from the different mass and current type multipole moments, we compute the spin weighted spherical harmonic decomposition of the instantaneous part of the gravitational waveform. These are terms which are functions of the retarded time and do not depend on the history of the binary evolution. Together with the hereditary part, which depends on the binary's dynamical history, these waveforms form the basis for construction of accurate templates for the detection of gravitational wave signals from binaries moving in quasi-elliptical orbits.

Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index

The axial dependence of femtosecond filamentation in air is measured under conditions of varying laser pulsewidth, energy, and focusing f-number. Filaments are characterized by the ultrafast z-dependent absorption of energy from the laser pulse and diagnosed by measuring the local single cycle acoustic wave generated. Results are compared to 2D + 1 simulations of pulse propagation, whose results are highly sensitive to the instantaneous (electronic) part of the nonlinear response of N2 and O2. We find that recent measurements of the nonlinear refractive index (n2) in Wahlstrand et al (2012 Phys. Rev. A 85 043820) provide the best match and an excellent fit between experiments and simulations.

Experimental investigation on uniaxial tensile creep behavior of cracked steel fiber reinforced concrete

This paper mainly investigates the uniaxial tensile creep behavior of pre-cracked steel fiber reinforced concrete. Hooked-end fiber RC65/60BN with fiber dosage of 80 kg/m3 was used with normal strength concrete. A suitable tensile creep frame and a pre-cracking test set-up were developed. Cylindrical specimens were pre-cracked at crack opening displacement (COD) of 0.05 and 0.2 mm respectively before the tensile creep test. The pre-cracked specimens were loaded at a load level of 30 % of the maximum pre-cracking load \(P_{\max }\). The specimens were unloaded after 3 months and then reloaded to 60 % of \(P_{\max}\). Time dependent COD were continuously measured by LVDTs under constant temperature of 20° and relative humidity of 60 %. The measured time dependent COD \(W_{\rm total}\) was considered as the summation of three parts, the irreversible part \(W_{\rm irr}\), the instantaneous part \(W_{\rm inst}\) and the creep part \(W_{\rm creep}\). It was observed that \(W_{\rm irr}\) and the loading level have a great impact on the tensile creep behavior. For the specimens with a pre-cracking COD of 0.05 mm, the maximum creep deformation \(W_{\rm creep}\) is almost the same as the initial instantaneous deformation \(W_{isnt.}\) after 3 months loading. For the specimens pre-cracked at 0.2 mm, the damage evolution at the fibre/matrix interface in terms of irreversible crack opening and load level is also discussed. It is interesting to be noted that the creep deformation under load level of 30 % will not introduce extra damage even though the \(W_{\rm irr}\) increases.

Modified constitutive equation for quasi-linear theory of viscoelasticity

The constitutive equation of the quasi-linear theory of viscoelasticity is modified with the view to simplify our understanding of the physical meaning of numerous kernel functions. In the resulting equation, the instantaneous and the regular parts have the same structure, and the instantaneous part coincides with the well-known constitutive equation of the nonlinear theory of elasticity.

Line-Interactive Single-Phase Dynamic Voltage Restorer With Novel Sag Detection Algorithm

This paper describes the development of a line-interactive single-phase dynamic voltage restorer (DVR) with a novel sag detection algorithm. The developed detection algorithm has a hybrid structure composed of an instantaneous detection part and the root-mean-square (rms) variation detection part. The source voltage passes through the instantaneous sag detection part. If instantaneous sag is detected, the rms variation detector-1 is selected to calculate the rms variation. The rms variation detector-2 is selected when the instantaneous sag occurs under the operation of the rms variation detector-1. The feasibility of proposed algorithm was verified through computer simulations and experimental works with a 3-kVA-rating prototype of line-interactive DVR. The line-interactive DVR with the proposed algorithm can compensate the input voltage sag or interruption within 2.0-ms delay. The developed DVR can be effectively utilized for the sensitive loads, such as a computer, communication device, and automation device.

Temporal Parts and Time Travel

This paper argues that, in light of certain scenarios involving time travel, Sider's definition of 'instantaneous temporal part' cannot be accepted in conjunction with a semantic thesis that perdurantists often assume. I examine a rejoinder from Sider, as well as Thomson's alternative definition of 'instantaneous temporal part', and show how neither helps. Given this, we should give up on the perdurantist semantic thesis. I end by recommending that, once we no longer accept such semantics, we should accept a new set of definitions, which are superior in certain respects to Sider's original set.

A general modal-based numerical simulation of transient heat conduction in a one-dimensional homogeneous slab

We present an analytical general solution of the well-known heat conduction problem in a one-dimensional homogeneous slab by using an expansion of the only delayed part of the temperature field function on an infinite eigen functions set. We propose to split the searched solution of the general problem in an instantaneous part and a delayed one which, with whatever boundary conditions combination, verifies Dirichlet conditions and then avoids the Gibbs problem. A space sampling and a reduction of the eigen basis produce a useful and usable numerical model which may be as accurate as required. The results we present may be used directly to numerically calculate solutions to a given problem and may be reused as a basis for more complex problems as multilayer walls or whole thermal systems studies.

Analysis of arch dam deformations

Predicting “regular” dam deformations for prevailing conditions and comparing them with observed deformations is an essential part of dam surveillance. In many cases prediction and comparison are carried out automatically and an alarm is triggered in the case of larger deviations. The main contributors to the deformations of arch dams are water loading and the fluctuation of concrete temperature. In general, the deformations exhibit an instantaneous elastic part, a time dependent reversible part and an irreversible part. Prediction of dam deformations can be based on deterministic models, purely statistical models or so-called hybrid models, which are a combination of the first two. Deterministic models rely on static analyses, statistical models on the statistical analysis of previous deformation data. For annual reservoirs, both water loading and temperature vary in cycles over a period of one year and it is extremely difficult to identify the various factors contributing to an observed deformation. This is particularly true for time-dependent reversible displacements due to the water loading and the portion caused by temperature variation. The present article deals with the analysis of arch dam deformations based on hybrid models. Particular attention is given to the analysis of the deformations due to temperature fluctuation and to the long-term deformations. The proposed procedure is employed for the analysis of the deformations of the 186 m high Zillergruendl arch dam.

Wilson loop from a Dyson equation

The Dyson equation proposed for planar temporal Wilson loops in the context of supersymmetric gauge theories is critically analyzed thereby exhibiting its ingredients and approximations involved. We reveal its limitations and identify its range of applicability in nonsupersymmetric gauge theories. In particular, we show that this equation is applicable only to strongly asymmetric planar Wilson loops (consisting of a long and a short pair of loop segments) and as a consequence the Wilsonian potential can be extracted only up to intermediate distances. By this equation the Wilson loop is exclusively determined by the gluon propagator. We solve the Dyson equation in Coulomb gauge for the temporal Wilson loop with the instantaneous part of the gluon propagator and for the spatial Wilson loop with the static gluon propagator obtained in the Hamiltonian approach to continuum Yang-Mills theory and on the lattice. In both cases we find a linearly rising color potential.

Elastic response in wood under moisture content variations: analytic development

Creep evolution of timber structures results from the interaction between mechanical stresses due to different loads and hydric stresses due to moisture content variations. This paper deals with a thermodynamic approach in order to take into account a realistic elastic behavior under moisture content variations. In this context, memory effect, experimentally observed, is introduced employing a mechano-sorptive stress driven by a function dependent of the moisture content variations. This new internal thermodynamic variable enables to define an original separation of the free energy into an instantaneous recoverable part and a stored part during the last drying phase. This energy enables the modeling of the nonreversible strain process during the unloading phase. The locate state method is employed in order to define the thermodynamic function which traduces an indirect hereditary behavior between moisture content history and the stress state in the material.

Mathematical modeling and practical verification of groundwater and contaminant transport in a chosen natural aquifer

The paper addresses the 2D mathematical equation of conservative contaminant transport in an aquifer for chosen contaminants. The contaminants (chlorides and sulfates) are subject to instantaneous reversible part of sorption process. The term of instantaneous reversible sorption in the presented equation has been described by the non-linear Freundlich adsorption isotherm, widely applied in practice in relation to static processes (for local equilibrium). The numerical solution (using the finite difference method) has been based on the previously calculated values of longitudinal and transverse dispersion coefficients and the non-linear adsorption parameters for the chosen contaminants. Based on this model, the values of chloride and sulfate concentration isolines have been calculated and compared with the measured maximal concentrations in the chosen natural aquifer (installed piezometers). Additionally, the values of chloride concentrations have been calculated taking into account the influence of radioactive decay term, using the numerical value of the firstorder decay rate constant for an adopted theoretical radionuclide.

Experimental determination of the limiting bulge height in hydromechanical deep drawing

Owing to fluid pressure, the unsupported blank between the punch and the drawing ring is bulged in the direction opposite to the punch movement. The blank is thus drawn over a fluid cushion and does not contact the drawing ring profile radius. The bulge is hence advantageous for ensuring class A surface quality of the workpiece. The blank is stretched bi-axially in the bulged region owing to the acting fluid pressure. This can result in blank fracture at high-fluid counter pressures. High-fluid counter pressures are, however, necessary to achieve higher geometrical accuracies and lower springback. High pressure can also be used to transfer small contours from the punch to the drawn cup. A high-pressure die set for hydraulic bulging has been designed in order to emulate the bulge formation in hydromechanical deep drawing. A series of experiments have been carried out in order to determine the limiting bulge height for different sheet materials. Different punch diameters have been used to determine the influence of drawing clearance on the limiting bulge height. The effect of fluid pressure on the smallest transferable radius has also been investigated. Results thus obtained can be used in determining the dedicated optimal counter pressure curve for a given workpiece geometry, material, and die set combination in order to design a robust computer-aided engineering (CAE) chain for the hydromechanical deep drawing process. Selected representative experimental results for hydromechanical deep drawing of complex part geometries have been shown. The counter pressure curve for hydromechanical deep drawing of the shown cups was selected in conformance to the allowable bulge height for the considered instantaneous sheet material, part shape, and process parameter combination.

Properties of color-Coulomb string tension

We study the properties of the color-Coulomb string tension obtained from the instantaneous part of gluon propagators in Coulomb gauge using quenched $SU(3)$ lattice simulation. In the confinement phase, the dependence of the color-Coulomb string tension on the QCD coupling constant is smaller than that of the Wilson loop string tension. On the other hand, in the deconfinement phase, the color-Coulomb string tension does not vanish even for $T/{T}_{c}=1\ensuremath{\sim}5$, the temperature dependence of which is comparable with the magnetic scaling, dominating the high temperature QCD. Thus, the color-Coulomb string tension is not an order parameter of quark-gluon plasma phase transition.

Intermolecular/interionic interactions in l-leucine-, l-asparagine-, and glycylglycine-aqueous electrolyte systems

Ultrasonic velocity and density values have been measured for ternary systems (amino acid/di-peptide + salt + water): l-leucine/ l-asparagine/glycylglycine each in 1.5 M aqueous solutions of NaCl or NaNO 3 or KNO 3 used as solvents for several concentrations of amino acids/di-peptide at different temperatures in the range of 298.15–323.15 K. The ultrasonic velocity values have been found to increase with increase in amino acids/di-peptide concentration and temperature in all the systems. The increase in ultrasonic velocity with increase in concentration has been discussed in terms of electrostatic interactions occurring between terminal groups of zwitterions (NH 4 + and COO −) and Na +, K +, Cl −, NO 3 − ions. The interactions of water dipoles with cations/anions and with zwitterions have also been taken into consideration. It has been observed that the ion-zwitterion and ion-dipole attractive forces are stronger than those of ion-hydrophobic repulsive forces. These interactions comprehensively introduce the cohesion into solutions under investigation. The cohesive forces are further enhanced on successive increases in solute concentration. Using ultrasonic velocity and density data, the parameters such as isentropic compressibility ( κ s), change (Δ κ s) and relative change (Δ κ s/ κ 0) in isentropic compressibility, specific acoustic impedance ( Z) and relative association (RA) have been computed. The isentropic compressibility values decrease with increase in the concentration of solutes as well as with temperature. The decrease in κ s values with increase in concentration of l-leucine, l-asparagine and glycylglycine in 1.5 M aqueous solutions of NaCl, NaNO 3 and KNO 3 have been explained in terms of an increase in the number of incompressible molecules/zwitterions in solutions and the formation of compact zwitterions–water dipole and zwitterions-ions structures in solutions. The decrease in κ s values with increase in temperature has been attributed to the corresponding decrease of κ relax. (relaxational part of compressibility) , which is dominant over the corresponding increase of κ ∞ (instantaneous part of compressibility). The trends of variations of Δ κ s, Δ κ s/ κ 0, Z and RA with change of concentration and temperature have also been interpreted in terms of various intermolecular/interionic interactions existing in the systems.