Exponential Ramp Research Articles

A novel methodology for the selection of the optimal velocity profile for planned point-to-point trajectories in 1-DoF manipulators

In this work, an approach based on velocity profile selection is developed and validated to decrease forces, acceleration, velocity, mechanical power, and energy consumption in 1 DOF Cartesian manipulators. Initially, a mathematical modeling of the kinematic and kinetic variables rising in linear, exponential, parabolic, sinusoidal, and s-curve ramp velocity profiles is proposed for different load conditions and saturation values of the velocity profiles, focusing on generic Cartesian manipulators moving a constant inertia load and not equipped with regenerative devices. Lastly, a summary table outlining the benefits and drawbacks of each velocity profile in relation to the relevant variables is given to the reader, along with a set of recommendations for selecting the best velocity profile in accordance with the load conditions and optimization goals. It was shown that, depending on the load conditions, the inappropriate choice of one type of speed profile can increase the required forces by up to 400%, the required maximum power by more than 88%, and the energy consumption by up to 77% with respect to the optimal speed profile.

A study of the SYK2 model with twisted boundary conditions

We study a version of the 2-body Sachdev-Ye-Kitaev (SYK2) model whose complex fermions exhibit twisted boundary conditions on the thermal circle. As we show, this is physically equivalent to coupling the fermions to a 1-dimensional external gauge field A(t). In the latter formulation, the gauge field itself can be thought of as arising from a radial symmetry reduction of a (2 + 1)-dimensional Chern-Simons gauge field Aμ(t,x). Using the diagnostic tools of the out-of-time-order correlator (OTOC) and spectral form factor (SFF), which probe the sensitivity to initial conditions and the spectral statistics respectively, we give a detailed and pedagogical study of the integrable/chaotic properties of the model. We find that the twisting has no effect on the OTOCs and, by extension, the early-time chaos properties of the model. It does, however, have two notable effects on the spectral form factor; an enhancement of the early-time slope and the emergence of an explicit twisting-dependent timescale needed for the manifestation of zero modes. These zero modes are responsible for the late-time exponential ramp in the quadratic SYK model.

Electron acceleration by elliptical q-Gaussian laser pulse in collisionless plasma with exponential density ramp: combined effect of self-focusing and self-compression

Electron acceleration by elliptical q-Gaussian laser pulse in collisionless plasma with exponential density ramp: combined effect of self-focusing and self-compression

Excitation of an upper hybrid wave by Laguerre–Gaussian pulse in plasma with a density ramp and electron acceleration

In this paper, the excitation of an upper hybrid wave (UHW) by propagation of a Laguerre–Gaussian (LG) laser pulse in an exponential density ramp plasma has been investigated in relativistic regime. A uniform static magnetic field was externally applied perpendicular to the propagation of the laser. The spatiotemporal dynamics of laser pulse have been studied by two coupled differential equations obtained via the moment theory approach. The propagating laser pulse excites an electron plasma wave, which further interacts with the laser pulse in the presence of applied transverse magnetic field and generates an UHW. The excited UHW further traps the plasma electrons and accelerates them. It has been observed that the presence of density ramp affects the laser dynamics, excited UHW, and electron acceleration. The applied magnetic field and modes of LG laser have also shown significant effect on electron acceleration. Energy gain of the order of 400 MeV/mm has been obtained for electrons.

Self-focusing of a q-gaussian laser beam under the influence of an exponential plasma density ramp in plasma

The goal of the current manuscript is to investigate how a plasma density ramp affects the ability of a q-Gaussian laser beam (q-GLB) to self-focus in plasma. The laser beam exhibits oscillatory self-focusing and defocusing behaviour with increasing distance of propagation. We used an exponential plasma density ramp to combat this defocusing tendency, allowing the particular laser beam to achieve a minimal spot size and nearly retain it up to several Rayleigh lengths. In addition to that, it has been observed that self-focusing increases with increasing q-values and the laser intensity. However, the lower values of q suggest strong self-focusing. By warily selecting the plasma and laser parameters, the density ramp could play a key role in the self-focusing of q-Gaussian laser. Self-focusing is seen to become stronger as propagation distance increases and the q-parameter affects the behaviour of the beam-width parameter in the plasma as shown.

Effect of shape and asymmetry of the voltage pulse on plasma sheath dynamics

In this paper, using particle-in-cell simulations and considering two symmetric voltage pulses with linear and exponential ramps, it is investigated how the voltage pulse shape affects the pulsed plasma sheath dynamics. Results show the formation, expansion, and shrinking of the sheath as well as the importance of the pulse shape in determining the sheath characteristics. The asymmetry effect of the pulse shape on the sheath evolution is also discussed. The ion kinetic energy and current density at the cathode surface are calculated. It is shown that the voltage change rate plays a significant role to determine the ion current density.

Self-focusing of a Bessel–Gaussian laser beam in plasma under density transition

The model given by Patil et al., for the self-focusing of lowest-order Bessel–Gaussian laser beam, is revisited by introducing the exponential plasma density ramp in this paper. Plasma density changes due to combined effect of the relativistic and ponderomotive nonlinearities, which arise due to the nonuniform spatial profile of the laser beam leading to stronger self-focusing. Under paraxial ray approximation, the expression for the evolution of laser-beam width parameter is obtained and solved numerically in order to achieve self-focusing. We have observed that as Bessel beam propagates through the plasma, it does not diffract and spread out, which is in contrast to the usual behavior of light that spreads out after being focused down to the small spot. Laser spot size decreases considerably under the presence of exponential density ramp. This study will be useful for better understanding the self-focusing mechanism of lasers as it becomes effective for the optimized parameters under the proposed situation. Bessel laser beams play an important role in enhancing the energy gain in laser-driven accelerators. In addition, for all laser-driven plasma-based accelerators, it appears possible to guide a laser beam over large distances using a plasma density channel, thus enhancing the acceleration length and the energy gain.

A method for the tribological assessment of oral pharmaceutical liquids

Objective Patient acceptance of pediatric formulations is critical to compliance and consequently therapeutic outcomes; thus, having an in vitro method to evaluate sensory perception of pharmaceutical products would be beneficial. The objective of this research is to develop a sensitive and reproducible tribological method to characterize pharmaceutical suspensions at low force and sliding speeds. Methods The discriminating potential of the method was examined using tribology profiles (coefficient of friction (COF) vs. sliding speed) for commercially available products and products made for this study with widely varying sweetness, thickness, and grittiness; these formulations were used to judge the sensitivity of the method. Samples were measured using 3M Transpore™ surgical tape to simulate the tongue surface, steel half ring geometry, constant gap setting, target axial force of 2 N in a 600 s exponential ramp for rotation speed. Results The COF ranged from 0.1 to 0.6. For the speeds studied, the high viscosity commercial suspension ibuprofen drops and acetaminophen suspension show a classic Stribeck curve with an increasing COF at the higher rotation speeds, which indicates these formulations entered the hydrodynamic lubrication phase, while the lower viscosity suspensions only reached the mixed lubrication phase. Conclusion The contribution of particles affects the COF in a dynamic tribologic pattern compared to products that are categorized as either low gritty or high viscosity. These results are important as they provide a potentially rapid in vitro method for screening pediatric medications and help to identify the factors that affect the palatability of pediatric formulations.

Emergence of many-body quantum chaos via spontaneous breaking of unitarity

It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as $K(\ensuremath{\eta},t)=\ensuremath{\langle}|\mathrm{Tr}exp(\ensuremath{-}\ensuremath{\eta}H+itH){|}^{2}\ensuremath{\rangle}$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the ``unitary'' $\ensuremath{\eta}=0$ case is different from the $\ensuremath{\eta}\ensuremath{\rightarrow}{0}^{\ifmmode\pm\else\textpm\fi{}}$ limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the noninteracting case, and gives rise to a nontrivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.

Universal dephasing mechanism of many-body quantum chaos

Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle. This paper demonstrates using both heuristic arguments and a microscopic calculation that a dephasing mechanism, similar to Altshuler-Aronov-Khmelnitskii dephasing in the theory of localization, underlies this transition to chaos. We focus on the behavior of the spectral form factor (SFF) as a function of “time” t, which characterizes level correlations in the many-body spectrum. The SFF can be expressed as a sum over periodic classical orbits and its behavior hinges on the interference of trajectories related to each other by a time translation. In the absence of interactions, time-translation symmetry is present for each individual particle, which leads to a fast exponential growth of the SFF and correspondingly loss of correlations between many-body levels. Interactions lead to dephasing, which disrupts interference, and breaks the massive time-translation symmetry down to a global time-translation/energy conservation. This in turn gives rise to the hallmark linear-in-t ramp in the SFF reflecting Wigner-Dyson level repulsion. This general picture is supported by a microscopic analysis of an interacting many-body model. Specifically, we study the complex SYK2+SYK22 model, which allows to tune between an integrable and chaotic regime. It is shown that the dephasing mass vanishes in the former case, which maps to the noninteracting complex SYK2 model via a time reparameterization. In contrast, the chaotic regime gives rise to dephasing, which suppresses the exponential ramp of the noninteracting theory and induces correlations between many-body levels.Received 14 November 2021Accepted 3 March 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L012037Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum chaosQuantum statistical mechanicsTechniquesSigma modelsCondensed Matter, Materials & Applied PhysicsStatistical Physics

Third harmonic generation of a relativistic self-focusing laser in plasma under exponential density ramp

Abstract Present study focuses on self-focusing and its effect on third harmonic generation (THG) of a Gaussian laser beam in plasma under the influence of exponential density ramp. Relativistic nonlinearity has been taken into account which is aroused due the modification of electron’s mass in the presence of high intensity laser. Under strong ponderomotive force, electrons acquire very high quiver velocity and mass variation takes place. Equations for beam width parameter of incident laser and the amplitude of THG have been derived under WKB and paraxial ray approximation, and solved them numerically. It is found that the presence of exponential plasma density ramp results strong self-focusing of laser which further leads to enhance the efficiency of THG. Wiggler magnetic field adds an additional momentum to the photons of third harmonic due to which appreciable gain is observed in the normalized amplitude of THG. Significant enhancement in the THG amplitude has been reported in the presence of exponential density ramp for optimum values of intensity of incident laser, wiggler magnetic field and plasma frequency.

Second harmonic generation of intense Laguerre-Gaussian beam in relativistic plasma having an exponential density transition

The present communication explores the second harmonic generation (SHG) of intense Laguerre-Gaussian beam (L-G beam) in relativistic plasma having an exponential density transition. The carrier redistribution is observed on account of relativistic nonlinearity in presence of intense L-G beam. This results in establishment of transverse intensity gradients thereby generating electron plasma wave (EPW) at the frequency of pump wave. Further, there is an interaction of pump beam with EPW resulting in production of second harmonics. The approach of method of moments is utilized for deriving 2nd order differential equation for beam waist of beam and yield of SHG. It is predicted from the results that a vital role is played by exponential density ramp and different L-G beam modes in enhancing focusing ability of beam and yield of SHG.

Enhanced self-focusing of Laguerre-Gaussian laser beam in relativistic plasma under exponential plasma density transition

In the current work, self-focusing of Laguerre-Gaussian laser beam under the influence of exponential plasma density transition in relativistic plasma is studied. It is observed that the spot size of laser beam shrinks as beam propagates into the plasma because of exponential plasma density ramp. The exponential plasma density ramp reduces the beam width parameter due to its slowly variation ramp profile. Also, with the rise in intensity of the laser beam, self-focusing enhances significantly. Our results in the present manuscript may be helpful in the field where strong self-focusing of the laser is required such as high-power laser driven fusion, explanation of devices involved in beam propagation in the various applications.

Influence of linear absorption and density ramp on self-focusing of the Hermite-Gaussian chirped pulse laser in plasma

An analysis of the self-focusing of Hermite Gaussian chirped pulse laser in the relativistic and ponderomotive regime under the influence of exponential plasma density ramp and linear absorption has been done. Differential equation for beam width parameter is derived by using paraxial ray approximation and then solved numerically. It is observed that self-focusing of the chirped pulse laser is strongly influenced by linear absorption. Also it is seen that with the increase in intensity of laser beam, plasma density ramp and chirped parameter value, self-focusing becomes more effective. Current work may be useful in understanding laser induced fusion, quantum dots etc.

Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model.

A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.

Many-Body Level Statistics of Single-Particle Quantum Chaos.

We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model)-a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.

Combined influence of axial electron temperature and exponential plasma density ramp on the self-focusing of a chirped laser in plasma

Abstract An analysis of the self-focusing of highly intense chirped pulse laser under exponential plasma density ramp with higher order value of axial electron temperature has been done. Beam width parameter is derived by using paraxial ray approximation and then solved numerically. It is seen that self-focusing of chirped pulse laser is intensely affected by the higher order values of axial electron temperature. Further, influence of exponential plasma density ramp is studied and it is concluded that self-focusing of laser enhances and occurs earlier. On the other hand defocusing of beam reduces to the great extent. It is noticed that the laser spot size reduces significantly under joint influence of the density ramp and the axial electron temperature. Present analysis may be useful for the analysis of quantum dots, the laser induced fusion and etc.

Utilizing pre-polarization to enhance SNMR signals—effect of imperfect switch-off

SUMMARYSurface nuclear magnetic resonance (SNMR) is a well-established technique for the hydrogeological characterization of the subsurface up to depths of about 150 m. Recently, SNMR has been adapted to investigate also the shallow unsaturated zone with small surface loop setups. Due to the decreased volume, a pre-polarization (PP) field prior to the classical spin excitation is applied to enhance the measured response signal. Depending on the strength and orientation of the applied PP-field, the enhancement can often reach several orders of magnitude in the vicinity of the PP-loop. The theoretically achievable enhancement depends on the assumption of an adiabatic, that is perfect, switch-off of the corresponding PP-field. To study the effect of imperfect switch-off, we incorporate full spin dynamics simulations into the SNMR forward modelling. The affected subsurface volume strongly depends on the chosen PP switch-off ramp and the geometry of the loop setup. Due to the imperfect switch-off, the resulting SNMR sounding curves can have significantly decreased signal amplitudes. For comparison, the signal amplitudes of either a 1 ms exponential or linear switch-off ramp are reduced by 17 and 65 per cent, respectively. Disregarding this effect would therefore yield an underestimation of the corresponding subsurface water content of similar magnitude.

A Novel Method for Predicting Power Transient CHF via the Heterogeneous Spontaneous Nucleation Trigger Mechanism

Using the Laplace transform for solving a two-region (cladding/liquid) conduction problem with an exponentially increasing heat flux boundary condition, an analytic temperature profile has been found. The rate of the temperature increase in the second region (liquid) is used to determine energy deposition in the thermal boundary layer of the liquid. Energy deposition rates are then compared to the latent heat capacity of the growing thermal boundary layer to create a condition for predicting transient critical heat flux (CHF) via the heterogeneous spontaneous nucleation (HSN) trigger mechanism. These analytic predictions are then compared to existing data for exponential power ramp transients with periods ranging from 5 ms up to 10 s. Comparison with experimental data show that the trends of the expected HSN-triggered CHF are in good agreement with the magnitude being controlled by the determination of the maximum boundary layer energy. This work presents the first known attempts to derive a mechanistic CHF prediction model for HSN. Though further work is necessary to develop the HSN model (and is being pursued in parallel to this research), this work will allow for a quantitative prediction of HSN-triggered CHF. Further developments of the HSN model will inform the boundary layer energy threshold that triggers CHF.

Relativistic Self-Focusing of Hermite-cosh-Gaussian Laser Beam in Magnetoplasma with Exponential Plasma Density Ramp

In the present manuscript, we analyse the effect of exponential plasma density ramp for relativistic self-focusing of Hermite-cosh-Gaussian laser pulse in magnetoplasma. The exponential plasma density ramp is found to be more prominent in achieving the stronger self-focusing of Hermite-cosh-Gaussian laser beam in comparison to the tangential plasma density ramp. We propose a theoretical model for propagation of Hermite-cosh-Gaussian laser pulse in magnetoplasma with exponential density ramp. The nonlinearity in the medium arises because of the relativistic motion of electrons, being responsible for relativistic self-focusing. Equation of the beam width parameter is set up by taking the expression for the dielectric function and following Wentzel-Kramers-Brillouin (WKB) with paraxial ray approximations for mode indices m = 0, 1 and 2. Effect of decentered parameter is also analysed, which results in stronger self-focusing of the Hermite-cosh-Gaussian laser beam. Stronger self-focusing of laser beam is more pronounced in high density plasma with higher magnetic field.