Perturbation Amplitude Research Articles

Combined effect mechanism of linear loading and disturbance with different amplitudes on sandstone

To comprehend the stress state and response characteristics of materials under complex conditions, researchers have decomposed stress states into fundamental paths and investigated diverse path combinations. To ensure comparability, four identical samples were carefully selected from a pool of 100 samples using ultrasonic tests based on the wave speed and waveform characteristics. These samples underwent specially designed stress paths to analyze the combined effects of linear loading and perturbation. Our result analysis centred on the perturbation amplitude and stress levels during composite action, revealing intricate relationships between the stress levels, strain, and nonlinear/linear energy evolution under complex stress paths. Simultaneously, 3D surface fractures were precisely reconstructed using the YOLOv5 and FAST feature point detection algorithms, elucidating the evolving patterns of the fractures. As a result of our study, the rotation trend of the main fracture was validated by integrating mechanics and P-wave reflection rules. Notably, our experimental results closely aligned with the theoretical predictions, showing the reliability of our study. These findings can significantly contribute to guiding safety protocols in the field of underground engineering.

Modeling the stability of thin liquid film flows on a uniformly heated slippery inclined substrate: A realistic approach

We investigate the stability of gravity-driven, Newtonian, thin liquid film falling down a uniformly heated slippery rigid inclined wall. The authors of previous research works considered specified temperature (ST) boundary condition to study the effects of slip length. However, the ST boundary condition does not include the effects of heat fluxes at wall–air and wall–liquid interfaces and so fails to incorporate the real situation. Consequently, we consider heat flux/mixed-type boundary condition as the thermal boundary condition on the rigid plate. This boundary condition involves the heat flux from the rigid plate to the surrounding liquid and the heat losses from the wall to the ambient air. Using long-wave expansion method, we construct a highly nonlinear evolution equation in terms of the film thickness at any instant. Using normal mode approach, the linear study reveals the stabilizing (destabilizing) behavior of the wall film Biot number (dimensionless slip length). It is found that the destabilizing tendency of the slip length is more in the absence of thermocapillary stress. The linear study reveals that the destabilizing role of MB may be controlled to some extent by increasing the wall film Biot number Bw. Using asymptotic expansions of the flow variables in terms of the small wave number k, the Orr–Sommerfeld boundary value problem gives an onset of instability in terms of critical Reynolds number. It slightly differs from that of the same as obtained by Benney's long-wave expansion method, due to the consideration of small free surface Biot number [B=O(ϵ)]. For arbitrary wave numbers, using Chebyshev spectral collocation method, the effect of Marangoni number (Ma), slip length (δ), and wall film Biot number (Bw) on the H, S, P, and shear modes of instability are discussed in detail. Near the threshold, both Ma and δ show the destabilizing effect on H mode of instability, whereas Bw gives the stabilizing effect. Interestingly, their roles on H mode of instability becomes diametrically opposite far from the onset of instability. For S mode, both Ma and Bw display the destabilizing effect, whereas δ plays the dual role. For P mode, both Ma and δ show the destabilizing effect, whereas Bw plays the stabilizing role. The slip length (δ) plays the stabilizing role, in the case of shear mode. In the absence of thermocapillary effect, the vorticity balance at the liquid–air interface explains that the amplitude of the vorticity perturbation amplifies the surface deformation due to the presence of inertia and the slip length. In the absence of the slip length, a weakly nonlinear study transforms the evolution equation to the famous Kuramoto–Sivashinsky (KS) equation.

Vibration effect on Rayleigh–Taylor instability of sedimenting suspension

In this paper, the effect of vertical vibration on the Rayleigh–Taylor instability at the lower interface of a sedimenting suspension layer sandwiched between viscous fluids is studied numerically and theoretically. It is shown numerically that the vibration suppresses the amplitudes of interface perturbations and enlarges the widths of granular fingers, postponing the nonlinear growth stage. By modeling the suspension as a fluid with its effective density and viscosity, stability analyses are carried out, and the dominant growth rate and the dominant wave number predicted by the dispersion relation agree with the numerical results, especially for cases with strong vibrations. Because of the small-scale flow induced by the particles, high vibration acceleration amplitude and low vibration frequency, which correspond to a large vibration power input, increase the kinetic energy spectra at the high wave number regime, a phenomenon contrary to the vibration effect for pure fluid cases.

Tailbeat perturbations improve swimming efficiency by reducing the phase lag between body motion and the resulting fluid response.

Understanding how animals swim efficiently and generate high thrust in complex fluid environments is of considerable interest to researchers in various fields, including biology, physics, and engineering. However, the influence of often-overlooked perturbations on swimming fish remains largely unexplored. Here, we investigate the propulsion generated by oscillating tailbeats with superimposed rhythmic perturbations of high frequency and low amplitude. We reveal, using a combination of experiments in a biomimetic fish-like robotic platform, computational fluid dynamics simulations, and theoretical analysis, that rhythmic perturbations can significantly increase both swimming efficiency and thrust production. The introduction of perturbations increases pressure-induced thrust, while reduced phase lag between body motion and the subsequent fluid dynamics response improves swimming efficiency. Moreover, our findings suggest that beneficial perturbations are sensitive to kinematic parameters, resolving previous conflicts regarding the effects of such perturbations. Our results highlight the potential benefits of introducing perturbations in propulsion generators, providing potential hypotheses for living systems and inspiring the design of artificial flapping-based propulsion systems.

Vertical convection regimes in a two-dimensional rectangular cavity: Prandtl and aspect ratio dependence

Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al., J. Fluid Mech., vol. 917, 2021, A6). We consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O( $10^8$ ). As a function of the Prandtl number, $Pr$ , and the height-to-width aspect ratio of the domain, $A$ , the base flow of each case is computed numerically and linear simulations are used to obtain the properties of the leading linear instability mode. Flow regimes depend on the presence of a circulation in the entire cavity, detachment of the thermal layer from the boundary or the corner regions and on the oscillation frequency relative to the natural frequency of oscillation in the stably temperature-stratified interior, allowing for the presence of internal waves or not. Accordingly, the regime is called slow or fast, respectively. Either the global circulation or internal waves in the interior may couple the top and bottom buoyancy currents, while their absence implies asymmetry in their perturbation amplitude. Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$ . For $Pr \lessapprox 0.4$ and $A>1$ , the base flow is driven by a large circulation in the entire cavity. For $Pr \gtrapprox 0.7$ , the thermal boundary layers are thin and the instability is driven by the motion along the wall and the detached boundary layer. A transition between these regimes is marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm 0.15$ and $A <2$ .

Scattering amplitudes for self-force

The self-force expansion allows the study of deviations from geodesic motion due to the emission of radiation and its consequent back-reaction. We investigate this scheme within the on-shell framework of semiclassical scattering amplitudes for particles emitting photons or gravitons on a static, spherically symmetric background. We first present the exact scalar two-point amplitudes for Coulomb and Schwarzschild, from which one can extract classical observables such as the change in momentum due to geodesic motion. We then present, for the first time, the three-point semiclassical amplitudes for a scalar emitting a photon in Coulomb and a graviton on linearised Schwarzschild, outlining how the latter calculation can be generalized to the fully non-linear Schwarzschild metric. Our results are proper resummations of perturbative amplitudes in vacuum but, notably, are expressed in terms of Hamilton’s principal function for the backgrounds, rather than the radial action.

Primordial black holes and secondary gravitational waves from generalized power-law non-canonical inflation with quartic potential

Here, generation of PBHs and secondary GWs from non-canonical inflation with quartic potential have been probed. It is illustrated that, quartic potential in non-canonical setup with a generalized power-law Lagrangian density can source a consistent inflationary era with the latest observational data. Besides, we show that our model satisfies the swampland criteria. At the same time, defining a peaked function of inflaton field as non-canonical mass scale parameter M(ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M(\\phi )$$\\end{document} of the Lagrangian, gives rise to slow down the inflaton in a while. In this span, namely Ultra-Slow-Roll (USR) stage, the amplitude of the curvature perturbations on small scales enlarges versus CMB scales. It has been illustrated that, further to the peaked aspect of the chosen non-canonical mass scale parameter, the amount of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} parameter of the Lagrangian has enlarging impact on the amplitude of the scalar perturbations. As a consequence of adjusting three parameter Cases of this model, three Cases of PBHs in proper mass scopes to explain LIGO-VIRGO events, microlensing events in OGLE data and DM content in its totality, could be produced. In the end, power-law behavior of the current density parameter of gravitational waves ΩGW0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\\mathrm{GW_0}}$$\\end{document} in terms of frequency has been examined. Also, the logarithmic power index as n=3-2/ln(fc/f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=3-2/\\ln (f_c/f)$$\\end{document} in the infrared regime is obtained.

Impact of Momentum Perturbation on Convective Boundary Layer Turbulence

AbstractMesoscale‐to‐microscale coupling is an important tool for conducting turbulence‐resolving multiscale simulations of realistic atmospheric flows, which are crucial for applications ranging from wind energy to wildfire spread studies. Different techniques are used to facilitate the development of realistic turbulence in the large‐eddy simulation (LES) domain while minimizing computational cost. Here, we explore the impact of a simple and computationally efficient Stochastic Cell Perturbation method using momentum perturbation (SCPM‐M) to accelerate turbulence generation in boundary‐coupled LES simulations using the Weather Research and Forecasting model. We simulate a convective boundary layer (CBL) to characterize the production and dissipation of turbulent kinetic energy (TKE) and the variation of TKE budget terms. Furthermore, we evaluate the impact of applying momentum perturbations of three magnitudes below, up to, and above the CBL on the TKE budget terms. Momentum perturbations greatly reduce the fetch associated with turbulence generation. When applied to half the vertical extent of the boundary layer, momentum perturbations produce an adequate amount of turbulence. However, when applied above the CBL, additional structures are generated at the top of the CBL, near the inversion layer. The magnitudes of the TKE budgets produced by SCPM‐M when applied at varying heights and with different perturbation amplitudes are always higher near the surface and inversion layer than those produced by No‐SCPM, as are their contributions to the TKE. This study provides a better understanding of how SCPM‐M reduces computational costs and how different budget terms contribute to TKE in a boundary‐coupled LES simulation.

Control of giant orbital angular momentum bursts of structured Laguerre-Gaussian beams in a medium with general astigmatism

We examined theoretically and experimentally the influence of astigmatic elements (for example, a cylindrical lens) on a structured Laguerre-Gaussian beam (sLG) when the lens axes are directed at an arbitrary angle to the laboratory coordinate axes (a general astigmatism). Although a structurally stable Laguerre-Gaussian (LG) beam contains a great number of axisymmetric modes (in the LG basis) with matching phases and amplitudes, their superposition already loses its original axial symmetry, but acquires new properties (for example, fast oscillations of the orbital angular momentum (OAM)), while the beam OAM cannot exceed the azimuthal number l of the original LG mode. The loss of axial symmetry occurs due to bringing phase and amplitude perturbations into each mode of the sLG beam, which destroy the ring dislocations. Since degenerate ring dislocations are formed by optical vortices with opposite topological charges, but with equal weights, their destruction is accompanied by appearing of vortex pairs in the form of topological dipoles (their number is equal to the radial number n). As a result, the mode spectrum of the sLG is extended to the value ±(2n + l). The astigmatic element (cylindrical lens) violates the equality of vortex weights in the dipoles, which leads to a sharp growing the OAM of the sLG beam. Moreover, the OAM can be controlled by changing the rotation of the cylindrical lens axes and the control parameters of the sLG beam. It is these processes that are discussed in detail in our article, both in theoretical and experimental aspects. We show that with a certain orientation of the cylindrical lens axes, the beam OAM can exceed the sum of the orbital and azimuthal numbers (OAM > n + l). Besides, we reveal that the intensity pattern of the astigmatic sLG beam can follow the rotation of the astigmatic element axes (the effect of the beam structure following the cylindrical lens axes) at certain relations between control parameters of the sLG beam and the astigmatic element.

Exploring Primordial Curvature Perturbation on Small Scales with the Lensing Effect of Fast Radio Bursts

Cosmological observations, e.g., cosmic microwave background, have precisely measured the spectrum of primordial curvature perturbation on larger scales, but smaller scales are still poorly constrained. Since primordial black holes (PBHs) could form in the very early Universe through the gravitational collapse of primordial density perturbations, constraints on the PBH could encode much information on primordial fluctuations. In this work, we first derive a simple formula for the lensing effect to apply PBH constraints with the monochromatic mass distribution to an extended mass distribution. Then, we investigate the latest fast radio burst observations with this relationship to constrain two kinds of primordial curvature perturbation models on small scales. This suggests that, from the null search result of lensed fast radio bursts in currently available observations, the amplitude of primordial curvature perturbation should be less than 8 × 10−2 at the scale region of 105–106 Mpc−1. This corresponds to an interesting mass range relating to binary black holes detected by LIGO–Virgo–KAGRA and future Einstein Telescope or Cosmic Explorer.

Processing of VLF Amplitude Measurements: Deduction of a Quiet Time Seasonal Variation

AbstractThe amplitude of Very Low Frequency (VLF) transmissions propagating from transmitter to receiver between the Earth's surface and the ionospheric D‐region is a useful measurement to detect changes in the ionization within the D‐region ranging from 60 to 90 km. The VLF signal amplitude is disturbed by geomagnetic, solar, and atmospheric phenomena. To be able to identify perturbations in the VLF signal amplitude, we determine its averaged seasonal variation under quiet solar and geomagnetic conditions. Here it is challenging, that long time series of the VLF signal amplitude show significant jumps and outliers, which are caused artificially by technical adjustments/maintenance work. This paper presents a new approach for processing long VLF data time series over multiple years resulting in level 2 data. The new level 2 data enables the consideration of time series with artificial jumps since the jumps are leveled. Moreover, the outliers are removed by a robust and systematic 2‐step outlier filtering. The average seasonal and diurnal variation for different transmitter‐receiver combinations can be computed with the new level 2 data by applying a composite analysis. A subsequently applied polynomial fit obtains the quiet time lines for daytime and nighttime, representing the typical seasonal variation under undisturbed conditions of the VLF signal amplitude for each considered link. The developed quiet time lines may serve as a tool to determine perturbations of the VLF signal amplitude with solar and geomagnetic as well as atmospheric origin. Also, they allow comparison of the VLF signal amplitude variation for different transmitter‐receiver links.

Analysis of single-mode Richtmyer–Meshkov instability using high-order incompressible vorticity—streamfunction and shock-capturing simulations

Two- and three-dimensional simulation results obtained using a new high-order incompressible, variable-density vorticity–streamfunction (VS) method and data from previous ninth-order weighted essentially nonoscillatory (WENO) shock-capturing simulations [M. Latini and O. Schilling, “A comparison of two- and three-dimensional single-mode reshocked Richtmyer-Meshkov instability growth,” Physica D 401, 132201 (2020)] are used to investigate the nonlinear dynamics of single-mode Richtmyer–Meshkov instability using a model of a Mach 1.3 air(acetone)/SF6 shock tube experiment [J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005)]. A comparison of the density fields from both simulations with the experimental images demonstrates very good agreement in the large-scale structure with both methods but differences in the small-scale structure. The WENO method captures the small-scale disordered structure observed in the experiment, while the VS method partially captures such structure and yields a strong rotating core. The perturbation amplitude growth from the simulations generally agrees well with the experiment. The simulation bubble and spike amplitudes agree well at early times. At later times, the WENO bubble amplitude is smaller than the VS amplitude and vice versa for the spike amplitude. The predictions of nonlinear single-mode instability growth models are shown to agree with the simulation amplitudes at early-to-intermediate times but underpredict the amplitudes at later times in the nonlinear regime. Visualizations of the mass fraction and enstrophy isosurfaces, velocity and vorticity fields, and baroclinic vorticity production and vortex stretching terms from the three-dimensional simulations indicate that, with the exception of the small-scale structure within the rollups, the VS and WENO results are in good agreement.

Local dynamic responses of magnetic reconnection to three-dimensional perturbations in a laboratory plasma

The dynamic responses of magnetic reconnection to localized three-dimensional (3D) magnetic field perturbations imposed by a pair of figure-8-shaped coils are investigated in the Magnetic Reconnection Experiment (MRX) device. Both the magnetic field geometry and current sheet profiles are altered by external perturbations. For the case when the inductive electric field associated with these perturbations aligns with the preexisting reconnection electric field, O-type magnetic structures appear within an elongated current sheet. When these magnetic structures are ejected downstream at the speed close to the ion outflow velocity, the inductive electric field is enhanced considerably. Despite that the imposed perturbation amplitude is larger than 30% of the original reconnecting magnetic field, the overall reconnection process remains robust without current sheet disruptions. This technique to form O-type magnetic structures can serve as an additional experimental knob for future systematic laboratory investigations of 3D magnetic reconnection and related instabilities without disrupting two-dimensional current sheet.

Defying eternal inflation in warm inflation with a negative running

It was pointed out previously [1] that a sufficiently negative running of the spectral index of curvature perturbations from (ordinary i.e. cold) inflation is able to prevent eternal inflation from ever occurring. Here, we reevaluate those original results, but in the context of warm inflation, in which a substantial radiation component (produced by the inflaton) exists throughout the inflationary period. We demonstrate that the same general requirements found in the context of ordinary (cold) inflation also hold true in warm inflation; indeed an even tinier amount of negative running is sufficient to prevent eternal inflation. This is particularly pertinent, as models featuring negative running are more generic in warm inflation scenarios. Finally, the condition for the existence of eternal inflation in cold inflation — that the curvature perturbation amplitude exceed unity on superhorizon scales — becomes more restrictive in the case of warm inflation. The curvature perturbations must be even larger, i.e. even farther out on the potential, away from the part of the potential where observables, e.g. in the Cosmic Microwave Background, are produced.

Inflationary quantum spectrum of the quasi-isotropic Universe

We investigate the quantum dynamics of the quasi-isotropic inflationary solution. This is achieved by deriving the Lagrangian and Hamiltonian for both the FLRW background and the inhomogeneous correction, via an expansion of the Einstein–Hilbert action up to second order in the perturbation amplitudes. Then we implement a semiclassical WKB scenario for which the inhomogeneous component of the Universe is treated as a “small” quantum subsystem, evolving on the classical isotropic background. Starting from the Wheeler–DeWitt equation, we recover a Schrödinger dynamics for the perturbations, in which the time dependence of the wave function emerges thanks to the classicality of the background, and we solve it for an inflationary phase. The main result of this paper is to show that, while the scalar component of the power spectrum has the standard scale invariant profile, the tensor one results to be not constrained by the inflationary expansion, apart from an overall normalization factor which guarantees a small tensor-to-scalar ratio. This means that the spatial distribution of the quasi-isotropic correction to the metric remains preserved, with the consequence that some information about the pre-inflationary Universe survives to the de Sitter expansion.

Ultra-high vacuum measurement based on <sup>8</sup>Li cold atoms manipulation

Stability plays a significant role in observing Fermi-Pasta-Ulam-Tsingou(FPUT) phenomenon in experiment successfully. However, few relevant studies have been documented in the literature. The primary object of this paper is to study the stability of FPUT phenomenon in the nonlinear fibers numerically. In this study, we take the sinusoidally perturbed continuous waves(CWs) with white noise imposed as the initial condition, which can be readily realized in real experiments. We find that both the perturbation amplitude and phase difference between the perturbation and pump can take drastic effects in affecting the stability of the resulting FPUT phenomenon. Firstly, as the perturbation amplitude increases, FPUT phenomenon becomes much more stable. When the perturbation amplitude reaches a critical value, the most stable FPUT phenomenon can be observed. As the further increase of the perturbation amplitude, the stability of the resulting FPUT phenomenon weakens. Secondly, the phase difference between the perturbation and pump take distinct effects on the stability of FPUT phenomenon for perturbation frequency locating in and outside of the conventional modulation instability (MI) band. For perturbation frequency locating inside the conventional MI band, as the phase difference between the perturbation and pump increases from zero, the corresponding FPUT phenomenon first becomes less stable; then most instable FPUT phenomenon can be observed at a critical phase difference; after then, the stability of the FPUT phenomenon enhances again. For perturbation frequency locating outside the conventional MI band, the stability of FPUT phenomenon enhances monotonously as the phase difference increases from 0 to π/2.To observe much more stable FPUT phenomenon, the above results show that the perturbation amplitude should be moderately large, and that the phase difference between the perturbation and the pump should be appropriate to avoid the most instable FPUT phenomenon that may arise.

Robustness and stability of doubly periodic patterns of the focusing nonlinear Schrödinger equation.

The nonlinear Schrödinger equation possesses doubly periodic solutions expressible in terms of the Jacobi elliptic functions. Such solutions can be realized through doubly periodic patterns observed in experiments in fluid mechanics and optics. Stability and robustness of these doubly periodic wave profiles in the focusing regime are studied computationally by using two approaches. First, linear stability is considered by Floquet theory. Growth will occur if the eigenvalues of the monodromy matrix are of a modulus larger than unity. This is verified by numerical simulations with input patterns of different periods. Initial patterns associated with larger eigenvalues will disintegrate faster due to instability. Second, formation of these doubly periodic patterns from a tranquil background is scrutinized. Doubly periodic profiles are generated by perturbing a continuous wave with one Fourier mode, with or without the additional presence of random noise. Effects of varying phase difference, perturbation amplitude, and randomness are studied. Varying the phase angle has a dramatic influence. Periodic patterns will only emerge if the perturbation amplitude is not too weak. The growth of higher-order harmonics, as well as the formation of breathers and repeating patterns, serve as a manifestation of the classical problem of Fermi-Pasta-Ulam-Tsingou recurrence.

Multi-scale dynamics of predator-prey systems with Holling-IV functional response

<abstract><p>In this paper, we propose a Holling-IV predator-prey system considering the perturbation of a slow-varying environmental capacity parameter. This study aims to address how the slowly varying environmental capacity parameter affects the behavior of the system. Based on bifurcation theory and the slow-fast analysis method, the critical condition for the Hopf bifurcation of the autonomous system is given. The oscillatory behavior of the system under different perturbation amplitudes is investigated, corresponding mechanism explanations are given, and it is found that the motion pattern of the non-autonomous system is closely related to the Hopf bifurcation and attractor types of the autonomous system. Meanwhile, there is a bifurcation hysteresis behavior of the system in bursting oscillations, and the bifurcation hysteresis mechanism of the system is analyzed by applying asymptotic theory, and its hysteresis time length is calculated. The final study found that the larger the perturbation amplitude, the longer the hysteresis time. These results can provide theoretical analyses for the prediction, regulation, and control of predator-prey populations.</p></abstract>

The interface instability development induced by the bulk density perturbations in accelerated media

The development of hydrodynamic instabilities has a significant impact on the operation of laser fusion systems. During radiation compression, the shells of a target are accelerated, resulting in the growth of perturbations at their interfaces. In this paper, we study the influence of density perturbations on the stability of the contact boundary during accelerated motion. The analysis is performed in a two-dimensional planar formulation using the linear approximation and assuming a weak spatial dependence on the temperature near the contact boundary. Due to the consideration of small time intervals, the phenomenon of heat conduction is not taken into account. The cases of acceleration of a medium described by the Mie–Grüneisen equation of state (EoS) into a vacuum and of acceleration of two contacting media, each described by the ideal plasma EoS, are considered. The time dependence of the amplitude of the boundary perturbation on time is obtained. The obtained values are in agreement with the results of numerical analysis. It is shown that the boundary curvature occurs independently of the acceleration direction. The theoretical results are compared with numerical results for laser fusion systems.

On the collision of railcars as an interaction of nonlinear shock wave-like perturbations

The article examines the collision of railcars based on the solution of hydrodynamic equations using shock waves during the transition from weak nonlinearity to perturbations of arbitrary amplitude. Several new mathematical issues have been set for the development of high-speed transport, which can be solved in the framework of hydrodynamics to describe the process of hydrodynamics, creating effective rolling stock dampers. which requires the improvement and development of the corresponding mathematical apparatus. In this work, we use a hydrodynamic approach to find the density distributions of matter during railcar collisions at high speeds, which is important in light of the problems of high-speed transport. In our approach, we found an analytical solution to the obtained hydrodynamic equations for the one-dimensional case. The equations under study were obtained taking into account nonequilibrium processes. To find a solution to the hydrodynamic equations, the shock wave approximation is used, similar to the soliton solutions we considered earlier. Taking into account possible deviations from the results of a one-dimensional problem is considered. Such a reduction of solutions of hydrodynamic equations to shock waves has not been considered previously and may be of interest for a wide variety of applied problems. The resulting consideration of railcar collisions is important for solving problems of transport safety and technospheric safety.