Low Initial Energy Research Articles

The Asymptotic Behavior and Blow-Up Rate of a Solution with a Lower Bound on the Highest Existence Duration for Semi-Linear Pseudo-Parabolic Equations

This note addresses the initial-boundary value problem for a class of semi-linear pseudo-parabolic equations defined on a smooth bounded domain, with an emphasis on determining the asymptotic behavior and blow-up rate of the solution. Our analysis considers both low-initial energy and critical-initial energy cases, with a specific focus on establishing a lower bound on the maximal existence time of the solutions to this problem.

A discrete CMUT self-biasing circuit towards implanted devices application

Wireless power transfer is an essential feature of biomedical engineering. It reduces the need for energy storage devices in medical implants. To recharge a body implanted battery, a convenient way is to transmit ultrasounds through the skin to a connected ultrasonic transducer. Lead-less, System-on-Chip compatible (SoC) and wideband, Capacitive Micromachined Ultrasonic Transducers (CMUT) are competitive with piezoelectric based technologies. However, their need for a high bias voltage is an obstacle to their use in implanted medical devices (IMDs). The voltage source required must meet precise specifications, such as reliability and volume, which the research community intends to respect. To meet this challenge, this work proposes an electronic circuit that allows a CMUT device to self-bias from a very low initial energy input. After presenting the electronic architecture and its main features, simulation and experimental results validate the solution’s working principle and operating points. With an electronic circuit made up of discrete components, a bias voltage of 60 V is built up from an implanted battery voltage of 2.2 V and an incident pressure of 120 kPa in water.

Unlocking the ultrafast laser response and low initiation energy of perchlorate-free tetrazine-based energetic coordination compounds

Laser ignition technology holds significant and diverse applications in the domains of weapon equipment, aerospace and engineering blasting because of its exceptional resistance to electromagnetic interference, outstanding ignition efficiency and flexible controllability. However, the commercial initiation material B/KNO3 still suffers the high minimum laser initiation energy (Emin = 723.2 mJ) and lengthy ignition delay time (ID=160 ms). In this study, we have successfully synthesized two perchlorate-free energetic coordination compounds (ECCs): [Cu(DHT)(NO3)(H2O)](NO3) 1 and [Ni(DHT)(H2O)2](NO3)22 (DHT=3,6-dihydrazine-1,2,4,5-tetrazine). Though two compounds with similar structures show high explosion parameter values, the behaviors of laser responsive ignition are different. Noteworthy, laser ignition tests demonstrate that Cu-based 1 exhibits excellent laser response characteristics with an ultra-low Emin value of 4.2 mJ and a short ID time of 20 ms, while Ni-based 2 shows extremely insensitivity to laser under identical conditions. Furthermore, theoretical calculations reveal that the higher sensitivity of 1 towards laser response activity might be attributed to the narrower band gap (Eg = 0.44 eV) resulting from Cu centers in contrast with 2. In addition, mechanical sensitivities between 1 and 2 are discussed sufficiently by theoretical and structural studies. Compared to the commercial B/KNO3, compound 1 has promise to serve as a competitive laser ignition material.

Transient behaviour analysis in silicon carbide alpha particle detector using TCAD and SRIM simulation

Time response characteristics of α particle detector are crucial for monitoring radiation fields varied with time and its characterization of pulse radiation field. Here, SRIM-informed TCAD simulation is utilized to visually investigate the transient behaviors of carriers and alpha particles in 4H-SiC Schottky barrier detectors for the time response characteristics. We identified external bias voltage and incident particle energy as key factors to influence transient current pulse broadening. Low-energy alpha particles result in low initial kinetic energy of the ionization-generated carriers, leading to transient current broadening and reduced time resolution characteristics. Conversely, high-energy alpha particles ionize carrier with high drift velocity, preventing the broadening effect. Our simulation provides a planform and valuable guidance for optimizing alpha particle detector, selecting appropriate bias voltages, and enhancing time resolution capabilities.

Numerical study on detonation initiation by multiple hot spots

Detonation initiation is important not only for the development of advanced detonation engines and but also for the control of accidental explosion. There are mainly two types of detonation initiation, i.e., direct initiation and indirect initiation. This work focuses on direct detonation initiation which has a short initiation distance but requires large amount of energy deposition. Specially, we investigate the reduction in the critical initiation energy through replacing the single hot spot by multiple hot spots. The transient detonation initiation process in a stoichiometric H2/O2/Ar mixture is examined through two-dimensional simulations considering detailed chemistry. It is found that under the same initiation energy, detonation initiation fails for a single large hot spot while successful detonation initiation can be achieved by employing six small hot spots. The collisions among adjacent transverse detonation waves induce new local explosions, which play a pivotal role in detonation initiation. To further assess the impact of wave collision, we change the hot spot energy used in the multiple hot spot configuration. For relatively low initiation energy, the blast wave quickly decays and decouples with the reaction zone. Consequently, the collision among transverse shock waves cannot induce new local explosion and detonation initiation fails. Increasing the initiation energy can enhance the blast wave and is favorable to the formation of local explosion, facilitating the rapid detonation initiation. Furthermore, the influence of hot spot number on detonation initiation is assessed. Interestingly the hot spot number is found to have non-monotonic effect on detonation initiation. Splitting a single hot spot into multiple hot spots enhances detonation initiation since the wave collision helps to induce local explosion. However, as the hot spot number increases, the energy of each hot spot is decreased and becomes excessively dispersed, which results in relatively weak blast wave and thereby weak wave interaction. Consequently, local explosion cannot be triggered and detonation initiation fails for relatively large hot spot numbers. This study provides insights on promoting detonation initiation through multiple hot spots.

Willmore flow of complete surfaces

We consider the Willmore flow equation for complete, properly immersed surfaces in Rn. Given bounded geometry on the initial surface, we extend the result in [5] and prove short time existence and uniqueness of the Willmore flow. We also show that a complete Willmore surface with low Willmore energy must be a plane, and that a Willmore flow with low initial energy and Euclidean volume growth must converge smoothly to a plane.

Infinite-time blowup and global solutions for a semilinear Klein–Gordan equation with logarithmic nonlinearity

In this article, our focus lies in investigating the existence of global solutions and the occurrence of infinite-time blowup for a nonlinear Klein–Gordon equation characterized by logarithmic nonlinearity, specifically in the form . Notably, our inquiry involves handling logarithmic functions within the reaction terms and accommodating the functions and in the boundary terms. Consequently, a pivotal task is to establish blowup conditions that intricately hinge on the characteristics of the domains and the boundary conditions. It is of significant note that our exploration incorporates domain and boundary information into the formulation of blowup conditions. By employing a combination of the potential well technique and energy estimation methodology, we delve into scenarios of low initial energy and critical initial energy. In doing so, we derive a set of sufficient conditions that encompass both the global existence and the potential explosive behaviour of solutions pertaining to this variant of the Klein–Gordon equation. This work contributes to enhancing our understanding of the intricate interplay between logarithmic nonlinearity, domain characteristics, and boundary conditions in shaping the behaviour of solutions in the realm of nonlinear wave equations.

Exploring the effects of turbulent field on propagation behaviors in confined hydrogen-air explosion using OpenFOAM

Explosion always happens in turbulent field, which is hard to measure in reality. This paper explores the influence of turbulent kinetic energy on the propagation behaviors of flame and pressure of stoichiometric hydrogen-air explosion in confined vessel, using large eddy simulation. The momentum equation and progressive variable equation are adapted to consider interaction of turbulence and flame. The results reveal that with initial turbulent kinetic energy increasing, its promoting effects on flame and pressure propagation weaken. For flame at low initial turbulent kinetic energy and low initial pressure, it undergoes three propagating stages: acceleration, steady propagation and deceleration. In addition, flame deceleration is caused by rapid decrease of flow velocity which falls faster with initial turbulent kinetic energy increasing. Furthermore, explosion pressure propagates faster with initial turbulent kinetic energy increasing. Sharp fluctuation of flow velocity appears in the flame zone where big pressure gradient exists.

Low energy electron injection for direct laser acceleration

The feasibility of ionization injection for Direct Laser Acceleration (DLA) of electrons up to hundreds of MeV has been studied analytically. Criteria for effective injection determining a range of background and in-channel plasma parameters, laser intensity, etc., were found using phase portraits of the system deduced from the simplified analytical model. The found optimal trajectory in the phase space corresponds to the electron with low (few eV) initial energy experiencing ∼109 times energy gain. For this to occur, electron density should be a few percent of the critical density, while the in-channel electron density should be ∼3 times lower. The analytically obtained dependence of the energy gain on the initial electron longitudinal and transverse momenta corresponds well to the results of exact numerical simulations of an electron motion in the plasma channel. To test the theory, a series of PIC simulations were carried out. PIC simulation confirms the model if the plasma channel has appropriate parameters. The developed approach can form the basis for further studies of electron injection in DLA varying plasma and laser parameters as well as initial electron energies.

Fractional nonlinear energy sinks

The cubic or third-power (TP) nonlinear energy sink (NES) has been proven to be an effective method for vibration suppression, owing to the occurrence of targeted energy transfer (TET). However, TET is unable to be triggered by the low initial energy input, and thus the TP NES would get failed under low-amplitude vibration. To resolve this issue, a new type of NES with fractional nonlinearity, e.g., one-third-power (OTP) nonlinearity, is proposed. The dynamic behaviors of a linear oscillator (LO) with an OTP NES are investigated numerically, and then both the TET feature and the vibration attenuation performance are evaluated. Moreover, an analogy circuit is established, and the circuit simulations are carried out to verify the design concept of the OTP NES. It is found that the threshold for TET of the OTP NES is two orders of magnitude smaller than that of the TP NES. The parametric analysis shows that a heavier mass or a lower stiffness coefficient of the NES is beneficial to the occurrence of TET in the OTP NES system. Additionally, significant energy transfer is usually accompanied with efficient energy dissipation. Consequently, the OTP NES can realize TET under low initial input energy, which should be a promising approach for micro-vibration suppression.

Spatial radiation features of the off-axis collision between a relativistic electron and a tightly focused linearly polarized laser

The collision between relativistic electrons and a tightly focused linearly polarized laser pulse produced nonlinear inverse Thomson scattering (NITS), which generates backward x-rays. The effects of the initial transverse position of electrons with varied initial energy on the angular distribution of radiation power and spectrum are studied through numerical simulation. For the electrons with low initial energy (i.e. ), the off-axis collision breaks the spatial symmetry of x-ray radiation compared with the axial collision, the radiation direction is also torqued towards the same off-axis direction. There exists an optimal initial transverse position of electrons, which means the electron emitted from this position obtains greater radiation power. For the high-energy () electrons, the effect of torsion is not significant. The impact of off-axial is mainly manifested in the high-order harmonic spectrum. These findings help obtain high quality x-rays and modulate NITS radiation symmetry by electron parameters.

ДОЗИМЕТРИЯ ТРИТИЯ НА КЛЕТОЧНОМ УРОВНЕ

Introduction 1. Tritium radioisotope and its energy spectrum 2. Methods for calculating doses from radiation of radionuclides 2.1 General equation for absorbed dose rate 2.2 Absorbed dose rate versus average energy 2.3 Formulas for calculating dose and S-values ​​from radiation of radionuclides 2.4 Method of dose point nuclei 2.5 MIRD effective stopping power method 2.6 Geometric factor 3. Analysis of S-value calculations by various methods 3.1 Values ​​of the CSDA range at low initial electron energies 3.2 Comparison of S-value calculations for low energy electrons 3.3 Comparison of tritium S-value calculations 4. Evaluation of S-value calculations in the absence of spherical symmetry Conclusion

Von Karman thermoelastic plates: Existence and nonexistence of global solutions

This paper undertakes a study of behavior of solutions corresponding to von Karman thermoelastic plates involving a nonlinear source. It is well-known that the source term gives rise to finite-time blow-up of solutions and drives the system to possible instability. So, it is of interest to explore the mechanism of the source and the dissipation. In this paper, on the one hand, for low initial energy, we apply modified potential well method and differential inequality argument to prove the solution globally exists and decays exponentially to zero if the initial data starts from the stable set and fails to exist globally when the initial data starts from the unstable set. On the other hand, for high initial energy, with the aid of the monotonicity of the $ L^{2} $ norm of the solution with a positive perturbed constant and some differential inequality argument as well as energy inequalities, we are in a position to prove that the solution to the studied problem blows up in finite time. At last, an explicit lower bound for blow-up time is obtained.

Blow-up phenomena for a damped plate equation with logarithmic nonlinearity

This paper is concerned with the finite time blow-up phenomena for a damped plate equation with logarithmic nonlinearity under the Navier boundary condition. Combining potential well method and modified differential inequality technique, we establish the finite time blow-up properties of solutions with low initial energy E(0)≤d and high energy. In particular, we consider the case where the initial displacement and initial velocity have the same (∫Ωu0u1dx>0) or different signs (∫Ωu0u1dx>−‖u0‖∗22) in the sense of L2 inner product at high energy level. Moreover, the lower bounds for the blow-up time in subcritical, critical, supercritical and ultra-supercritical cases are also derived.

Exploration of the induced fluid-disturbance effect in CBM co-production in a superimposed pressure system

Fluid disturbance in coalbed methane co-production in a superimposed pressure system is universal. Two sets of tests were conducted with different constant outlet pressure values and reservoir pressure gradients to explore the fluid-disturbance characteristics. First, in the constant outlet pressure mode, reservoirs with large differences in the initial fluid energy are prone to fluid disturbance in the early stage of co-production, and the dynamic pressure balance drives part of the fluid from reservoirs with a high initial fluid energy to flow to reservoirs with a low initial fluid energy. Second, an increase in the constant outlet pressure value reduces the intensity of the fluid disturbance, and the reservoir pressure gradient has a positive effect on the fluid-disturbance effect. The design of a constant-pressure co-production must incorporate disturbance-reduction measures and appropriately increase the constant outlet pressure at the wellbore outlet. Alternatively, reservoirs with smaller reservoir pressures should be selected for co-production. Third, the gas-production mode of a single reservoir under the constant-pressure co-production can be separated into three major categories and seven subcategories: the conventional mode is applicable to reservoirs with a high initial fluid energy, the inhibition mode is primarily for reservoirs with a medium-low initial fluid energy, and the backflow mode is primarily for reservoirs with a low initial fluid energy.

Long-term multi-wavelength variability and extreme spectral properties of the TeV-detected blazar 1ES 0033+595

Context. The multi-wavelength (MWL) properties of some TeV-detected blazars are still poorly understood. By studying the MWL properties of the BL Lacertae source 1ES 0033+595, we make further progress in our understanding of the instable physical processes responsible for particle acceleration to ultra-relativitic energies and the observed emission properties. Aims. This paper presents the results of a detailed X-ray timing and spectral analysis of the source 1ES 0033+595, allowing us to draw conclusions about the physical mechanisms responsible for particle acceleration and the generation of X-ray emission. We also examined the long-term MWL behaviour of the source and interband cross-correlations. Methods. Our study focused on the observations performed with the X-Ray Telescope on board the Neil Gehrels Swift Observatory (Swift-XRT) in the period 2005–2022. The MWL data sets were obtained with several space and ground-based instruments. We analysed the MWL flaring behaviour during the entire period, as well as in particular subperiods selected on the basis of the X-ray flaring activity of the target; constructed histograms characterising the distributions of the different spectral parameters and MWL fluxes; and checked cross-correlations between these parameters and/or MWL fluxes. The obtained results are compared with the predictions of the various theoretical studies and simulations presented by the different authors to date. Results. The source showed extreme spectral properties with dominance of high spectral curvature, frequent occurrence of very and extremely hard photon indices, and the presence of a synchrotron spectral energy distribution (SED) peak in the hard X-ray range (sometimes at energies beyond 10 keV). These properties reveal the importance of first-order Fermi acceleration with very low initial particle energy distribution, along with the co-existence of stochastic acceleration and hadronic processes. The source was characterised by very uneven and erratic flaring activity in diverse epochs: the period of strong flares (2013–2016) was preceded by a moderate variability and followed by a gradual long-term decrease in MWL flaring activity. We detected a number of instances of intraday 0.3–10 keV variability, which were sometimes observed within a few hundred seconds and explained by the interaction between the relativistic shock front and jet inhomogeneities with strong magnetic fields. The X-ray and γ-ray fluxes showed a lognormal distribution, which hints at the imprint of accretion disc instabilities on the blazar jet.

Iron and Copper Doped Zinc Oxide Nanopowders as a Sensitizer of Industrial Energetic Materials to Visible Laser Radiation.

The development of methods ensuring reliable control over explosive chemical reactions is a critical task for the safe and efficient application of energetic materials. Triggering the explosion by laser radiation is one of the promising methods. In this work, we demonstrate a technique of applying the common industrial high explosive pentaerythritol tetranitrate (PETN) as a photosensitive energetic material by adding zinc oxide nanopowders doped with copper and iron. Nanopowders of ZnO:Fe and ZnO:Cu able to absorb visible light were synthesized. The addition of one mass percent nanopowders in PETN decreased the threshold energy density of its initiation through Nd:YAG laser second harmonic (2.33 eV) by more than five times. The obtained energetic composites can be reliably initiated by a CW blue laser diode with a wavelength of 450 nm and power of 21 W. The low threshold initiation energy and short irradiation exposure of the PETN-ZnO:Cu composite makes it applicable in laser initiation devices. PETN-ZnO:Cu also can be initiated by an infrared laser diode with a wavelength of 808 nm. The proposed photochemical mechanism of the laser-induced triggering of the explosion reaction in the studied energetic composites was formulated. The results demonstrate the high promise of using nanomaterials based on zinc oxide as a sensitizer of industrial energetic materials to visible laser radiation.

Cyclic behaviour of demountable metallic corrugated shear panel dampers

This study aims to develop a new demountable corrugated shear panel damper (DCSPD). The developed device is to upgrade the flat shear panel of the classical shear panel damper (classical SPD) using a corrugated shear panel. And the energy dissipating parts of the damper are demountable, allowing for easy processing, transport, and assembly onsite. Moreover, the new damper can make full use of the geometrical properties of the corrugated shear panel to overcome the shortcomings of the classical SPD, such as low initial stiffness and poor energy dissipation. A series of tests were conducted to systematically study the seismic performance of the proposed damper under quasi-static cyclic loading conditions. The effects of three key design parameters are discussed, including the corrugated direction and thickness of the shear panel and the thickness of the flange plate. The experimental results demonstrate that the direction of the corrugated shear panel changes the plastic failure modes of the dampers, resulting in the overall out-of-plane buckling failure of demountable horizontally corrugated shear panel damper (DCSPD-H) and the local buckling failure of demountable vertically corrugated shear panel damper (DCSPD-V). Therefore, the shear bearing capacity, ductility coefficient, and energy dissipation capacity of DCSPD-H are 5.56%, 10.23%, and 35.37% higher than those of the DCSPD-V, respectively. Moreover, an increase in the thickness of the shear panel will significantly improve the seismic performance of the damper, whereas an increase in the thickness of the flange plate may hinder the deformability of the damper. Further, the finite element models of tested dampers were established, and the plastic collapse mechanisms and the sharing of energy-absorbing of each part were investigated. Finally, simple design equations are presented through parametric studies of dampers with different geometric dimensions.

Global existence and blow up of the solution for nonlinear Klein-Gordon equation with variable coefficient nonlinear source term

Abstract This article is devoted to study the existence of global solutions and finite time blow-up of local solution for nonlinear Klein-Gordon equation with variable coefficient nonlinear source term. By applying the potential well and energy estimation method, in low initial energy and critical initial energy, we derive some sufficient conditions which are global existence and explosion of the solutions for this type of Klein-Gordon equation.

Global existence and blow up for a class of pseudo-parabolic equations with logarithmic nonlinearity

In this paper, we discuss the initial–boundary value problem for a class of pseudo-parabolic equations with logarithmic nonlinearity ut−aΔut−Δu+bu=|u|p−2ulog|u|. By the method of Galerkin approximation, we obtain the global existence of weak solutions with low initial energy and critical initial energy J(u0)≤d in the case of 1<p<2. What is more, we discuss the finite time blow up of weak solutions, and the ground-state solution of the corresponding steady-state equation under the condition of 2<p<2∗.