Establishment of control equations and adjoint equations using block-pulse functions for optimal control of linear systems with time delays

Control equation and adjoint equation are established by using block pulse functions, which transforms the linear time varying systems with time delays into a system of algebraic equations and the optimal control problems are transformed into an optimization problem of multivariate functions thereby achieving the optimal control of linear systems with time delays.

Transcranial pulse current stimulation improves the locomotor function in a rat model of stroke

Previous studies have shown that transcranial pulse current stimulation(tPCS) can increase cerebral neural plasticity and improve patients' locomotor function.However, the precise mechanisms underlying this effect remain unclear.In the present study, rat models of stroke established by occlusion of the right cerebral middle artery were subjected to tPCS, 20 minutes per day for 7 successive days.tPCS significantly reduced the Bederson score, increased the foot print area of the affected limbs, and reduced the standing time of affected limbs of rats with stroke compared with that before intervention.Immunofluorescence staining and western blot assay revealed that tPCS significantly increased the expression of microtubule-associated protein-2 and growth-associated protein-43 around the ischemic penumbra.This finding suggests that tPCS can improve the locomotor function of rats with stroke by regulating the expression of microtubule-associated protein-2 and growth-associated protein-43 around the ischemic penumbra.These findings may provide a new method for the clinical treatment of poststroke motor dysfunction and a theoretical basis for clinical application of tPCS.The study was approved by the Animal Use and Management Committee of Shanghai University of Traditional Chinese Medicine of China(approval No.PZSHUTCM190315003) on February 22, 2019.

Synchronous measurements of prefrontal activity and pulse rate variability during online video game playing with functional near-infrared spectroscopy

Interactions between the central nervous system(CNS)and autonomic nervous system(ANS)play a crucial role in modulating perception,cognition,and emotion production.Previous studies on CNS–ANS interactions,or heart–brain coupling,have often used heart rate variability(HRV)metrics derived from electrocardiography(ECG)recordings as empirical measurements of sympathetic and parasympathetic activities.Functional near-infrared spectroscopy(fNIRS)is a functional brain imaging modality that is increasingly used in brain and cognition studies.The fNIRS signals contain frequency bands representing both neural activity oscillations and heartbeat rhythms.Therefore,fNIRS data acquired in neuroimaging studies can potentially provide a single-modality approach to measure task-induced responses in the brain and ANS synchronously,allowing analysis of CNS–ANS interactions.In this proof-of-concept study,fNIRS was used to record hemodynamic changes from the foreheads of 20 university students as they each played a round of multiplayer online battle arena(MOBA)game.From the fNIRS recordings,neural and heartbeat frequency bands were extracted to assess prefrontal activities and shortterm pulse rate variability(PRV),an approximation for short-term HRV,respectively.Under the experimental conditions used,fNIRS-derived PRV metrics showed good correlations with ECG-derived HRV golden standards,in terms of absolute measurements and video game playing(VGP)-related changes.It was also observed that,similar to previous studies on physical activity and exercise,the PRV metrics closely related to parasympathetic activities recovered slower than the PRV indicators of sympathetic activities after VGP.It is concluded that it is feasible to use fNIRS to monitor concurrent brain and ANS activations during online VGP,facilitating the understanding of VGP-related heart–brain coupling.

Numerical Solution of Two-Dimensional Nonlinear Stochastic Ito-Volterra Integral Equations by Applying Block Pulse Functions

This paper investigates the numerical solution of two-dimensional nonlinear stochastic Itô-Volterra integral equations based on block pulse functions. The nonlinear stochastic integral equation is transformed into a set of algebraic equations by operational matrix of block pulse functions. Then, we give error analysis and prove that the rate of convergence of this method is efficient. Lastly, a numerical example is given to confirm the method.

Time-dependent density functional theoretical studies on the photo-induced dynamics of an HCI molecule encapsulated in C60 under femtosecond laser pulses

By using first-principles simulations based on time-dependent density functional theory, the chemical reaction of an HCl molecule encapsulated in C60 induced by femtosecond laser pulses is observed. The H atom starts to leave the Cl atom and is reflected by the C60 wall. The coherent nuclear dynamic behaviors of bond breakage and recombination of the HCl molecule occurring in both polarized parallel and perpendicular to the H-Cl bond axis are investigated. The radial oscillation is also found in the two polarization directions of the laser pulse. The relaxation time of the H-Cl bond lengths in transverse polarization is slow in comparison with that in longitudinal polarization. Those results are important for studying the dynamics of the chemical bond at an atomic level.

Integral Transformation of the Pulse Function for High Voltage Technique

One function for approximating pulse quantities in high voltage technique is presented in this paper. The function derivative, its integral, as well as its Laplace and Fourier transform are obtained analytically. Integral transformations of the pulse function are needed in frequency domain calculations of lightning induced effects in the case of a lossy ground. The pulse function having adequately chosen parameters is applied in lightning discharge modeling for lightning electromagnetic field calculation, and the results are in agreement with the results from literature. The choice of function parameters is based on their influence on the pulse waveshape which is presented in the paper. Numerical results for the Fourier transform are presented for different usually used pulse functions. The advantages of this function are simple choice of its parameters according to the desired waveshape characteristics and analytical solutions useful in lightning discharge modeling, electromagnetic field computation and induced effects calculations.

Single-pulse chaotic dynamics of functionally graded materials plate

Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained for this sys- tem, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predic- tions. And from our analysis, when the chaotic motion oc- curs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplemen- tary subspace.

Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils

The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows： 1） the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2） the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3） the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180°, there are two additional reverse concentrative areas on both sides of x axis.

Regeneration of Acid Orange 7 Exhausted Granular Activated Carbon Using Pulsed Discharge Plasmas

In this paper, a pulsed discharge plasma （PDP） system with a multi-needle-to-plate electrodes geometry was set up to investigate the regeneration of acid orange 7 （AO7） exhausted granular activated carbon （GAC）. Regeneration of GAC was studied under different conditions of peak pulse discharge voltage and water pH, as well as the modification effect of GAC by the pulse discharge process, to figure out the regeneration efficiency and the change of the GAC structure by the PDP treatment. The obtained results showed that there was an appropriate peak pulse voltage and an optimal initial pH value of the solution for GAC regeneration. Analyses of scanning electron microscope （SEM）, Boehm titration, Brunauer-Emmett-Teller （BET）, Horvath-Kawazoe （HK）, and X-ray Diffraction （XRD） showed that there were more mesopore and macropore in the regenerated GAC and the structure turned smoother with the increase of discharge voltage; the amount of acidic functional groups on the GAC surface increased while the amount of basic functional groups decreased after the regeneration process. From the result of the XRD analysis, there were no new substances produced on the GAC after PDP treatment.

Altered heart rate variability and pulse-wave velocity after spinal cord injury

BACKGROUND Heart rate variability(HRV) and pulse-wave velocity(PWV),indicators of cardiac function,are altered in patients with spinal cord injury(SCI),suggesting that autonomic cardiac function and arterial stiffness may underlie the high risk of cardiovascular complications in these patients.No study has simultaneously investigated HRV and PWV in the same patients.AIM To evaluate cardiovascular complications in SCI patients by comparing HRV and PWV between patients with and without SCI.METHODS In this cross-sectional pilot study,patients with(n = 60) and without SCI(n = 60) were recruited from December 7,2019 to January 21,2020.Each participant received a five-minute assessment of HRV and the cardiovascular system using the Medicore HRV Analyzer SA-3000 P.Differences in HRV and PWV parameters between participants with and without SCI were statistically examined.RESULTS We observed a significant difference between participants with and without SCI with respect to the standard deviation of all normal-to-normal intervals,square root of the mean sum of squared successive risk ratio interval differences,physical stress index,total power,very-low frequency,low frequency,high frequency,and arterial elasticity.CONCLUSION Patients with SCI have weaker sympathetic and parasympathetic activity as well as lower arterial elasticity compared to those without,suggesting that SCI may increase cardiac function loading.

Selective stimulation of smaller nerve fibers by single electrode using Biphasic Rectangular Pulses

Based on the F-H model, a simulation system to study the excitation properties of myelinated nerve fibers was developed. In order to minimize electrochemical damage of nerve tissue, a method was studied to selectively stimulate the smaller nerve fibers by single electrode employing charge-balanced biphasic rectangular pulses, in which an anode pulse with lower amplitude and longer pulse width was added before a cathode pulse with higher amplitude and short pulse width. The simulation results proved that the method is effective in selective stimulation of smaller nerve fibers in a compound nerve trunk in certain conditions. The feasibility of this method was also verified by animal experiments on the sciatic nerve trunks of toads. The amplitude and delay of compound action potential and the results of collision experiments proved that the method is valid. These methods will be very useful in functional neuromuscular stimulation.

Study on Ultra-Short Laser Pulse Ablation of Metals by Molecular Dynamics Simulation

The dynamical progresses involved in ultra-short laser pulse ablation of face-centered cubic metals under stress confinement condition are described completely using molecular dynamics method. The laser beam absorption and thermal energy turning into kinetics energy of. atoms are taken into account to give a detailed picture of laser metal interaction. Superheating phenomenon is observed, and the phase change from solid to liquid is characterized by a destroyed atom configuration and a decreased number density. The steep velocity gradients are found in the systems of Cu and Ni after pulse in consequence of located heating and exponential decrease of fluences following the Lambert-Beer expression. The shock wave velocities are predicted to be about 5 000 m/s in Cu and 7 200 m/s in Ni. The higher ablation rates are obtained from simulations compared with experimental data as a result of a well-defined crystalline surface irradiated by a single pulse. Simulation results show that the main mechanisms of ablation are evaporation and thermoelastic stress due to located heating.

Pulsed Sound Waves in a Compressible Fluid

The propagation along oz of pulsed sound waves made of sequences of elementary unit pulses U (sin τ) where U is the unit step function and τ = kz -ωt is analyzed using the expansion of U (sin τ) and of the Dirac distribution δ (sin τ) in terms of τ-nπ where n is an integer. Their properties and how these pulsed sound waves could be generated are discussed.

Time-Grating for the Generation of STUD Pulse Trains

Spike train of uneven duration or delay(STUD)pulses hold potential for laser-plasma interaction(LPI)control in laser fusion.The technique based on time grating is applied to generate an STUD pulse train.Time grating,a temporal analogy of the diffraction grating,can control the pulse width,shape,and repetition rate easily through the use of electro-optical devices.The pulse width and repetition rate are given by the modulation frequency and depth of the phase modulation function in theory and numerical calculation.The zero-chirped phase modulation is good for the compression effect of the time grating.A principle experiment of two pulses interfering is shown to verify the time grating function.

Exact Solutions to Short Pulse Equation

In this paper, dependent and independent variable transformations are introduced to solve the short pulse equation. It is shown that different kinds of solutions can be obtained to the short pulse equation.

Modeling of Material Shielding Effectiveness Against Electromagnetic Pulse in Time-domain

To characterize the shielding effectiveness(SE) of materials against electromagnetic pulse(EMP) that cannot be adequately evaluated by traditional test methods,a transfer function model of SE is proposed.Using homemade broadband coaxial fixture,the SE of a metal fabric material against square-pulse and electrostatic discharge(ESD) EMP is tested in the time domain.The peak SE calculated from the test results matches well with that obtained theoretically.Based on the system identification theory,we propose the transfer function model of SE,which takes the square pulse and human body model ESD EMP data obtained in the tests as training data and takes the machine model as verification data,as well as a second-order expression of the transfer function.Using the transfer function model,the waveforms of the shield-penetrated square-pulse EMP and the ESD EMP are actually predicted.From the perspective of system identification,this accurate prediction of the shielded waveform of EMP provides a reliable way for evaluating SE of materials against EMP.

High-order harmonic generation of the cyclo[18]carbon molecule irradiated by circularly polarized laser pulse

High-order harmonic generation of the cyclo[18]carbon(C_(18) ) molecule under few-cycle circularly polarized laser pulse is studied by time-dependent density functional theory. Compared with the harmonic emission of the ring molecule C_(6)H_(6) having similar ionization potential, the C_(18) molecule has higher efficiency and cutoff energy than C_(6)H_(6) with the same laser field parameters. Further researches indicate that the harmonic efficiency and cutoff energy of the C_(18) molecule increase gradually with the increase of the laser intensity of the driving laser or decrease of the wavelength, both are larger than those of the C_(6)H_(6) molecule. Through the analysis of the time-dependent evolution of the electronic wave packets, it is also found that the higher efficiency of harmonic generation can be attributed to the larger spatial scale of the C_(18) molecule,which leads to a greater chance for the ionized electrons from one atom to recombine with others of the parent molecule.Selecting the suitable driving laser pulse, it is demonstrated that high-order harmonic generation in the C_(18) molecule has a wide range of applications in producing circularly polarized isolated attosecond pulse.

A Flexible Multichannel Digital Random Pulse Generator Based on FPGA

The present paper describes a multichannel digital random pulse generator implemented in a 65-nm FPGA device. The random time interval generation is based on inverse transformation method. The output pulse generation rate, pulse width and the probability distribution function (PDF) of each channel might be individually selected by the computer through a USB cable connection. Statistical properties of the output channels can be adjusted and recorded in a fully dynamic flexible manner. The Poisson and uniform PDFs were tested and implemented for up to eight different channels in experiment, however, the implementation of any arbitrary PDF is possible by programming capability of the device as well. Detailed experimental results are expressed in the manuscript. The proposed equipment makes it possible to verify the complicated multichannel detection systems without having the radioactive experimental tests. This is a low cost instrumentation due to the FPGA-based construction.

FREQUENCY-CODED OPTIMIZATION OF HOPPED-FREQUENCY PULSE SIGNAL BASED ON GENETIC ALGORITHM

The Frequency-Coded Pulse (FCP) signal has good performance of range and Doppler resolution. This paper first gives the mathematical expression of the ambiguity function for FCP signals, and then presents a coding rule for optimizing FCP signal. The genetic algorithm is presented to solve this kind of problem for optimizing codes. Finally, an example for optimizing calculation is illustrated and the optimized frequency coding results are given with the code length N=64 and N=128 respectively.

Cognate pulse sorting method based on beam missions characteristics

In most multi-function phased array radar applications, multiple missions, including airspace searching and target tracking, are usually performed simultaneously by the digital beam-forming technique and the time dividing method. This paper presents a novel method to classify pulses of different missions from an interleaved pulse sequence emitted by the same radar, which is significant in radar electronic reconnaissance and electronic support measure. Firstly, two hypotheses, i.e., pulse relativity within the same mission and pulse independence among different missions, are proposed by analyzing the antenna pattern and the beam scheduling method of the phased array radar. Based on the above two hypotheses, an optimal model for pulse classification is exploited with pulse amplitude series, where the absolute-value sum of second order difference is taken as the optimal kernel to measure sequence smooth continuity. Finally, several pieces of sequences under different numbers of missions and tracking data rates are simulated for algorithm verification. The simulation results show that the long data length and the high data rate will increase classification efficiency due to the validity of the two hypotheses in sufficient pulse amplitude sequence.