Far-field vector-diffraction of off-axis parabolic mirror under oblique incidence

Based on a full vector-diffraction theory, a detailed theoretical study is carried out, aiming at providing a clear insight into the effects of different focusing and off-axis parabola parameters on far-field vector-diffraction properties of an offaxis parabolic mirror in the presence of misalignments of the incoming beam. The physical origin of these effects is also explored. The results show that the far-field intensity profile is altered by the distortion-, coma-, and astigmatism-like aberrations, which are caused by oblique incidence rather than inherent aberrations for the off-axis configuration. The radius of 90% encircled energy also increases but does not change monotonically with incident beam size increasing, or rather,it first decreases and then increases. The focal shift strongly depends on the effective focal length and oblique incidence angle, but it is almost independent of the beam size, which affects the focusing spot patterns. The intensity distribution produces a higher astigmatic image with off-axis angle increasing. Coma-like aberration starts to become dominant with beam size increasing and results in larger curved propagation trajectory. The incident polarization also affects the intensity distribution. The variation in the Strehl ratio with oblique incidence angle strongly depends on the misalignment direction and beam size as well. In addition, we find that the difference in locus between the catacaustic and the diffraction focus in the meridian is small. But the locus of the sagittal foci is obviously different from the locus of the meridian foci and the catacaustic focus. Moreover, the peak intensity of the sagittal focus is maximum, and the ratio of the peak intensity to that in the meridian plane is approximately 1.5. Understanding these effects is valuable for assessing a practical focused intensity and describing the motion of charged particles under a strong electric field in ultraintense laser–matter interaction.

Configuration optimization of off-axis parabolic mirror for enhancing the focusability of a laser beam

We demonstrate a configuration optimization process of an off-axis parabolic mirror to maximize the focused peak intensity based on a precise knowledge of the tight focusing properties by using a full vector-diffraction theory and obtain an optimum configuration scaling rule, which makes it possible to achieve the maximum peak intensity. In addition, we also carry out an assessment analysis of the offset and off-axis angle tolerances corresponding to a 5% drop of the maximum focused peak intensity and present scaling laws for the tolerances of the offset and off-axis angle. Understanding these scaling laws is important to enhance the focusability of a laser beam by an off-axis parabolic mirror in the optimum configuration, in particular, which is valuable for structural design and selection of an off-axis parabolic mirror in ultrashort and ultraintense laser–matter interaction experiments.

Intra-cycle depolarization of ultraintense laser pulses focused by off-axis parabolic mirrors

A study of the structure of the electric and magnetic fields of ultraintense laser pulses focused by an off-axis parabolic mirror is reported. At first, a theoretical model is laid out, whose final equations integration allows the space and time structure of the fields to be retrieved. The model is then employed to investigate the field patterns at different times within the optical cycle, for off-axis parabola parameters normally employed in the context of ultraintense laser–plasma interaction experiments. The results show that nontrivial, complex electromagnetic field patterns are observed at the time at which the electric and magnetic fields are supposed to vanish. The importance of this effect is then studied for different laser polarizations, f numbers and off-axis angles.

Optimization-based mode selection scheme for OAM millimeter wave system in the off-axis misalignment case

Millimeter-wave transmission combined with Orbital Angular Momentum(OAM)has the advantage of reducing the loss of beam power and increasing the system capacity.However,to fulfill this advantage,the antennas at the transmitter and receiver must be parallel and coaxial;otherwise,the accuracy of mode detection at the receiver can be seriously influenced.In this paper,we design an OAM millimeter-wave communication system for overcoming the above limitation.Specifically,the first contribution is that the power distribution between different OAM modes and the capacity of the system with different mode sets are analytically derived for performance analysis.The second contribution lies in that a novel mode selection scheme is proposed to reduce the total interference between different modes.Numerical results show that system performance is less affected by the offset when the mode set with smaller modes or larger intervals is selected.

Collision off-axis position dependence of relativistic nonlinear Thomson inverse scattering of an excited electron in a tightly focused circular polarized laser pulse

This paper presents a novel view of the impact of electron collision off-axis positions on the dynamic properties and relativistic nonlinear Thomson inverse scattering of excited electrons within tightly focused, circularly polarized laser pulses of varying intensities. We examine the effects of the transverse ponderomotive force, specifically how the deviation angle and speed of electron motion are affected by the initial off-axis position of the electron and the peak amplitude of the laser pulse. When the laser pulse intensity is low, an increase in the electron's initial off-axis distance results in reduced spatial radiation power, improved collimation, super-continuum phenomena generation, red-shifting of the spectrum's harmonic peak, and significant symmetry in the radiation radial direction. However, in contradiction to conventional understandings,when the laser pulse intensity is relatively high, the properties of the relativistic nonlinear Thomson inverse scattering of the electron deviate from the central axis, changing direction in opposition to the aforementioned effects. After reaching a peak, these properties then shift again, aligning with the previous direction. The complex interplay of these effects suggests a greater nuance and intricacy in the relationship between laser pulse intensity, electron position, and scattering properties than previously thought.

Heat Transfer Enhancement of the Absorber Tube in a Parabolic Trough Solar Collector through the Insertion of Novel Cylindrical Turbulators

This study includes an experimental and numerical analysis of the performances of a parabolic trough collector(PTC)with and without cylindrical turbulators.The PTC is designed with dimensions of 2.00 m in length and 1.00 m in width.The related reflector is made of lined sheets of aluminum,and the tubes are made of stainless steel used for the absorption of heat.They have an outer diameter of 0.051 m and a wall thickness of 0.002 m.Water,used as a heat transfer fluid(HTF),flows through the absorber tube at a mass flow rate of 0.7 kg/s.The dimensions of cylindrical turbulators are 0.04 m in length and 0.047 m in diameter.Simulations are performed using the ANSYS Fluent 2020 R2 software.The PTC performance is evaluated by comparing the experimental and numerical outcomes,namely,the outlet temperature,useful heat,and thermal efficiency for a modified tube(MT)(tube with novel cylindrical turbulators)and a plain tube(PT)(tube without novel cylindrical turbulators).According to the results,the experimental outlet temperatures recorded 63.2°C and 50.5°C for the MT and PT,respectively.The heat gain reaches 1137.5 Win the MT and 685.8 Win the PT.Compared to the PT collector,the PTC exhibited a(1.64 times)higher efficiency.

BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).

Optimization of the Physical Aperture of the Parabolic Reflector Antenna

In fields like astronomy and radar technology, high-gain antennas are required for long-distance communication. Due to its relatively large gain, the use of parabolic antennas has become very popular over time, because they can easily achieve gains of above 30 dB at microwave and higher frequencies. Today, most systems’ success depends on how well the antennas perform. These antennas are available in different types and sizes. Each antenna’s effective area usually has less than the actual physical area of the antenna surface. This means that the unused area of the antenna is massive, and a waste. The aim of the research is to show that the actual physical aperture of a parabolic antenna can be reduced as much as possible to equal the effective area, as given by the antenna formula, thereby saving manufacturing costs, improve the aesthetics. In other words, the focus of this work is to experimentally show that reflector antenna can be made of smaller sizes but better performance. Measurements were taken from different positions from a parabolic antenna, the signal level measured and compared with signal levels for optimal performance.

Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.

Improving Heat Transfer in Parabolic Trough Solar Collectors by Magnetic Nanofluids

A parabolic trough solar collector(PTSC)converts solar radiation into thermal energy.However,low thermal efficiency of PTSC poses a hindrance to the deployment of solar thermal power plants.Thermal performance of PTSC is enhanced in this study by incorporating magnetic nanoparticles into the working fluid.The circular receiver pipe,with dimensions of 66 mm diameter,2 mm thickness,and 24 m length,is exposed to uniform temperature and velocity conditions.The working fluid,Therminol-66,is supplemented with Fe3O4 magnetic nanoparticles at concentrations ranging from 1%to 4%.The findings demonstrate that the inclusion of nanoparticles increases the convective heat transfer coefficient(HTC)of the PTSC,with higher nanoparticle volume fractions leading to greater heat transfer but increased pressure drop.The thermal enhancement factor(TEF)of the PTSC is positively affected by the volume fraction of nanoparticles,both with and without a magnetic field.Notably,the scenario with a 4%nanoparticle volume fraction and a magnetic field strength of 250 G exhibits the highest TEF,indicating superior thermal performance.These findings offer potential avenues for improving the efficiency of PTSCs in solar thermal plants by introducing magnetic nanoparticles into the working fluid.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

Investigation and simulation of parabolic trough collector with the presence of hybrid nanofluid in the finned receiver tube

The present study discusses the thermal performance of the receiver tube,which contains a wall with various fin shapes in the parabolic trough collector.Inserted fins and bulge surfaces of the inner wall of the receiver tube increase the turbulent fluid flow.In pursuance of uniform distribution of heat transfer,various fin shapes such as square-shape,circle-shape,triangle-shape,and combined square-circle shapes were inserted,examined,and compared.A study of the temperature differences and fluid flow is meaningful for this project therefore finite volume method was used to investigate heat transfer.Also,hybrid Nano-Fluid AL_(2)O_(3-)CuO,TiO_(2-)Cu,and AgMgO were applied to increase thermal diffusivity.When the combined square-circle-shaped fin was inserted,the thermal peak of fluid flow in the receiver tube was lower than the other studied fin shapes by almost 1%.Besides,the hybrid nano-fluid Ag-MgO Syltherm-oil-800 has lower thermal waste in comparison to others by more than 3%.

ALMOST SURELY TIME-SPACE INTERMITTENCY FOR THE PARABOLIC ANDERSON MODEL WITH A LOG-CORRELATED GAUSSIAN FIELD

In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.

Simultaneous detection of CH_(4)and CO_(2)through dual modulation off-axis integrated cavity output spectroscopy

This study established a novel method for the simultaneous detection of two-component gases.Radio frequency(RF)white noise disturbance laser current and wavelength modulation were simultaneously used to improve the off-axis integrated cavity output spectroscopy technique,and a high-precision dual modulation OA-ICOS(RF-WM-OA-ICOS)system was established.The two laser beams were coupled into one laser beam that was applied incident to the cavity of RF-WM-OA-ICOS system.The second harmonic signals of CH_(4)and CO_(2)gas simultaneously appeared in the rising or falling edge of a triangular wave.This method was used to measure CH_(4)and CO_(2)with different concentrations.The results indicated that the proposed system has high stability and can accurately and simultaneously measure the concentrations of CH_(4)and CO_(2),with an optimal integration time of 220 s.The minimum detection limit was 10 ppb for CH_(4)and 1.5 ppm for CO_(2).The corresponding noise equivalent absorption sensitivity values were calculated as 2.67×10^(-13)cm^(-1)·Hz^(-1/2)and 5.18×10^(-11)cm^(-1)·Hz^(-1/2),respectively.The proposed dual-component gas simultaneous detection method can also be used for high-precision simultaneous detection of other gases.Therefore,this study may serve as a reference for developing portable multicomponent gas analyzers.

Glancing incidence x-ray fluorescence spectrometry based on a single-bounce parabolic capillary

Glancing incidence x-ray fluorescence spectrometry using a single-bounce parabolic capillary is proposed for the analysis of layered samples.The divergence of the x-ray beam was 0.33 mrad.In this paper,we used this instrumental setup to analyze a Si single crystal and a 50 nm HfO_(2) single-layer film deposited on a Si substrate.

Characteristic Analysis of Off-Axis Meta-Lens

Meta-lens are a new type of planar optical element that can flexibly manipulate the phase, polarization and amplitude of the beam, and are currently receiving a great deal of attention as they are easier to process and manufacture. Off-axis meta-lens are a special type of meta-lens with a certain degree of dispersion that can be used as a beam-splitting element, providing a unique and feasible way to realize micro-miniature instruments. We analyze the effects of different numerical apertures and off-axis angles on the spectral resolution, focusing efficiency and simulation results of off-axis meta-lens to provide ideas for subsequent research and application of off-axis meta-lens. A number of off-axis meta-lens with parameters NA = 0.408 α = 13°, NA = 0.18 α = 13° and NA = 0.408 α = 20° were simulated through Lumerical software. The results show that the off-axis angle is related to the resolution;the larger the angle, the better the spectral resolution but the lower the focusing efficiency;when the numerical aperture is smaller, the smaller the coverage of the phase distribution, which will lead to a larger deviation between simulation and theory. The designer needs to balance the numerical aperture, off-axis angle and other parameters reasonably according to the requirements in order to achieve the desired effect. The findings of this study have important reference values for the theoretical analysis of off-axis meta-lens and the design of parameters in practical applications. .

Entropy Formulation for Triply Nonlinear Degenerate Elliptic-Parabolic-Hyperbolic Equation with Zero-Flux Boundary Condition

In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.

IDENTIFICATION OF PARAMETERS IN SEMILINEAR PARABOLIC EQUATIONS

An optimization theoretic approach of coefficients in semilinear parabolic equation is presented. It is based on convex analysis techniques. General theorems on existence are proved in L1 setting. A necessary condition is given for the solutions of the parameter estimatioll problem.

BLOW-UP AND GLOBAL EXISTENCE FOR A COUPLED SYSTEM OF DEGENERATE PARABOLIC EQUATIONS IN A BOUNDED DOMAIN

This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - （l -p1）（m- q2）, the initial data, and the domain Ω.

Blow-Up Phenomena for a Class of Parabolic Systems with Time Dependent Coefficients

Blow-up phenomena for solutions of some nonlinear parabolic systems with time dependent coefficients are investigated. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.