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.

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.

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.

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).

Investigative Review of Design Techniques of Parabolic Trough Solar Collectors

Parabolic trough solar collectors(PTCs)are among the most cost-efficient solar thermal technologies.They have several applications,such as feed heaters,boilers,steam generators,and electricity generators.A PTC is a concentrated solar power system that uses parabolic reflectors to focus sunlight onto a tube filled with heattransfer fluid.PTCs performance can be investigated using optical and thermal mathematical models.These models calculate the amount of energy entering the receiver,the amount of usable collected energy,and the amount of heat loss due to convection and radiation.There are several methods and configurations that have been developed so far;however,it is usually difficult for a designer to choose the appropriate method or configuration for his application.The present work investigates different PTC configurations and methods of solution,compares their efficiency and accuracy,summarizes their key behaviors and trends,and improves the available methods by maximizing the positives and minimizing the negatives among them.We investigated three methods and seven configurations.The findings suggest that optimizing the collector structure,tracking system,and reflector can lead to high PTC performance and reduced capital costs.After investigating and comparing the recent mathematical models,the study identified a clear deficiency in estimating the output temperature.Three PTC’s solution methods are investigated,and a novel method is developed to give more accurate estimations of the output temperature.

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.

A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces

In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.

Design and Development of a Parabolic Trough Solar Air Heater for a Greenhouse Dryer

Design and Development of a Parabolic Trough Solar Air Heater (PTSAH) for a Greenhouse Dryer (GD) was done to improve the dryer’s performance. The materials used for the fabrication of the PTSAH included galvanized sheets covered with aluminium foil, an absorber tube made of GI pipe painted matt black to increase heat absorbance at the focal line, mild steel square tubes, shutter plywood, and an axial fan to push air through the absorber tube. Key geometrical parameters used for the design of the PTSAH were a rim angle of 98 degrees, focal length of 0.2608 m, height of 0.3451 m, length of 2 m, and an aperture width of 1.2 m. The PTSAH’s total aperture surface area was 2.4 m2, while its absorber tube surface area was 0.1587 m2. The PTSAH was experimentally tested to establish its thermal performance. It was found that the ambient air recorded an average value of 31.1˚C and that the air heater could increase the air temperature by 45.6˚C above ambient with a thermal efficiency of 5.3%. It can, therefore, be concluded that the PTSAH can significantly improve the performance of a GD by supplying the GD with air at a higher temperature than ambient.

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.

A-high-order Accuraqcy Implicit Difference Scheme for Solving the Equation of Parabolic Type

In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.

An Explicit Difference Scheme with High Accuracy and Branching Stability for Solving Parabolic Partial Differential Equation

This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.

Oscillation of Systems of Parabolic Differential Equations with Deviating Arguments

To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.

A Family of High_order Accuracy Explicit Difference Schemes for Solving 2-D Parabolic Partial Differential Equation

A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).

A Fractional-Dimension Variational Approach for the Bound Polaron in Parabolic Quantum Wells

The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional- dimensional variational method. The numerical results for the binding energies of the bound polaron and longitudinal-optical phonon contributions in GaAs/Al0.3 Ga0.7 AS parabolic quantum well structures are obtained as functions of the well width. It is shown that the binding energies of the bound polaron are obviously reduced by the electron-phonon interaction and the phonon contribution is observable and cannot be neglected.

Blow-Up Rate for a Semilinear Parabolic System

This paper deals with the blow-up rate of positive solution for a semilinearparabolic system coupled in the equations and boundary condition. The upper and lower bounds ofblow-up rates are obtained.