Ellipticity-dependent ionization/dissociation of carbon dioxide in strong laser fields

Ionization and dissociation of linear triatomic molecules, carbon dioxide, are studied in 50-fs 800-nm strong laser fields using time-of-flight mass spectrometer. The yields of double charged ions CO2^2＋ and various fragment ions（CO^＋,O^n＋, and C^n＋（n = 1, 2）） are measured as a function of ellipticity of laser polarization in the intensity range from 5.0 ×10^13W/cm2 to 6.0 × 10^14W/cm^2. The results demonstrate that non-sequential double ionization, which is induced by laser-driven electron recollision, dominates double ionization of CO2 in the strong IR laser field with intensity lower than2.0 × 10^14W/cm^2. The electron recollision could also have contribution in strong-field multiple ionization and formation of fragments of CO2 molecules. The present study indicates that the intensity and ellipticity dependence of ions yields can be used to probe the complex dynamics of strong-field ionization/dissociation of polyatomic molecules.

Amplitude and rotation of the ellipticity of harmonics from a linearly polarized laser field

We simulate the dynamic response of H^(+)_(2) in a linearly polarized laser field by numerically solving the time-dependent Schr?dinger equation.The elliptically polarized high-order harmonics generated by H^(+)_(2)irradiated by the linearly polarized laser field are systematically investigated.The result shows that the amplitude and rotation of the ellipticity of harmonics are affected by the alignment angle and internuclear distance of the molecule.Analyzing the change in forces acted on the ionized electrons and the trajectories of the electrons,the phenomena are found to be due to the change in the direction of the total Coulomb forces from the two nuclei felt by the recollided ionized electrons in the direction perpendicular to the laser polarization direction.Based on the influence law,we can select the harmonics with a specific frequency band under different alignment angles and then synthesize the isolated attosecond pulses with different rotations,which can be continuously converted from right-handed circular polarization,linear polarization,and left-handed circular polarization by changing the alignment angle.This study provides a new possible approach to the real-time detection of molecular states by using attosecond pulses and obtaining more optimized harmonics with molecular properties.

Orientation and ellipticity dependence of high-order harmonic generation in nanowires

It has been predicted that high-order harmonic generation(HHG) in nanowires has the potential to scale up photon energy and harmonic yield.However,studies on HHG in nanowires are still theoretical and no relevant experimental results have been reported as yet.Our experimental observation of the high-order harmonic in cadmium sulfide nanowires(CdS NWs) excited by a mid-infrared laser is,to our knowledge,the first of such study,and it verifies some of the theoretical results.Our experimental results show that the observed harmonics are strongest when a pump laser is parallel to the nanowires.Therefore,the theoretical prediction that harmonics are strongest under the nanowires parallel to the laser field is confirmed experimentally,and this can be used to determine the orientation of the nanowire.In addition,harmonics are sensitive to the variation of pump light ellipticities.This orientation dependence opens new opportunities to access the ultrafast and strong-field physics of nanowires.

Ellipticity-dependent ionization yield for noble atoms

The photoionization in the frame of the Ammosov-Delone-Krainov theory has been theoretically examined for noble gases,argon,krypton,and xenon,in an elliptically polarized laser field.We consider the intermediate range of the Keldysh parameter,γ~1,and analyze the influence of shifted ionization potential and temporal profile to eliminate disagreement between theoretical and experimental findings.By including these effects in the ionization rates,we solve rate equations in order to determine an expression for the ionization yield.The use of modified ionization potential shows that the ionization yields will actually decrease below the values predicted by original(uncorrected)formulas.This paper will discuss the causes of this discrepancy.

Study on the effect of ellipticity and misalignment on OAM modes in a ring fiber

Based on the optical fiber mode theory and employing the expertized software COMSOL,we study the effect of ellipticity and misalignment on the effective refractive indices,walk-off and intensity distribution of the even and odd eigenmodes that form the basis of the orbital angular momentum(OAM)modes in a ring fiber.Our results show that the effective refractive index difference and the walk-off increase with the ellipticity and misalignment,thus reducing the stability of the OAM modes.We find that the misalignment has a greater impact on the OAM modes than the ellipticity,and both the misalignment and ellipticity affect the lower-order OAM modes more significantly,suggesting that the higher-order OAM modes are more stable during propagation.

Investigation of ellipticity and pump power in a passively mode-locked fiber laser using the nonlinear polarization rotation technique

An elliptical initial polarization state is essential for generating mode-locked pulses using the nonlinear polarization rotation technique. In this work, the relationship between the ellipticity ranges capable of maintaining mode-locked operation against different pump power levels is investigated. An increasing pump power, in conjunction with minor adjustments to the polarization controller＇s quarter waveplate, results in a wider ellipticity range that can accommodate mode-locked operation. Other parameters such as noise, pulsewidth, and average output power are also observed to vary as the ellipticity changes.

Elliptical encirclement control capable of reinforcing performances for UAVs around a dynamic target

Most researches associated with target encircling control are focused on moving along a circular orbit under an ideal environment free from external disturbances.However,elliptical encirclement with a time-varying observation radius,may permit a more flexible and high-efficacy enclosing solution,whilst the non-orthogonal property between axial and tangential speed components,non-ignorable environmental perturbations,and strict assignment requirements empower elliptical encircling control to be more challenging,and the relevant investigations are still open.Following this line,an appointed-time elliptical encircling control rule capable of reinforcing circumnavigation performances is developed to enable Unmanned Aerial Vehicles(UAVs)to move along a specified elliptical path within a predetermined reaching time.The remarkable merits of the designed strategy are that the relative distance controlling error can be guaranteed to evolve within specified regions with a designer-specified convergence behavior.Meanwhile,wind perturbations can be online counteracted based on an unknown system dynamics estimator(USDE)with only one regulating parameter and high computational efficiency.Lyapunov tool demonstrates that all involved error variables are ultimately limited,and simulations are implemented to confirm the usability of the suggested control algorithm.

GLOBAL BOUND ON THE GRADIENT OF SOLUTIONS TO p-LAPLACE TYPE EQUATIONS WITH MIXED DATA

In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

Efficient single-pixel imaging encrypted transmission based on 3D Arnold transformation

Single-pixel imaging(SPI)can transform 2D or 3D image data into 1D light signals,which offers promising prospects for image compression and transmission.However,during data communication these light signals in public channels will easily draw the attention of eavesdroppers.Here,we introduce an efficient encryption method for SPI data transmission that uses the 3D Arnold transformation to directly disrupt 1D single-pixel light signals and utilizes the elliptic curve encryption algorithm for key transmission.This encryption scheme immediately employs Hadamard patterns to illuminate the scene and then utilizes the 3D Arnold transformation to permutate the 1D light signal of single-pixel detection.Then the transformation parameters serve as the secret key,while the security of key exchange is guaranteed by an elliptic curve-based key exchange mechanism.Compared with existing encryption schemes,both computer simulations and optical experiments have been conducted to demonstrate that the proposed technique not only enhances the security of encryption but also eliminates the need for complicated pattern scrambling rules.Additionally,this approach solves the problem of secure key transmission,thus ensuring the security of information and the quality of the decrypted images.

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field

High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.

Morphological Classification of Infrared Galaxies Based on WISE

This study introduces a novel convolutional neural network,the WISE Galaxy Classification Network(WGC),for classifying spiral and elliptical galaxies using Wide-field Infrared Survey Explorer(WISE)images.WGC attains an accuracy of 89.03%,surpassing the combined use of K-means or SVM with the Color-Color method in more accurately identifying galaxy morphologies.The enhanced variant,WGC_mag,integrates magnitude parameters with image features,further boosting the accuracy to 89.89%.The research also delves into the criteria for galaxy classification,discovering that WGC primarily categorizes dust-rich images as elliptical galaxies,corresponding to their lower star formation rates,and classifies less dusty images as spiral galaxies.The paper explores the consistency and complementarity of WISE infrared images with SDSS optical images in galaxy morphology classification.The SDSS Galaxy Classification Network(SGC),trained on SDSS images,achieved an accuracy of 94.64%.The accuracy reached 99.30% when predictions from SGC and WGC were consistent.Leveraging the complementarity of features in WISE and SDSS images,a novel variant of a classifier,namely the Multi-band Galaxy Morphology Integrated Classifier,has been developed.This classifier elevates the overall prediction accuracy to 95.39%.Lastly,the versatility of WGC was validated in other data sets.On the HyperLEDA data set,the distinction between elliptical galaxies and Sc,Scd and Sd spiral galaxies was most pronounced,achieving an accuracy of 90%,surpassing the classification results of the Galaxy Zoo 2 labeled WISE data set.This research not only demonstrates the effectiveness of WISE images in galaxy morphology classification but also represents an attempt to integrate multi-band astronomical data to enhance understanding of galaxy structures and evolution.

Enabling Efficient Data Transmission in Wireless Sensor Networks-Based IoT Application

The use of the Internet of Things(IoT)is expanding at an unprecedented scale in many critical applications due to the ability to interconnect and utilize a plethora of wide range of devices.In critical infrastructure domains like oil and gas supply,intelligent transportation,power grids,and autonomous agriculture,it is essential to guarantee the confidentiality,integrity,and authenticity of data collected and exchanged.However,the limited resources coupled with the heterogeneity of IoT devices make it inefficient or sometimes infeasible to achieve secure data transmission using traditional cryptographic techniques.Consequently,designing a lightweight secure data transmission scheme is becoming essential.In this article,we propose lightweight secure data transmission(LSDT)scheme for IoT environments.LSDT consists of three phases and utilizes an effective combination of symmetric keys and the Elliptic Curve Menezes-Qu-Vanstone asymmetric key agreement protocol.We design the simulation environment and experiments to evaluate the performance of the LSDT scheme in terms of communication and computation costs.Security and performance analysis indicates that the LSDT scheme is secure,suitable for IoT applications,and performs better in comparison to other related security schemes.

Remote sensing image encryption algorithm based on novel hyperchaos and an elliptic curve cryptosystem

Remote sensing images carry crucial ground information,often involving the spatial distribution and spatiotemporal changes of surface elements.To safeguard this sensitive data,image encryption technology is essential.In this paper,a novel Fibonacci sine exponential map is designed,the hyperchaotic performance of which is particularly suitable for image encryption algorithms.An encryption algorithm tailored for handling the multi-band attributes of remote sensing images is proposed.The algorithm combines a three-dimensional synchronized scrambled diffusion operation with chaos to efficiently encrypt multiple images.Moreover,the keys are processed using an elliptic curve cryptosystem,eliminating the need for an additional channel to transmit the keys,thus enhancing security.Experimental results and algorithm analysis demonstrate that the algorithm offers strong security and high efficiency,making it suitable for remote sensing image encryption tasks.

Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

Sensitive Information Security Based on Elliptic Curves

The elliptic curve cryptography algorithm represents a major advancement in the field of computer security. This innovative algorithm uses elliptic curves to encrypt and secure data, providing an exceptional level of security while optimizing the efficiency of computer resources. This study focuses on how elliptic curves cryptography helps to protect sensitive data. Text is encrypted using the elliptic curve technique because it provides great security with a smaller key on devices with limited resources, such as mobile phones. The elliptic curves cryptography of this study is better than using a 256-bit RSA key. To achieve equivalent protection by using the elliptic curves cryptography, several Python libraries such as cryptography, pycryptodome, pyQt5, secp256k1, etc. were used. These technologies are used to develop a software based on elliptic curves. If built, the software helps to encrypt and decrypt data such as a text messages and it offers the authentication for the communication.

The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

Ellipticity of motion of particle in field of inhomogeneous plane wave

The elliptic motion of particle in the fields of the inhomogeneous plane wavs that are generated on a liquid thermoviscoelastic solid interface is studied.. Calculations show that the ellipticity of the motion of Particle is related to the incident angle that the homogeneous plane wave incidents upon the interface. The influeree of viscous properties of solid on the ellipticity of particle's motion is small and shows near the critical angles of longitudinal and transversal wavs. Under the incidence at Rayleigh angle, the change of the ellipticity of motion of the particle is periodic in the wake of its Rayleigh wavelength and its elliptic locus is couoter clockwise and clockwise rotation periodically.