General Dispersion Research Articles

Hawking-Page transition on a spin chain

The accessibility of the Hawking-Page transition in AdS5 through a one-dimensional (1D) Heisenberg spin chain is demonstrated. We use the random matrix formulation of the Loschmidt echo for a set of spin chains, and randomize the ferromagnetic spin interaction. It is shown that the thermal Loschmidt echo, when averaged, detects the predicted increase in entropy across the Hawking-Page transition. This suggests that a 1D spin chain exhibits characteristics of black hole physics in 4+1 dimensions. We show that this approach is equally applicable to free fermion systems with a general dispersion relation. Published by the American Physical Society 2024

QED-vacuum response and Cherenkov radiated energy in non-linear and Lorentz-symmetry violating scenarios

We explore the physical effects of non-linear electrodynamic coupled to parameters that indicate a violation of Lorentz-symmetry breaking (LSV). To do this, we consider a general non-linear photonic Lagrangian that is coupled to the Carroll–Field–Jackiw’s model (CFJ). Our investigation reveals how the constitutive properties of the vacuum and wave propagation are affected by the interference of the parameters LSV with the specific non-linear electrodynamic model under consideration. We also analyze the refractive indices for this new medium characterized by the coupling between non-linearities and the operators that carry the LSV message. Our results show that the QED-vacuum responds with birefringence and a dispersive propagation of waves. After that, we study the electromagnetic radiation produced by a moving charged particle interacting with this new medium. Our analysis shows that the emitted radiation is similar (resembles) to that of the Cherenkov effect for certain intensities of background magnetic fields. Finally, we compute the static potential profile within the framework of the gauge-invariant, but path-dependent, variables formalism. We find a logarithmic correction to the usual static Coulomb potential stemming from the LSV parameter, and there are also corrections due to the non-linearity. However, the logarithm behavior disappears whenever the LSV parameter is switched off.

Analysis of hyperbolic magneto-hydrodynamic [HMHD] wave propagation through neutrino-coupled plasma

By using the Hyperbolic Magneto Hydrodynamic model, we investigated the propagation dynamics of a neutrino-coupled plasma system, with the influence of Hall current, rotation, viscosity and finite electrical resistivity. The general dispersion relation is obtained from the perturbed equations for both the Jean’s and neutrino beam instability. The effect of different parameters has been discussed in both parallel and perpendicular modes of wave propagation. The Jean’s instability condition is modified due to the presence of Hall current, Magnetic field and neutrino in both modes of propagation. The growth rate of the neutrino beam is affected by Hall current, viscosity magnetic field and rotation in both propagating modes. We also show the effect of different parameters on the growth rate of a neutrino-coupled plasma system through a graphical presentation.

Spatially varied stacking fault energy induced low twinning ability in high entropy alloys

Nanostructured high-entropy alloys (HEAs) are promising candidates for extreme load-bearing applications due to their superior performance. In this work, we investigate the deformation behaviors of CoCrFeMnNi HEA under high-speed impact by molecular dynamics simulations. Compared with Al, Ni, and Cu representing pure metals with low to high stacking fault energies, it is found that the CoCrFeMnNi HEA exhibits remarkably low twinning density under shock, despite its extremely low stacking fault energy. Shear loading is then applied to stacking-faulted HEAs and these pure metals to study the evolution of stacking faults under shear stress. The results further show a low tendency for stacking faults to transform into deformation twinning in HEAs, regardless of the initial density of stacking faults. The energy path for deformation twins and stacking faults was calculated, and a direct comparison of fault energies could not explain the deformation mechanism of HEA. We reveal that the inhomogeneous energy profile of dislocation slip caused by the inherent heterogeneity of HEA leads to dispersed stacking fault propagation, which suppresses twinning formation. These results address the spatially tunable defects and further urgent need for the synergistic design of components and microstructures in HEAs.

Exact solution of the propagation of ON-OFF signals by dispersive waves

The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly calculated for two types of dispersion relations. Further, the analysis of these solutions shows that the ON-OFF signal propagates with the group velocity and that the boundary thickness of the signal increases with time, typically at a rate proportional to the square root of time, owing to dispersion. Additionally, an approximate solution for a general dispersion relation is derived, and for a higher-complexity ON-OFF switching pattern is constructed.

Discrete heat equation for a periodic layered system with allowance for the interfacial thermal resistance: General formulation and dispersion analysis.

Discrete heat equations for the multilayered periodic systems with allowance for the thermal resistance between the layers and corresponding dispersion relations in ω-k space have been derived and analyzed. The discrete equations imply a finite velocity of thermal disturbances and guarantee the positiveness of the solutions. Analytical expressions for the attenuation distance, and phase and group velocities have been obtained as functions of frequency and thermal resistance between the discrete layers. These functions demonstrate unusual behavior at high frequency compared to the continuum case. Furthermore, the maximum allowed frequency and wave number for the discrete heat equation are limited, whereas there are no such limits in a continuum. The discrete equation contains an infinite hierarchy of continuous partial differential equations, which starts with the Fourier law, proceeds with the hyperbolic equation, the Guyer-Krumhansl (or Jeffreys type) equation, and then with higher-order equations. The partial differential equations with a finite number of terms are only approximations of the discrete equation, which implies that on the ultrashort space and timescales the discrete approach is preferable. This work provides a relatively simple, easy-to-adopt, conceptual tool, together with analytical expressions allowing one to study ultrafast wavelike heat conduction regimes in periodic multilayered metamaterials.

Emission of five OAM dispersive waves in dispersion-engineered double-ring core fiber

Beams carrying orbital angular momentum (OAM) have exhibited significant potential across various fields, such as metrology, image coding, and optical communications. High-performance broadband coherent OAM sources are critical to the operation of optical systems. The emission of dispersive waves facilitates the efficient transfer of energy to distant spectral domains while preserving the coherence among the generated frequency components. Light sources that maintain consistency over a wide range can increase the efficiency of optical communication systems and improve the measurement accuracy in imaging and metrology. In this work, we propose a germanium-doped double ring-core fiber for five OAM dispersive waves (DWs) generation. The OAM1,1 mode supported in the fiber exhibits three zero-dispersion wavelengths (ZDWs) located at 1275, 1720 and 2325 nm. When pumped under normal dispersion, the output spectrum undergoes broadening and exhibits five DWs, situated around 955, 1120, 1450, 2795 and 2965 nm, respectively. Concomitant with blue-shifted and red-shifted dispersive waves, the spectrum spans from 895 to 3050 nm with high coherence. The effect of the fiber and input pulse parameters on DWs generation, as well as the underlying dynamics of the dispersive wave generation process, are discussed. As expected, the number and location of DWs generated in the output spectrum have agreement with the prediction of the phase-matching condition. Overall, this multiple DWs generation method in the proposed fiber paves the way for developing efficient and coherent OAM light sources in fiber-based optical systems.

Dispersive wave generation in single higher-order modes of a large-core silica step-index fiber with pulse energies up to 12 nJ.

The generation of light in a laser system is constrained by the gain medium, limiting the available wavelengths. We demonstrate in-fiber generation of ultrafast pulses between ∼550 and 800 nm via dispersive wave generation (DWG), in higher-order modes (HOMs). Using higher-order modes enables power scaling, due to their large effective area compared to the fundamental modes of single-mode fibers and dispersion engineering, even in simple step-index fibers. The process occurs in a single higher-order mode, which we excite using passive glass components (an axicon and two telescopes). The output pulses have energies up to 12 nJ at the biologically relevant wavelength of 705 nm.

Fatigue Behavior and Fracture Surface Analysis of Corroded High-Strength Bridge Cable Wires.

Bridge cable wires suffer from alternating stress and environmental erosion, leading to premature failure prior to its design life. This paper investigates the fatigue and mechanical behaviors of corroded bridge cable wires with a zinc-aluminum (Zn-Al) alloy coating. Based on the salt spray corrosion test and microstructure analysis, the anti-corrosion resistance and corrosion appearance characteristics of the Zn-Al alloy coating and galvanized coating were investigated. The Zn-Al alloy coating was superior in resistance to corrosion fatigue for the improvement in toughness and the generation of anti-corrosion Zn-Al and Fe-Zn-Al phases. Equations of the accelerated corrosion depth of the steel wires had been regressed to roughly estimate the corrosion life of the Zn-Al alloy coating, which can reach 29.1 years with a thickness of 70 μm. The fatigue and mechanical properties of the bare wires after the salt spray test were further studied based on tensile tests and fatigue tests. The fatigue properties of the bridge cable wire would decrease with the corrosion degree due to the deterioration and embrittlement of materials, where ductility characterized by the elongation rate was the most affected. Fracture surfaces of the wires were captured and analyzed based on a method for recognizing graphical contours. Insufficient fatigue life may occur in the steel wires after corrosion and increase with the degree of corrosion. The pit depth logarithmically weakened the fatigue life of steel wires for the weakening of fatigue toughness and the bearing area. The flat fracture was more common with a single fatigue source, while multiple fatigue sources led to step-like fractures for the generation of multiple dispersed crack propagation regions. Corrosion fatigue was more sensitive to the existence of fatigue sources than the reduction. Multiple initiation sources significantly reduced the fatigue life due to the cracking facilitation of the joint effect of multiple pits. The electrochemical reactions of corrosion can lead to material embrittlement and a reducing effect on the fracture toughness of the steel wires.

Linear to circular conversion in the polarized radio emission of a magnetar

AbstractRadio emission from magnetars provides a unique probe of the relativistic, magnetized plasma within the near-field environment of these ultra-magnetic neutron stars. The transmitted waves can undergo birefringent and dispersive propagation effects that result in frequency-dependent conversions of linear to circularly polarized radiation and vice versa, thus necessitating classification when relating the measured polarization to the intrinsic properties of neutron star and fast radio burst emission sites. We report the detection of such behaviour in 0.7–4 GHz observations of the P = 5.54 s radio magnetar XTE J1810−197 following its 2018 outburst. The phenomenon is restricted to a narrow range of pulse phase centred around the magnetic meridian. Its temporal evolution is closely coupled to large-scale variations in magnetic topology that originate from either plastic motion of an active region on the magnetar surface or free precession of the neutron star crust. Our model of the effect deviates from simple theoretical expectations for radio waves propagating through a magnetized plasma. Birefringent self-coupling between the transmitted wave modes, line-of-sight variations in the magnetic field direction and differences in particle charge or energy distributions above the magnetic pole are explored as possible explanations. We discuss potential links between the immediate magneto-ionic environments of magnetars and those of fast radio burst progenitors.

Mechanistic insight into the colloidal gas aphrons stability in the presence of petroleum hydrocarbons

This study is primarily focusing on the development, generation, and characterization of a colloidal dispersion of microbubbles, known as colloidal gas aphrons as an effective flushing/invading agent during subsurface processes. A major challenge facing the subsurface applications of such colloidal systems, for example for the in-situ remediation of petroleum hydrocarbons contaminated soils or enhanced oil recovery, is the influence of petroleum constituents on colloidal gas aphrons’ structure, consequently their stability. To investigate this issue which was not considered before, first, a series of bulk-scale experiments to study and optimize the properties of colloidal gas aphrons in terms of chemical formulation, structure, stability, the size distribution of bubbles, and gas content were designed and conducted. Then, the effect of the presence of two types of hydrocarbons, namely asphaltenic crude oil, and kerosene, on colloidal gas aphrons’ properties was evaluated. Results show that the unique multilayer structure of the colloidal gas aphrons developed in this research prevents the severe entry and spread of petroleum hydrocarbons into and on the layers of this colloidal system and provides proper colloidal stability than conventional foams in the presence and absence of petroleum hydrocarbons. In the absence of petroleum hydrocarbons, the best colloidal gas aphrons sample had a half-life time of 1621.9 min. The value decreased to 1302.6 min and 699.7 min when crude oil and kerosene were present, respectively. Generally, the results reveal that colloidal gas aphrons’ stability is not considerably influenced by the presence of petroleum constituents, and this suggested colloidal dispersion could be a viable alternative to conventional foams and other chemical-based strategies used in subsurface processes.

Damage Monitoring of Steel Bars Based on Torsional Guided Waves.

Ultrasonic guided waves represent a new development in the field of non-destructive testing. Longitudinal guided waves are mostly used to monitor the damage of steel bars, but the received signal is usually degraded and noisy owing to its dispersive propagation and multimodal behavior, making its implementation and location challenging. The torsional mode of T (0, 1) is not dispersive in the propagation of a steel bar and only produces circumferential displacement. It was chosen, in this study, to conduct guided wave-based damage monitoring on steel bars to reduce the signal processing complexity. The defects of steel bars, including circular surface defects, internal defects, and uniform damage defects, were thoroughly investigated, respectively, using numerical simulation. The waves were excited and received using the pitch-and-catch technique and the collected monitoring signals were processed using Hilbert transformation to highlight the amplitude and time-of-flight values of the wave signals, which were used for defect identification. In this paper, the reflectivity of guided waves is compared between torsional waves and longitudinal waves, in each case. The impact of defect size changes on damage monitoring is studied and the sensitivity of both the wave frequency and the wave mode (L and T) is also discussed. The results show that the monitoring method based on the torsional wave T (0, 1) is more sensitive to surface defects than the conventional method based on longitudinal waves. The reflectivity of the torsional wave T (0, 1) can be twice that of the longitudinal wave L (0, 1) when the depth of the defect in the circumferential grooves is less than 50% of the diameter of the steel bar. It is more sensitive to shallow surface defects within half of the bar's radius, and it can also effectively identify defects under the conditions of the uniform damage defects of steel bars, even when the measurements are heavily noise-polluted. This proves the superiority of the torsional guided wave T (0, 1) in defect monitoring and provides a theoretical basis for the application of the torsional guided wave T (0, 1) in actual monitoring.

Acoustic source localization on finite structures using remote sensors

Acoustic waves are well-suited for remote sensing applications and structural health monitoring purposes because they convey information about their source and can be measured using non-contacting methods. Source localization is an important structural health monitoring task; however, traditional time-of-flight array signal processing techniques used to localize acoustic sources are ill-suited for many structural engineering applications due to the potential for complicated propagation paths, the dispersive propagation of acoustic waves in structures, and the coupling of the vibrating structure and the surrounding medium. Thus, source localization experiments were conducted using matched field processing (MFP) for a 0.9-m diameter round aluminum plate excited by the impact of a 1.3-cm stainless-steel ball bearing dropped from 7.6-cm. A 14-sensor linear remote acoustic array placed 8.9-cm above the plate measured the sound radiated by the 0.64-cm thick plate. MFP array signal processing localization techniques were used along with a physics-based finite element acoustic model to localize the excitation on the structure. Source localization results in both a quiet environment and environment with additive white Gaussian noise are discussed, and these results are compared to those from an acoustic model where plate edge reflections are neglected. [Work was sponsored by a SMART Scholarship and the NEEC.]

Soliton and dispersive wave generation with third-order dispersion and temporal boundary

We investigate the pulse evolution and energy conservation condition at the temporal boundary under third-order dispersion. When the fundamental soliton crosses the temporal boundary and forms two reflected pulses and one transmitted pulse, the power of the transmitted pulse first increases and then decreases as the incident spectrum shifts toward the blue side. If the transmitted spectrum lies in the anomalous group-velocity dispersion region, second-order soliton is formed and dispersive wave is radiated. We present a modified phase-matching condition to predict the resonance frequencies. The predicted results are in good agreement with the results obtained by numerically solving the nonlinear Schrödinger equation.

Porous core fiber with hybrid cladding for ultra-flattened dispersion and low loss propagation of terahertz waves

This work proposes a design of a porous-core photonic crystal fiber (PC-PCF) made of a cyclic olefin copolymer, Zeonex, with a hybrid cladding for low-loss terahertz (THz) wave transmission. A combination of circular and elliptical air holes is employed, resulting in a very low material absorption loss of 0.045 cm-1 at Dcore = 450 µm and f = 1 THz. A flat dispersion of 0.73 ± 0.13 ps/THz/cm is obtained for a broad frequency range of 0.5–1.4 THz. Core diameter and frequency response of other key features such as normalized frequency (V-parameter), confinement loss, effective area, nonlinearity and the percentage of the power flow through different sections of the proposed PC-PCF are also analyzed. Comparing to state-of-the-art, our design is superior in terms of loss, dispersion and power fraction. Our proposed design can be manufactured using the established extrusion process and be used for long distance low-loss Terahertz (THz) communication.

Streamwise dispersion of soluble matter in solvent flowing through a tube

For the dispersion of soluble matter in solvent flowing through a tube as investigated originally by G.I. Taylor, a streamwise dispersion theory is developed from a Lagrangian perspective for the whole process with multi-scale effects. By means of a convected coordinate system to decouple convection from diffusion, a diffusion-type governing equation is presented to reflect superposable diffusion processes with a multi-scale time-dependent anisotropic diffusivity tensor. A short-time benchmark, complementing the existing Taylor–Aris solution, is obtained to reveal novel statistical and physical features of mean concentration for an initial phase with isotropic molecular diffusion. For long times, effective streamwise diffusion prevails asymptotically corresponding to the overall enhanced diffusion in Taylor's classical theory. By inverse integral expansions of local concentration moments, a general streamwise dispersion model is devised to match the short- and long-time asymptotic solutions. Analytical solutions are provided for most typical cases of point and area sources in a Poiseuille tube flow, predicting persistent long tails and skewed platforms. The theoretical findings are substantiated through Monte Carlo simulations, from the initial release to the Taylor dispersion regime. Asymmetries of concentration distribution in a circular tube are certified as originated from (a) initial non-uniformity, (b) unidirectional flow convection, and (c) non-penetration boundary effect. Peculiar peaks in the concentration cloud, enhanced streamwise dispersivity and asymmetric collective phenomena of concentration distributions are illustrated heuristically and characterised to depict the non-equilibrium dispersion. The streamwise perspective could advance our understanding of macro-transport processes of both passive solutes and active suspensions.

Dark matter vorticity and velocity dispersion from truncated Dyson-Schwinger equations

Large-scale structure formation is studied in a kinetic theory approach, extending the standard perfect pressureless fluid description for dark matter by including the velocity dispersion tensor as a dynamical degree of freedom. The evolution of power spectra for density, velocity and velocity dispersion degrees of freedom is investigated in a non-perturbative approximation scheme based on the Dyson-Schwinger equations. In particular, the generation of vorticity and velocity dispersion is studied and predictions for the corresponding power spectra are made, which qualitatively agree well with results obtained from N-body simulations. It is found that velocity dispersion grows strongly due to non-linear effects and at late times its mean value seems to be largely independent of the initial conditions. By taking this into account, a rather realistic picture of non-linear large-scale structure formation can be obtained, albeit the numerical treatment remains challenging, especially for very cold dark matter models.

High-frequency dissipative MHD waves in straight magnetic cylindrical plasma: Coronal loops heating application

The theoretical model for analyzing the waves and oscillatory behavior in the structured solar corona using straight magnetic cylindrical geometry filled with uniform low-β plasma has been recognized as the most preferable classical model for the last few decades. A number of observations, since the first observation of the transition region and coronal explorer to the latest ones, have been adequately explained by adopting this model. In order to analytically formulate the oscillatory characteristics of magnetohydrodynamic (MHD) waves, most of the studies have considered the nature of plasma as an ideal fluid, particularly in the context of solar physics. However, a departure from ideal plasma consideration to non-ideal may lead to a number of modifications in the characteristics of the MHD waves, including its damping too. In what follows, we derive a more general analytical dispersion relation by extending the classical dispersion relation of [Edwin and Roberts, “Wave propagation in a magnetic cylinder,” Sol. Phys. 88, 179–191 (1983)] taking into account the effect of plasma viscosity as a non-ideal term in the existing formulations of the classical model. Consequently, the effects of viscosity on the damping of sausage and kink modes are examined in detail. Multiple trapped body waves of different frequencies exist for both kink and sausage modes in which trapped sausage body wave of comparatively high frequency is damped potentially to generate enough energy to balance the radiative losses of the coronal loop regions. For the coronal loop's plasma parameters, it is found that trapped first radial overtone body wave of sausage type is able to balance the radiative losses of coronal loop structure provided magnetic field strength does not exceed its value of more than 20G.

Plasma elongation effects on energetic particle-induced geodesic acoustic modes in tokamaks

Plasma elongation effects on energetic particle-induced geodesic acoustic modes (EGAMs) are theoretically investigated by using gyro-kinetic equations and the Miller local equilibrium model. Including an arbitrary elongation κ and a finite radial derivative sκ=r∂rκ/κ , a general EGAM dispersion relation is obtained for an arbitrary energetic particle (EP) distribution. In particular, we obtain analytical EGAM dispersion relations for both the double-shifted Maxwellian distribution and the standard slowing-down distribution of EPs. In both cases, the frequency of the unstable EGAM branch decreases slowly with increasing elongation, while its growth rate decreases rapidly with κ when the ratio of the EP to the bulk ion density, nh/ni⩾0.1 . These trends agree well with previous GENE and ORB5 simulations (Di Siena et al 2018 Nucl. Fusion 58 106014), but differ significantly from the elongation effects on geodesic acoustic modes (GAMs) (Gao et al 2009 Nucl. Fusion 49 045014). The portion of the EGAM dispersion relation accounting for the first-order finite-orbit-width shows greater sensitivity to frequency compared to that of GAM, which explains the smaller variations in the frequency of EGAM as κ changes. When the EP number is small (typically, nh/ni≈5% ) in the double-shifted Maxwellian case, the growth rate of EGAMs first increases with the increasing elongation and then decreases, while it monotonically increases with κ in the slowing-down case. Furthermore, the effects of s κ on EGAMs are similar to the elongation κ effects but weaker.

Testing by wave packets and modified scattering in nonlinear dispersive pde’s

Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely. An interesting example is that of problems with cubic nonlinearities in one space dimension. The method of testing by wave packets was introduced by the authors as a tool to efficiently capture the asymptotic equations associated to such flows, and thus establish the modified scattering mechanism in a simpler, more efficient fashion, and at lower regularity. In these expository notes we describe how this method can be applied to problems with general dispersion relations.