Slow Mode Research Articles

Fast-Wave Averaging with Phase Changes: Asymptotics and Application to Moist Atmospheric Dynamics

Many systems involve the coupled nonlinear evolution of slow and fast components, where, for example, the fast waves might be acoustic (sound) waves with a small Mach number or inertio-gravity waves with small Froude and Rossby numbers. In the past, for some such systems, an interesting property has been shown: the slow component actually evolves independently of the fast waves, in a singular limit of fast wave oscillations. Here, a fast-wave averaging framework is developed for a moist Boussinesq system with additional complexity beyond past cases, now including phase changes between water vapor and liquid water. The main question is: Do phase changes induce coupling between the slow component and fast waves? Or does the slow component evolve independently, according to moist quasi-geostrophic equations? Compared to the dry dynamics, a substantial challenge is that the method needs to be adapted to a piecewise operator with variable coefficients, due to phase changes. A formal asymptotic analysis is presented here. For purely saturated flow without phase changes, it is shown that precipitation does not induce coupling, and the slow modes evolve independently. With phase changes present, the limiting equations show that phase boundaries could possibly induce coupling between the slow modes and fast waves.

Probing the Conformational Dynamics of Affinity-Enhanced T Cell Receptor Variants upon Binding the Peptide-Bound Major Histocompatibility Complex by Hydrogen/Deuterium Exchange Mass Spectrometry.

Binding of the T cell receptor (TCR) to its cognate, peptide antigen-loaded major histocompatibility complex (pMHC) is a key interaction for triggering T cell activation and ultimately elimination of the target cell. Despite the importance of this interaction for cellular immunity, a comprehensive molecular understanding of TCR specificity and affinity is lacking. We conducted hydrogen/deuterium exchange mass spectrometry (HDX-MS) analyses of individual affinity-enhanced TCR variants and clinically relevant pMHC class I molecules (HLA-A*0201/NY-ESO-1157-165) to investigate the causality between increased binding affinity and conformational dynamics in TCR-pMHC complexes. Differential HDX-MS analyses of TCR variants revealed that mutations for affinity enhancement in TCR CDRs altered the conformational response of TCR to pMHC ligation. Improved pMHC binding affinity was in general observed to correlate with greater differences in HDX upon pMHC binding in modified TCR CDR loops, thereby providing new insights into the TCR-pMHC interaction. Furthermore, a specific point mutation in the β-CDR3 loop of the NY-ESO-1 TCR associated with a substantial increase in binding affinity resulted in a substantial change in pMHC binding kinetics (i.e., very slow kon, revealed by the detection of EX1 HDX kinetics), thus providing experimental evidence for a slow induced-fit binding mode. We also examined the conformational impact of pMHC binding on an unrelated TRAV12-2 gene-encoded TCR directed against the immunodominant MART-126-35 cancer antigen restricted by HLA-A*0201. Our findings provide a molecular basis for the observed TRAV12-2 gene bias in natural CD8+ T cell-based immune responses against the MART-1 antigen, with potential implications for general ligand discrimination and TCR cross-reactivity processes.

Recognizing spoken words in semantically-anomalous sentences: Effects of executive control in early-implanted deaf children with cochlear implants

Objectives To investigate differences in speech, language, and neurocognitive functioning in normal hearing (NH) children and deaf children with cochlear implants (CIs) using anomalous sentences. Anomalous sentences block the use of downstream predictive coding during speech recognition, allowing for investigation of rapid phonological coding and executive functioning. Methods: Extreme groups were extracted from samples of children with CIs and NH peers (ages 9 to 17) based on the 7 highest and 7 lowest scores on the Harvard-Anomalous sentence test (Harvard-A). The four groups were compared on measures of speech, language, and neurocognitive functioning. Results: The 7 highest-scoring CI users and the 7 lowest-scoring NH peers did not differ in Harvard-A scores but did differ significantly on measures of neurocognitive functioning. Compared to low-performing NH peers, highperforming children with CIs had significantly lower nonword repetition scores but higher nonverbal IQ scores, greater verbal WM capacity, and excellent EF skills related to inhibition, shifting attention/mental flexibility and working memory updating. Discussion: High performing deaf children with CIs are able to compensate for their sensory deficits and weaknesses in automatic phonological coding of speech by engaging in a slow effortful mode of information processing involving inhibition, working memory and executive functioning.

Adiabatic hydrodynamization in rapidly-expanding quark–gluon plasma

We propose a new scenario characterizing the transition of the quark–gluon plasma (QGP) produced in heavy-ion collisions from a highly non-equilibrium state at early times toward a fluid described by hydrodynamics at late times. We develop an analogy to the evolution of a quantum mechanical system that is governed by the instantaneous ground states. In the simplest case, these slow modes are “pre-hydrodynamic” in the sense that they are initially distinct from, but evolve continuously into, hydrodynamic modes. For a class of collision integrals, the pre-hydrodynamic mode represents the angular distribution (in momentum space) of those gluons that carry most of the energy. We illustrate this scenario using a kinetic description of weakly-coupled Bjorken expanding plasma. Rapid longitudinal expansion drives a reduction in the degrees of freedom at early times. In the relaxation time approximation for the collision integral, we show quantitatively that the full kinetic theory evolution is dominated by the pre-hydrodynamic mode. We elaborate on the criterion for the dominance of pre-hydrodynamic slow modes and speculate that adiabatic hydrodynamization may describe the pre-equilibrium behavior of the QGP produced in heavy-ion collisions.

Nonlinear propagation of fast and slow magnetosonic waves in collisional plasmas

AbstractLow‐frequency fast and slow magnetosonic waves propagating in electron ion plasmas with damping effects through ions and neutral atoms collisions are investigated. Linear wave analysis is performed to obtain dispersion relation. The reductive perturbation method is applied and it is shown that fast and slow modes of nonlinear magnetosonic wave are governed by damped Korteweg‐de Vries (DKdV) equation in the presence of ion neutral collisions in plasmas. The analytical solution of DKdV soliton is presented under the assumption of weak collisional effects and numerical solutions of DKdV equation are also obtained using two‐level finite difference scheme with the help of Runge–Kutta method at different plasma parameters. The damping of nonlinear fast and slow magnetosonic wave structures at different times are discussed in the context of space plasma situations where ions and neutral atoms collisions exist.

The Effect of Flow on the Resonance Absorption of Slow MHD Waves in Magnetic Flux Tubes

Abstract In this paper, we study kink and sausage oscillations in the presence of longitudinal background flow. We study the resonance absorption of kink and sausage modes in the slow continuum, under magnetic pore conditions, in the presence of flow. We determine the dispersion relation, and solve it numerically to find the frequencies and damping rates of the slow kink and sausage surface modes. We also obtain an analytical solution for the damping rate of the slow surface mode in the long wavelength limit. We show that in the presence of plasma flow, resonance absorption can result in strong damping for forward waves, and can be considered as an efficient mechanism to justify the extremely rapid damping of slow surface sausage waves observed in magnetic pores. Moreover, the plasma flow reduces the efficiency of resonance absorption to damp backward waves. With respect to pore conditions, resonance instability is avoided in our model.

Transverse bifurcation of viscous slow MHD shocks

We study by a combination of analytical and numerical Evans function techniques multi-D viscous and inviscid stability and associated transverse bifurcation of planar slow Lax MHD shocks in a channel with periodic boundary conditions. Notably, this includes the first multi-D numerical Evans function study for viscous MHD. Our results suggest that, rather than a planar shock, a nonplanar traveling wave with the same normal velocity is the typical mode of propagation in the slow Lax mode. Moreover, viscous and inviscid stability transitions appear to agree, answering (for this particular model and setting) an open question of Zumbrun and Serre.

Designing and Manufacturing of Automatic Robotic Lawn Mower

This study is about the manufacturing of a personified automatic robotic lawn mower with image recognition. The system structure is that the platform above the crawler tracks is combined with the lawn mower, steering motor, slide rail, and webcam to achieve the purpose of personification. Crawler tracks with a strong grip and good ability to adapt to terrain are selected as a moving vehicle to simulate human feet. In addition, a lawn mower mechanism is designed to simulate the left and right swing of human mowing to promote efficiency and innovation, and then human eyes are replaced by Webcam to identify obstacles. A human-machine interface is added so that through the mobile phone remote operation, users can choose a slow mode, inching mode, and obstacle avoidance mode on the human-machine interface. When the length of both sides of the rectangular area is input to the program, the automatic robotic lawn mower will complete the instruction according to the specified path. The chip of a Digital Signal Processor (DSP) TMS320F2808 is used as the core controller, and Raspberry Pi is used as image recognition and human-machine interface design. This robot can reduce labor costs and improve the efficiency of mowing by remote control. In addition to the use as an automatic mower on farms, this study concept can also be used in the lawn maintenance of golf courses and school playgrounds.

Urban transportation at an inflection point: An analysis of potential influencing factors

Urban transportation is in the midst of a two-fold transformation: On the one hand, cities are beginning to acknowledge their climate responsibilities and are seeking to establish environmentally-friendly, sustainable transport systems. On the other hand, new transportation trends, such as shared mobility and autonomous driving, carry the potential to disruptively change conventional practices. In this study, we develop an activity-based transport demand model to quantify the effects of potential influencing factors on urban transportation in a synthetic city. We develop 18 scenarios to investigate urban transportation against the backdrop of mode availability, the deployment of shared mobility services, urban structure and societal change, such as urbanization and an aging population, as well as behavioral shifts in mode choice preferences. With respect to the results, we highlight the derived modal split for a city without private cars but with access to shared autonomous vehicles for all agents: We find a distribution of mode choices of 55% for walking and biking, 40% for public transportation and 5% for shared modes. Given this modal split, the total driven distance, as well as the total number of vehicles in the city, decreases by over 90% against current levels. Thus, an efficient future urban transport system should build upon public transportation for meeting the major share of transport demand, with slow modes for convenient travel across short distances and shared mobility for the intermodal connection of both.

Fast and slow beam mode ion-acoustic solitons in plasmas with counterstreaming cold protons

It was recently shown (Lakhina et al (2020), Physica Scr. 95, 105601) that in a plasma of hot electrons and two counterstreaming warm proton beams, a slow ion-acoustic solitary mode occurred, where the soliton speeds decreased from the critical acoustic speeds, while the amplitudes increased. This contradicts conventional wisdom that solitons are inherently ‘super-acoustic’, the soliton speeds exceeding the linear acoustic speed, and that amplitudes grow with soliton speed. To elucidate and further elaborate on these findings, a simpler model is considered, in which the ion beam species are cold, neglecting their thermal effects. This retains the essence of the physics, but simplifies the analysis. It permits a full parametric discussion of the existence ranges for such solitons, not only for the critical Mach numbers, but also for the limit amplitudes, by using fluid density restrictions for the ions. If the beam speed exceeds a threshold, two acoustic regimes are found: a fast beam mode with the usual super-acoustic solitons, and a slow beam mode, where solitons are sub-acoustic, at least in the laboratory frame. This confirms the earlier result, but shows that it is primarily a beam effect, rather than an ion thermal effect. The observation can be explained: in the ion beam frame, the solitons are indeed super-acoustic. However, those travelling in the negative direction are swept forwards by the fast beam and hence are observed in the laboratory frame as being sub-acoustic. A similar approach is used for a case of asymmetric proton beams, with unequal ion densities and beam speeds.

Large amplitude slow ion-acoustic solitons, supersolitons, and double layers in a warm negative ion plasma with superthermal electrons

The pseudopotential approach is used to investigate the ion thermal and electron superthermal effects on the slow mode solitary wave propagation characteristics in a negative ion plasma, comprising warm positive and negative ions and kappa-distributed electrons. The Sagdeev pseudopotential for the plasma model is derived and analyzed in a systematic way. While it is well known that a negative ion plasma supports the propagation of the fast mode normal solitons, it is found that it supports, in addition to the slow mode normal solitons, the propagation of the slow mode supersolitons and double layers for high values of the negative ion density. The double layers occur as the lower limit to the supersoliton existence range and as the limiting factor for the propagation of normal solitons. When the relative temperature of the two ion species decreases, it is found that the Mach number range supporting the propagation of the nonlinear structures reduces, while the amplitudes of solitons and supersolitons decrease, and these effects are enhanced by the superthermal behavior of the electrons. The amplitudes of the double layers increase with a decrease in the relative temperature of the two ion species but decrease with an increase in the electron superthermality.

Damping of Slow Surface Kink Modes in Solar Photospheric Waveguides Modeled by One-dimensional Inhomogeneities

Abstract Given the recent interest in magnetohydrodynamic (MHD) waves in pores and sunspot umbrae, we examine the damping of slow surface kink modes (SSKMs) by modeling solar photospheric waveguides with a cylindrical inhomogeneity comprising a uniform interior, a uniform exterior, and a continuous transition layer (TL) in between. Performing an eigenmode analysis in linear, resistive, gravity-free MHD, our approach is idealized in that, among other things, our equilibrium is structured only in the radial direction. We can nonetheless address two damping mechanisms simultaneously, one being the ohmic resistivity and the other being the resonant absorption of SSKMs in the cusp and Alfvén continua. We find that the relative importance of the two mechanisms depends sensitively on the magnetic Reynolds number (R m). Resonant absorption is the sole damping mechanism for realistically large values of R m, and the cusp resonance in general dominates the Alfvén one unless the axial wavenumbers are at the lower end of the observationally relevant range. We also find that the thin-boundary approximation holds only when the TL-width-to-radius ratios are much smaller than nominally expected. The ohmic resistivity is far more important for realistically small R m. Even in this case, SSKMs are only marginally damped, with damping-time-to-period ratios reaching ∼10 in the parameter range we examine.

Hypersonic boundary layer receptivity on flat plate with blunt leading edge due to acoustic disturbance

In the process of hypersonic boundary layer transition, the leading edge receptivity due to free-stream acoustic disturbance provides unstable perturbations in boundary layer with initial amplitudes, which is one of hot issues in the study about transition mechanism. The receptivity of leading edge is influenced by many factors, involving geometry parameters, disturbance types, etc., among which the bluntness plays a key role for generating disturbances. In order to reveal the mechanism of bluntness influence on the boundary layer transition, investigations into the acoustic receptivity on flat plates with sharp and blunt leading edge are carried out. The flow conditions are as follows: Mach number 6, Reynolds number 1e7/m, adiabatic wall. By introducing two-dimensional plane fast and slow acoustic waves into the free-stream, the whole receptivity process of free-stream disturbances passing through shock wave into boundary layer is simulated with high-order accuracy DNS method. With sharp leading edge as a reference, the generation mechanism of the perturbations near blunt leading edge and its influence on the boundary layer downstream are analyzed. Some conclusions are obtained: for acoustic disturbances in hypersonic free-streams, the receptivity mechanism of blunt leading edge is different from that of sharp leading edge; both the fast and the slow mode can be produced respectively near the sharp leading edge by the fast and the slow acoustic wave, while only fast mode appears near the blunt leading edge; the receptivity of blunt leading edge due to the fast acoustic is stronger than that due to slow acoustic, and is also stronger than that of the sharp leading edge in a certain region of boundary layer downstream.

The effect of the magnetic field on the damping of slow waves in the solar corona

Context. Slow magnetoacoustic waves are routinely observed in astrophysical plasma systems such as the solar corona, and they are usually seen to damp rapidly. As a slow wave propagates through a plasma, it modifies the equilibrium quantities of density, temperature, and the magnetic field. In the corona and other plasma systems, the thermal equilibrium is comprised of a balance between continuous heating and cooling processes, the magnitudes of which vary with density, temperature and the magnetic field. Thus the wave may induce a misbalance between these competing processes. Its back reaction on the wave has been shown to lead to dispersion, and amplification or damping, of the wave. Aims. This effect of heating and cooling misbalance has previously been studied in the infinite magnetic field approximation in a plasma whose thermal equilibrium is comprised of optically thin radiative losses and field-aligned thermal conduction, balanced by an (unspecified) heating process. In this work we extend this analysis by considering a non-zero β plasma. The importance of the effect of the magnetic field in the rapid damping of slow waves in the solar corona is evaluated and compared to the effects of thermal conduction. Methods. A linear perturbation under the thin flux tube approximation is considered, and a dispersion relation describing the slow magnetoacoustic modes is found. The dispersion relation’s limits of strong non-adiabaticity and weak non-adiabaticity are studied. The characteristic timescales were calculated for plasma systems with a range of typical coronal densities, temperatures, and magnetic field strengths. Results. The number of timescales characterising the effect of the misbalance is found to remain at two, as with the infinite magnetic field case. In the non-zero β case, these two timescales correspond to the partial derivatives of the combined heating and cooling function with respect to constant gas pressure and with respect to constant magnetic pressure. The predicted damping times of slow waves from thermal misbalance in the solar corona are found to be of the order of 10–100 min, coinciding with the wave periods and damping times observed. Moreover, the slow wave damping by thermal misbalance is found to be comparable to the damping by field-aligned thermal conduction. The change in damping with plasma-β is complex and depends on the coronal heating function’s dependence on the magnetic field in particular. Nonetheless, we show that in the infinite field limit, the wave dynamics is insensitive to the dependence of the heating function on the magnetic field, and this approximation is found to be valid in the corona so long as the magnetic field strength is greater than approximately 10 G for quiescent loops and plumes, and 100 G for hot and dense loops. Conclusions. A thermal misbalance may damp slow magnetoacoustic waves rapidly in much of the corona, and its inclusion in our understanding of slow mode damping may resolve discrepancies between the observations and theory relying on compressive viscosity and thermal conduction alone.

Effect of Phonon Focusing on the Drag Thermopower in Single-Crystal Potassium Nanowires at Low Temperatures

The role of shear waves and the effect of phonon focusing on the anisotropy of the thermopower of the electron–phonon drag in single-crystal potassium nanowires at low temperatures are analyzed in this work. The deformation potential theory is used for the longitudinal components of elastic modes. For the shear components of vibrational modes, the electron–phonon interaction constant is used, which was determined previously from comparing the results of calculating the thermoelectric power with experimental data for bulk potassium crystals. It is shown that shear waves make a significant contribution to the drag thermopower of nanowires. In the regime of the Knudsen phonon gas flow for nanowires with a cross-section side D = 5 × 10–6 cm, the contribution of the slow transverse mode t2 with allowance for only the longitudinal component in the [111] directions turned out to be 32% smaller and, with allowance for the shear component of the t2 mode, 12% greater than the contribution of longitudinal phonons. Directions corresponding to the maximum and minimum values of the drag thermopower of nanowires are determined. It is shown that, under conditions of competition between the boundary and bulk mechanisms of phonon relaxation with an increase in the cross section of nanowires, the anisotropy of the drag thermopower changes nonmonotonically. It exceeds 30% not only in the Knudsen phonon gas flow regime, but also when the sample thickness is two orders of magnitude greater. This makes the anisotropy of thermopower available for experimental studies.

Solvation dynamics in electronically polarizable solvents: Theoretical treatment using solvent-polarizable three-dimensional reference interaction-site model theory combined with time-dependent density functional theory.

The theory of solvation structure in an electronically polarizable solvent recently proposed by us, referred to as the "solvent-polarizable three-dimensional reference interaction-site model theory," is extended to dynamics in this study through the combination with time-dependent density functional theory. Test calculations are performed on model charge-transfer systems in water, and the effects of electronic polarizability on solvation dynamics are examined. The electronic polarizability slightly retards the solvation dynamics. This is ascribed to the decrease in the curvature of the nonequilibrium free energy profile along the solvation coordinate. The solvent relaxation is bimodal, and the faster and the slower modes are assigned to the reorientational and the translational modes, respectively, as was already reported by the surrogate theory combined with the site-site Smoluchowski-Vlasov equation. The relaxation path along the solvation coordinate is a little higher than the minimum free energy path because the translational mode is fixed in the time scale of the reorientational relaxation.

Tapping modes in the Atomic Force Microscope model with Lennard-Jones force and slow-fast base motion

Abstract Based on the idea of slow-fast dynamics, two tapping modes are investigated in the Atomic Force Microscope (AFM) model with Lennard-Jones force and slow-fast base motion. According to the approximation derived from Taylor expansion in the vicinity of static equilibrium of the linearized system, we give a prediction about harmonic responses of the fast sub-system (FSS). Then a truncated version of harmonic balancing method (HBM) is combined with the Floquet theory to give the distribution and stability of the harmonic responses, which indicates the contact and non-contact modes dominated by cycle manifolds. By directly integrating the FSS, the numerical bifurcation diagrams and the frequency spectrums corresponding to the periodic solutions are obtained to verify the results given by the half-analytic process. Moreover, distribution of basins of attraction shows that, when the tri-stability is destroyed by fold bifurcation of cycle, due to the highly fragmented fractal structures in basins, transition between different mode manifolds may present an weak irregular way. On the other hand, when the slow excitation is introduced, the regular and irregular “cycle-cycle” type mixed mode oscillations (MMOs) triggered by “fold of cycle/fold of cycle” hysteresis can be observed, which results in two tapping mode, .i.e., the slow tapping mode and the “compound of contact/snap tapping” mode. Besides that, our results show that, for the AFM under slow and near-resonant excitation, the beneficial effects of constant contact mode and snap tapping mode can be utilized.

On the Mutual Relationships between Molecular Probe Mobility and Free Volume and Polymer Dynamics in Organic Glass Formers: cis-1,4-poly(isoprene).

We report on the reorientation dynamics of small spin probe 2,2,6,6-tetramethylpiperidinyl-1-oxyl (TEMPO) in cis-1,4-poly(isoprene) (cis-1,4-PIP10k) from electron spin resonance (ESR) and the free volume of cis-1,4-PIP10k from positron annihilation lifetime spectroscopy (PALS) in relation to the high-frequency relaxations of cis-1,4-PIP10k using light scattering (LS) as well as to the slow and fast processes from broadband dielectric spectroscopy (BDS) and neutron scattering (NS). The hyperfine coupling constant, 2Azz′(T), and the correlation times, τc(T), of cis-1,4-PIP10k/TEMPO system as a function of temperature exhibit several regions of the distinct spin probe TEMPO dynamics over a wide temperature range from 100 K up to 350 K. The characteristic ESR temperatures of changes in the spin probe dynamics in cis-1,4-PIP10k/TEMPO system are closely related to the characteristic PALS ones reflecting changes in the free volume expansion from PALS measurement. Finally, the time scales of the slow and fast dynamics of TEMPO in cis-1,4-PIP10k are compared with all of the six known slow and fast relaxation modes from BDS, LS and NS techniques with the aim to discuss the controlling factors of the spin probe reorientation mobility in polymer, oligomer and small molecular organic glass-formers.

Comparative study of pluronic-chitosan and pluronic-guar gum composite thermogels

Triblock copolymers display, in water, a rich phase behavior with changes in temperature and concentration that makes them particularly attractive for many industrial and biomedical applications. In an attempt to develop smart carriers with improved properties, additives such as polysaccharides are often included in the poloxamer formulations. In the present work, we examine and compare the associative properties of concentrated aqueous solutions of pluronic F127 in presence of chitosan and guar gum. Dynamic light scattering was used to analyze the effects of the two polysaccharides on the different self-assembled structures formed within these solutions as a function of temperature from the micellization to the sol-gel transition. The most marked differences between the two systems can be observed above the sol-gel transition, where the analysis of the correlation functions evidenced the presence of three processes: a fast process that represents unimers diffusion, an intermediate process related to individual hydrated micelles, and a slow mode due to the presence of large micellar aggregates. We hypothesize that the different molecular weight and ionic character of the polysaccharides are responsible for the different size of the diffusing entities as well for the nature of the bonds which hold together the extended network between micelles formed above the sol-gel transition.

Wave Simulation in Partially Saturated Porothermoelastic Media

In wave propagation in rocks, the strain field affects the internal energy such that compressed regions become hotter and expanded regions cooler. This thermoelastic effect is that the lack of thermal equilibrium between various parts of the vibrating medium and energy is dissipated when irreversible heat flow driven by the temperature gradient occurs. Moreover, rocks are generally partially saturated and the interfacial tension between fluids affects the acoustic properties and induces additional slow P waves. To model these phenomena, we develop a generalized porothermoelasticity theory, including the Lord–Shulman (LS) and Green–Lindsay (GL) theories, for wave propagation in partially saturated nonisothermal media. The dynamical equations have as solutions the classical P1 and S waves and three slow waves modes, namely, the slow P2, slow P3, and the thermal (T) waves, which present diffusive behavior depending on the viscosity, frequency, and thermal properties. We compute the wavefields with a direct meshing algorithm by using an optimized finite-difference (FD) method to obtain the spatial derivatives and a first-order explicit Crank–Nicolson method for temporal extrapolation. The simulated snapshots and waveforms for the homogeneous and heterogeneous models with two different sets of thermal properties illustrate the characteristics of propagation as a function of frequency and saturation, which are consistent with the plane-wave analyses. The GL model can predict a higher thermal attenuation of the P1 wave and, consequently, a larger velocity dispersion than the LS theory. The thermal relaxation peak moves to low frequencies as the conductivity increases. This study is relevant to understand wave propagation in porous rocks and high temperature and pressure fields.