Maxwell Time Research Articles

Tidal dissipation within an elongated asteroid with satellite, and application to asteroid (216) Kleopatra

(216) Kleopatra is a highly elongated dumbbell shaped asteroid, which is spinning rapidly (spin period 5.38 h), and has two satellites. The tidal migration rate of its outer satellite (related to asteroid tidal despinning) has been measured by Broz et al. (2021), and is used here to deduce the elastic properties of the asteroid, in particular its rigidity μ. For this purpose the satellite is modeled as an homogeneous elongated axisymmetric body, whose shape is described either as a cylinder or more realistically as a dumbbell. Such model asteroid is regarded as a beam (or rod) that undergoes tidal disturbances from the satellite. Due to the deformability of the asteroid, the tidal stresses produced within the body rise a compression tide in the direction of the asteroid's long axis, and a bending tide in the perpendicular direction. We compute the tidal amplitude of the total elastic energy stored within the asteroid, as a function of Young's modulus E. Provided that the tidal quality factor Q is known, this permits to deduce the power tidally dissipated within the asteroid. This is compared to the tidal dissipation deduced from Broz et al. (2022) observations of the tidal migration of Kleopatra's outer satellite. This permits to deduce the asteroid's Young's modulus E (or equivalently the rigidity μ through μ ≈ E/(2.6 ± 0.1)). Using our dumbbell model for Kleopatra, we obtain a rigidity μ ≈ 1.94 × 107 Pa if one assumes Q ≈ 40, or μ ≈ 1.40 × 107 Pa if one assumes Q = 100. Such tidal dissipation is found to be >2 orders of magnitude higher than the tidal dissipation which would occur in a hypothetical spherical asteroid of same density and rigidity as Kleopatra, with radius equal to the volume equivalent radius (RV ≈ 59.1 km). Among model asteroids with same long axis length as Kleopatra (2 L ≈ 267 km), dissipation is also found to be strongly dependent upon the shape of the asteroid (dumbbell, cylinder, or ellipsoid). Here the asteroid is regarded as an elastic solid, whereas it is presumably a weak rubble pile medium. The formalism developed here is however relevant provided that the asteroid may be regarded as a Maxwell material, because tidal frequencies are expected to be much higher than the inverse Maxwell time.

Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory.

We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine displacements and the consequent Goldstone phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field-nonaffinity-which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave vector in liquids, thus giving a formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the α relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a nonequilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids, and glasses has to be identified with the associated generalized higher-form global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).

Гравиметрические исследования на научном полигоне «Мыс Шульца»

Gravity measurements with different kind of absolute gravimeters and spring gravimeters were started at the Marine Experimental Observatory Shults Cape of Il'ichev Oceanological Institute, Far East Branch of Russian Academy of Sciences from 2010 year. Simultaneously, on the polygone, located in the South of Primorie, started the geodetic measurements by GNSS methods for determination of the coordinates and study of gravimetric points’ displacements. Gravimetric measurements are used to solve structural and monitoring tasks. Planned and high-altitude geodetic measurements are necessary for the correct interpretation of gravimetric results and obtaining reduced gravity values. Complex measurements with absolute and relative gravimeters are used to test the metrological characteristics of relative gravimeters such as SCINTREX and GPhone. As a result of the analysis of tidal variations of gravity, corrections to the absolute data were obtained. Carrying out measurements at different altitudes using absolute gravimeters of the GABLM-M type made it possible to reduce the values of gravity and compare experimental and theoretical estimates. The results are used in structural geological studies in Primorie. The second task of the research was to determine the level of time variations of gravity, 3D displacements of the earth's surface and determine their nature. According to measure-ments in the period 2010–2020, the effects associated with the Japanese earthquake of 11.03.2011 with a magnitude of M = 9,0 were investigated. At a distance of 1000 km from the epicenter, the mag-nitude of post-seismic subsidence for the period 2012–2020 was 22 m, gravity increased by 6 microgal. According to the shape of the attenuation curve of vertical displacements, a model was selected and an estimate of Maxwell's time (T = 3 years) was obtained. Within the framework of a two-layer model, the viscosity of the earth's crust lower part – the asthenosphere on the edge of the continent – was determined.

Magmatic sill formation during dike opening

AbstractThe origin of horizontal magma-filled sills is disputed, particularly for extensional settings where the opening of vertical dikes is the predicted mode of magma intrusion. We simulate long-term extension followed by short-term dike opening in a two-dimensional viscoelastic medium representing a plate spreading center. We show that dike opening in extensionally stressed lithosphere can reduce sublithospheric vertical stresses enough for sill opening given three conditions: (1) the Maxwell time of the asthenosphere is <5× the time interval between dike episodes; (2) the average density of the lithosphere is not much greater than the magma density; and (3) the depth of an axial valley is smaller than a few hundred meters. This mechanism explains the presence of sills along much of the axis of faster-spreading ridges and their absence along slower-spreading centers where thick dense lithosphere and/or sizeable axial valleys exist.

Co-seismic and post-seismic deformation for the 1995 Colima–Jalisco and 2003 Tecomán thrust earthquakes, Mexico subduction zone, from modelling of GPS data

SUMMARYWe invert ∼25 yr of campaign and continuous Global Positioning System daily positions at 62 sites in southwestern Mexico to estimate co-seismic and post-seismic afterslip solutions for the 1995 Mw = 8.0 Colima–Jalisco and the 2003 Mw = 7.5 Tecomán earthquakes, and the long-term velocity of each GPS site. Estimates of the viscoelastic effects of both earthquakes from a 3-D model with an elastic crust and subducting slab, and linear Maxwell viscoelastic mantle are used to correct the GPS position time-series prior to our time-dependent inversions. The preferred model, which optimizes the fit to data from several years of rapid post-seismic deformation after the larger 1995 earthquake, has a mantle Maxwell time of 15 yr (viscosity of 2 × 1019 Pa s), although upper-mantle viscosities as low as 5 × 1018 Pa s cannot be excluded. Our geodetic slip solutions for both earthquakes agree well with previous estimates derived from seismic data or via static co-seismic offset modelling. The afterslip solutions for both earthquakes suggest that most afterslip coincided with the rupture areas or occurred farther downdip and had cumulative moments similar to or larger than the co-seismic moments. Afterslip thus appears to relieve significant stress along the Rivera plate subduction interface, including the area of the interface between a region of deep non-volcanic tremor and the shallower seismogenic zone. We compare the locations of the seismogenic zone, afterslip and tremor in our study area to those of the neighbouring Guerrero and Oaxaca segments of the Mexico subduction zone. Our newly derived interseismic GPS site velocities, the first for western Mexico that are corrected for the co-seismic and post-seismic effects of the 1995 and 2003 earthquakes, are essential for future estimates of the interseismic subduction interface locking and hence the associated seismic hazard.

GPS-derived interseismic fault locking along the Jalisco–Colima segment of the Mexico subduction zone

SUMMARYNortheastward subduction of the oceanic Rivera and Cocos plates in western Mexico poses a poorly understood seismic hazard to the overlying areas of the North America plate. We estimate the magnitude and distribution of interseismic locking along the northern ∼500 km of the Mexico subduction zone, with a series of elastic half-space inversions that optimize the fits to the velocities of 57 GPS stations in western Mexico. All velocities were corrected for the co-seismic, afterslip and viscoelastic rebound effects of the 1995 Colima–Jalisco and 2003 Tecomán earthquakes. We explore the robustness of interseismic locking estimates to a variety of mantle Maxwell times that are required for the viscoelastic corrections, to the maximum permitted depth for locking of the subduction interface and to the location assigned to the Rivera–Cocos–North America plate triple junction offshore from western Mexico. The best-fitting locking solutions are associated with a maximum locking depth of 40 km, a triple junction location ∼50 km northwest of the Manzanillo Trough and a mantle Maxwell time of 15 yr (viscosity of 2 × 1019 Pa s). Checkerboard tests show that the locking distribution is best resolved at intermediate depths (10–40 km). All of our inversions define a gradual transition from strong locking (i.e. 70–100 per cent) of most (70 per cent) of the Rivera–North America subduction interface to strong but less uniform locking below the Manzanillo Trough, where oceanic lithosphere transitional between the Cocos and Rivera plate subducts, to weak to moderate locking (averaging 55 per cent) of the Michoacán segment of the Cocos–North America interface. Strong locking of the ∼125-km-long trench segment offshore from Puerto Vallarta and other developed coastal areas, where our modelling indicates an average annual elastic slip-rate deficit of ∼20 mm yr−1, implies that ∼1.8 m of unrelieved plate slip has accrued since the segment last ruptured in 1932, sufficient for an M ∼ 8.0 earthquake.

Conjugate Time in the Sub-Riemannian Problem on the Cartan Group

The Cartan group is the free nilpotent Lie group of rank 2 and step 3. We consider the left-invariant sub-Riemannian problem on the Cartan group defined by an inner product in the first layer of its Lie algebra. This problem gives a nilpotent approximation of an arbitrary sub-Riemannian problem with the growth vector (2,3,5). In previous works, we described a group of symmetries of the sub-Riemannian problem on the Cartan group, and the corresponding Maxwell time — the first time when symmetric geodesics intersect one another. It is known that geodesics are not globally optimal after the Maxwell time. In this work, we study local optimality of geodesics on the Cartan group. We prove that the first conjugate time along a geodesic is not less than the Maxwell time corresponding to the group of symmetries. We characterize geodesics for which the first conjugate time is equal to the first Maxwell time. Moreover, we describe continuity of the first conjugate time near infinite values.

Effusion Rate From a Volcanic Conduit Subject to Pressure Oscillations in a Viscoelastic Medium

AbstractEffusion rate in basaltic eruptions typically depends on time: there is an initial, relatively fast increase followed by a much slower decrease until the eruption vanishes; in addition, changes are observed in the effusion rate having durations much shorter than the total duration of the eruption. For an effusive eruption, we calculate the deformation of the volcanic conduit due to short‐term pressure oscillations. The model considers an elliptical conduit embedded in a viscoelastic medium, described by a Maxwell body. As a consequence of pressure oscillations, the semi axes of the conduit are quasi periodic functions of time with the same period as pressure. For volcanic fissures the viscoelastic rheology entails a remarkable increase in oscillation amplitude of flow rate with respect to the elastic case and a time delay in flow rate oscillation with respect to overpressure oscillation. For a given value of overpressure amplitude, this effect is controlled by the conduit eccentricity and the ratio between overpressure period and Maxwell time; for larger values of this ratio and/or for eccentricity values closer to unity, flow rate oscillates around a value larger than its initial value and can vary from 5% to 30% with respect to it. The model can approximate the in‐situ observations of short‐time fluctuations of flow rate during the 2018 eruption of Kı̄lauea Volcano.

A Simple Method for Photoconductivity Measurement in Lithium Niobate

A simple and effective technique to characterize the photoconductivity (PC) of lithium niobate is presented. The technique is based on the modulation of the external field and on the observation of the optical response of the material as a function of the intensity of a gaussian beam using a Tardy’s polarimetric setup in the r 22 configuration. When the temporal period of the modulation is larger than the Maxwell time of the material, the effect of the PC can be detected observing the kinetics of the screening effect of the external applied field. This approach allows measuring a wide dynamic range up to high light intensities with good accuracy using a standard oscilloscope and with no need for charge collection electrodes. The technique is demonstrated by comparing two samples, the first possessing a standard congruent composition, the second being doped with Zn in order to boost the PC.

Shock waves of viscoelastic Burgers equations

Travelling wave solutions of the front, kink or shock wave type are obtained analytically for one–dimensional viscoelastic Burgers equations with an objective Gordon–Schowalter time derivative in the constitutive law by means of a novel formulation based on changes of the independent and dependent variables that reduces the number of parameters to three. It is shown that, for the upper– and lower–convected Maxwell and Jaumann time derivatives, the thickness of the shock wave decreases as a nondimensional relaxation parameter is increased and that the velocity profiles for the Jaumann and lower–convected derivatives evolve from a sigmoid shape to linear piecewise ones as the relaxation parameter is increased. It is also shown that stress is a negative, even function that reaches a nil value at the upstream and downstream boundaries, and its width decreases as the relaxation parameter is increased for the Jaumann and upper–convected Maxwell derivatives. It is also reported that, at each location, the stress is larger for the lower–convected Maxwell derivative than for the Jaumann and upper–convected Maxwell derivatives.

“Measures of Dissipation in Viscoelastic Media” Extended: Toward Continuous Characterization Across Very Broad Geophysical Time Scales

AbstractWe develop a conceptual/quantitative framework whereby measurements of Earth's viscoelasticity may be assessed across the broad range of geophysical processes, spanning seismic wave propagation, postseismic relaxation, glacial isostatic adjustment, and mantle convection. Doing so requires overcoming three challenges: (A) separating spatial variations from intrinsic frequency dependence in mechanical properties; (B) reconciling different conceptual and constitutive viscoelastic models used to interpret observations at different frequencies; and (C) improving understanding of linear and nonlinear transient deformation mechanisms and their extrapolation from laboratory to earth conditions. We focus on (B), first demonstrating how different mechanical models lead to incompatible viscosity estimates from observations. We propose the determination of the “complex viscosity”—a frequency‐dependent parameter complementary to other measures of dissipation (including frequency‐dependent moduli and attenuation)—from such observations to reveal a single underlying broadband mechanical model. The complex viscosity illuminates transient creep in the vicinity of the Maxwell time, where most ambiguity lies.

Relation between mean stress, thermodynamic, and lithostatic pressure

AbstractPressure is one of the most important parameters to be quantified in geological problems. However, in metamorphic systems the pressure is usually calculated with two different approaches. One pressure calculation is based on petrological phase equilibria and this pressure is often termed thermodynamic pressure. The other calculation is based on continuum mechanics, which provides a mean stress that is commonly used to estimate the thermodynamic pressure. Both thermodynamic pressure calculations can be justified by the accuracy and applicability of the results. Here, we consider systems with low‐differential stress (<1 kbar) and no irreversible volumetric deformation, and refer to them as conventional systems. We investigate the relationship between mean stress and thermodynamic pressure. We discuss the meaning of thermodynamic pressure and its calculation for irreversible processes such as viscous deformation and heat conduction, which exhibit entropy production. Moreover, it is demonstrated that the mean stress for incompressible viscous deformation is essentially equal to the mean stress for the corresponding viscous deformation with elastic compressibility, if the characteristic time of deformation is five times longer than the Maxwell viscoelastic relaxation time that is equal to the ratio of shear viscosity to bulk modulus. For typical lithospheric rocks, this Maxwell time is smaller thanc. 10,000 years. Therefore, numerical simulations of long‐term (>10 kyr) geodynamic processes, employing incompressible deformation, provide mean stress values that are close to the mean‐stress value associated with elastic compressibility. Finally, we show that for conventional systems the mean stress is essentially equal to the thermodynamic pressure. However, mean stress and, hence, thermodynamic pressure can be significantly different from the lithostatic pressure.

Structural relaxation and highly viscous flow.

The highly viscous flow is due to thermally activated Eshelby transitions which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. A self-consistent determination of the viscosity in this picture explains why the average structural relaxation time is a factor of eight longer than the Maxwell time. The physical reason for the short Maxwell time is the very large contribution of strongly strained inherent states to the fluidity (the inverse viscosity). At the Maxwell time, the viscous no-return processes coexist with the back-and-forth jumping retardation processes.

Real magnetic charges as a negation of the electric magnetism Maxwell and electrified Dirac’s monopole

The main reasons that real magnetic charges were "buried alive" in modern theories are physics of their confinement in atoms and substance which is radically different from the confinement of electrons, as well as the vicious electromagnetic theory of Maxwell. This theory which should be referred to as Maxwell's electric magnetism is the result of superficial perception by the Great Physicist of the famous Oersted's Experience when only external factors of Experience were taken into account: the electric current and the magnetic field around the conductor. It was with Maxwell's "light hand" that electrons moving in the composition electric current were erroneously declared to be the direct sources of the magnetic field what on 145 years has "deprived" the magnetic charges, which make up about half of the spinor particles in real World of the opportunity to engage its professional activities. It is important to note that the real physical processes taking place in the body of a conductor with an electric current as in Maxwell's time, so and until now, as this not paradoxically, remain outside beyond our detailed knowledge. Maxwell's electric magnetism can be represented as the "cancerous tumor" in the "body" of physical science the metastases of which struck, virtually, all the directions of the fundamental physical theory. With taking into account the historical conditions of formation and the scales of the negative impact on civilization, the vicious electromagnetic concept of Maxwell is quite adequate with to such surface-primitive concepts as Flat Earth or near-Earth rotation of Sun. As a result of all these circumstances, many useful and effective technical projects that could improve the quality of people's lives, as well as expand the technological capabilities of our civilization could not take place. So, for example, in the absence of magnetic charges in physical representations was impossible to find out the real physics of the gravitational field. Therefore it turned was not possible to implement such important project both the technical Gravitational Levitation in which can use the inexhaustible, stable and environmentally friendly energy of the gravitational field directly. It should be noted that the project of technical Gravitational Levitation is just one of many missed opportunities that were closed as a result of the negative exposure of Maxwell's electric magnetism on the physical science. In 1931 P. Dirac proposed his the famous theory of magnetic monopole. But in order for this monopole to emit a magnetic field, this field must first be produced with the help of an electric current in the filamentary solenoids of Dirac. The Dirac monopole, given the all circumstances of its formation, can be called an electrified magnetic pole, based, implicitly, on the same vicious electromagnetic conception of Maxwell.

A thick-walled sphere rotating in a uniform magnetic field: The next step to de-spin a space object

Modeling the interaction between a moving conductor and a static magnetic field is critical to understanding the operation of induction motors, eddy current braking, and the dynamics of satellites moving through Earth's magnetic field. Here, we develop the case of a thick-walled sphere rotating in a uniform magnetic field, which is the simplest, non-trivial, magneto-statics problem that leads to complete closed-form expressions for the resulting potentials, fields, and currents. This solution requires knowledge of all of Maxwell's time independent equations, scalar and vector potential equations, and the Lorentz force law. The paper presents four cases and their associated experimental results, making this topic appropriate for an advanced student lab project.

The Enigma of Large-Scale Permeability of Gas Shale: Pre-Existing or Frac-Induced?

The existing commercial programs for simulation of hydraulic fracturing (aka fracking, or frac) of gas (or oil) shale predict parallel vertical cracks to spread in vertical parallel planes, with no lateral branching. These cracks emanate from the perforation clusters on the horizontal wellbore casing, typically spaced 10 m apart or more. For such a large spacing, the rate of gas production observed at the wellhead can be explained only upon making the hypothesis that the large-scale (or regional) permeability of shale is (even at 3 km depth) about 10,000 times higher than the gas permeability of shale measured in the lab on drilled (nondried) shale cores under confining pressures corresponding to shale at the depth of about 3 km. This hypothesis has recently been rendered doubtful by a new three-phase medium theory that takes into account the body forces due to pressure gradients of pore water diffusing into the pores. This theory predicts the fracking to produce a dense system of branched vertical hydraulic cracks with the spacing of about 0.1 m. This value matches the crack spacing deduced from the gas production rate at wellhead based on the actual lab-measured permeability. It is calculated that, to boost the permeability 10,000 times, the width of the pre-existing open (unfilled) natural cracks or joints (whose ages are distributed from one to several hundred million years) would have to be about 2.8 μm (not counting possible calcite deposits in the cracks). But this width is improbably high because, over the geologic time span, the shale must exhibit significant primary and secondary creep or flow. It is shown that the creep must close all the cracks tightly (except for residual openings of the order of 10 nm) even if the cracks are propped open by surface asperities. The inevitability of secondary creep (or steady-state flow) is explained theoretically by activation of new creep sites at stress concentrations caused by prior creep deformation. The time of transition from primary to secondary creep is taken equal to the Maxwell time estimate from geology. The overall conclusion is that the 10,000-fold increase of large-scale permeability is most likely not pre-existing but frac-induced. Although this conclusion will make little difference for long-term forecasts, it would make a major difference for the understanding and control of the frac process.

Radiative transfer equation and direct simulation prediction of reflection and absorption by particle deposits

Two methods for computing the normal incidence absorptance and hemispherical reflectance from plane parallel layers of wavelength–sized spherical particles are presented. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a system of randomly–positioned spherical particles excited by an incident plane wave. The second method is based upon the scalar radiative transport equation (RTE) applied to a plane parallel medium. Comparisons are made using five values of particle refractive index, sphere size parameters ranging from 1 to 4, and particle volume concentrations ranging from 0.05 to 0.4. The results indicate that the multiple sphere T matrix method (MSTM) and RTE predictions of hemispherical reflectance and absorptance converge when particle volume fraction becomes small. At higher volume fractions the RTE can yield results for hemispherical reflectance that, depending on the particle size and refractive index, significantly depart from the exact predictions. On the other hand, RTE and MSTM predictions of absorptance have a much closer agreement which is largely independent of the sphere optical properties and volume concentration.

Maxwell Strata and Conjugate Points in the Sub-Riemannian Problem on the Lie Group SH(2)

We study local and global optimality of geodesics in the left invariant sub-Riemannian problem on the Lie group SH(2). We obtain the complete description of the Maxwell points corresponding to the discrete symmetries of the vertical subsystem of the Hamiltonian system. An effective upper bound on the cut time is obtained in terms of the first Maxwell times. We study the local optimality of extremal trajectories and prove the lower and upper bounds on the first conjugate times. We also obtain the generic time interval for the n-th conjugate time which is important in the study of sub-Riemannian wavefront. Based on our results of n-th conjugate time and n-th Maxwell time, we prove a generalization of Rolle's theorem that between any two consecutive Maxwell points, there is exactly one conjugate point along any geodesic.

Determining Physical Properties of the Cell Cortex

Actin and myosin assemble into a thin layer of a highly dynamic network underneath the membrane of eukaryotic cells. This network generates the forces that drive cell- and tissue-scale morphogenetic processes. The effective material properties of this active network determine large-scale deformations and other morphogenetic events. For example, the characteristic time of stress relaxation (the Maxwell time τM) in the actomyosin sets the timescale of large-scale deformation of the cortex. Similarly, the characteristic length of stress propagation (the hydrodynamic length λ) sets the length scale of slow deformations, and a large hydrodynamic length is a prerequisite for long-ranged cortical flows. Here we introduce a method to determine physical parameters of the actomyosin cortical layer in vivo directly from laser ablation experiments. For this we investigate the cortical response to laser ablation in the one-cell-stage Caenorhabditis elegans embryo and in the gastrulating zebrafish embryo. These responses can be interpreted using a coarse-grained physical description of the cortex in terms of a two-dimensional thin film of an active viscoelastic gel. To determine the Maxwell time τM, the hydrodynamic length λ, the ratio of active stress ζΔμ, and per-area friction γ, we evaluated the response to laser ablation in two different ways: by quantifying flow and density fields as a function of space and time, and by determining the time evolution of the shape of the ablated region. Importantly, both methods provide best-fit physical parameters that are in close agreement with each other and that are similar to previous estimates in the two systems. Our method provides an accurate and robust means for measuring physical parameters of the actomyosin cortical layer. It can be useful for investigations of actomyosin mechanics at the cellular-scale, but also for providing insights into the active mechanics processes that govern tissue-scale morphogenesis.

A second order dispersive FDTD algorithm for transverse electric Maxwell’s equations with complex interfaces

This work overcomes the difficulty of the finite-difference time-domain (FDTD) algorithm in solving the transverse electric (TE) Maxwell’s equations with inhomogeneous dispersive media. For such TE problems, the electric fields are discontinuous across the dispersive interfaces. Moreover, such discontinuities are time variant. A novel matched interface and boundary time-domain (MIBTD) method is proposed to solve such problems through new developments in both mathematical formulations and numerical algorithms. Mathematically, instead of handling all zeroth and first order jump conditions in a local coordinate, we directly construct the TE jump conditions which are needed in the FDTD computations in the Cartesian coordinate. Such Cartesian direction conditions depend on the time, as well as tangential and normal components of the electric flux. Driven by the jump condition modeling, we adopt the standard Maxwell’s equations in coupling with the Debye auxiliary differential equations for the electric flux as the governing equations. Computationally, the leapfrog scheme is employed for integrating the Maxwell system and time dependent jump conditions. Sophisticated interface treatments are developed in both producing the TE jump conditions and enforcing them in the FDTD algorithm, based on a staggered Yee lattice. The numerical accuracy, stability, and efficiency of the proposed scheme are investigated by considering dispersive interfaces of various shapes. The MIBTD method achieves a spatially second order of convergence in all tests. To the best of our knowledge, the present MIBTD scheme is the first FDTD method in the literature that can restore second order accuracy in treating curved dispersive interfaces for the TE Maxwell system.