Two-plate Model Research Articles

Supernova emission of secretly interacting neutrino fluid: Theoretical foundations

Neutrino-neutrino scattering could have a large secret component that would turn neutrinos within a supernova (SN) core into a self-coupled fluid. Neutrino transport within the SN core, emission from its surface, expansion into space, and the flux spectrum and time structure at Earth might all be affected. We examine these questions from first principles. First, diffusive transport differs only by a modified spectral average of the interaction rate. We next study the fluid energy transfer between a hot and a cold blackbody surface in plane-parallel and spherical geometry. The key element is the decoupling process within the radiating bodies, which themselves are taken to be isothermal. For a zero-temperature cold plate, mimicking radiation into free space by the hot plate, the energy flux is 3%–4% smaller than the usual Stefan-Boltzmann law. The fluid energy density just outside the hot plate is numerically 0.70 of the standard case, the outflow velocity is the speed of sound vs=c/3, conspiring to a nearly unchanged energy flux. Our results provide the crucial boundary condition for the expansion of the self-interacting fluid into space, assuming an isothermal neutrino sphere. We also derive a dynamical solution, assuming the emission suddenly begins at some instant. A neutrino front expands in space with luminal speed, whereas the outflow velocity at the radiating surface asymptotically approaches vs from above. Asymptotically, one thus recovers the steady-state emission found in the two-plate model. A sudden end to neutrino emission leads to a fireball with constant thickness equal to the duration of neutrino emission. Published by the American Physical Society 2024

The Moving Element Method for the Dynamic Responses of Floating Double-Plate Structures on the Shallow Water

In this paper, the dynamic behavior of floating double-plate structures under a moving load is investigated in great detail with different factors utilizing the moving element method (MEM). The structures in this study are very large floating structures (VLFSs). The Kirchhoff–Love theory is used to model two floating plates connected by a Winkler-type elastic core, whilst the water surrounding the structure is simulated by the shallow linear water wave theory. In order to improve the computational efficiency of moving load problems, the MEM is adopted. Since the MEM uses fewer discrete elements than those of the traditional finite element method (FEM), the computational cost is reduced. The proposed two-plate model helps to reduce the influence of the surrounding water on the upper plate. Several numerical results are presented to investigate the influence of the ratio of thickness between layers as well as core stiffness on the displacements with different water depths, and load speeds.

The modeling of simultaneous three metals codeposition investigated by cyclic voltammetry

A co-deposition of three metals as bismuth, lead, and cadmium in acetate buffer (pH = 4.6) was studied using the cyclic voltammetry (CV) technique. The electroreduction process as a whole was recognized as electrocatalytic and analyzed in frames of the two-plate model. The model includes all of the coupled responses of the three electronation/deelectronation systems. It was demonstrated that the cyclic voltammetry technique and two-plate approach are sufficient to achieve a complete explanation of the considered co-deposition process. The applied two-plate model with included BET adsorption equation and obtained values of electrochemical kinetic parameters were validated and discussed. The specific role of the deposited bismuth layer in the whole co-deposition process was established. • The co-deposition of Bi, Pb and Cd was investigated by cyclic voltammetry. • The deposited Bi layer was recognized as electrocatalytic for further deposition. • The whole co-deposition process was described by the two-plate mathematical model. • The estimated values of kinetic parameters were three way validated and discussed.

Mechanics of the Ideal Double-Layer Capacitor

The mechanical state within a parallel-plate electrolytic capacitor is examined by appending a local momentum balance to a quasielectrostatic theory that describes charge screening in both the electrolyte and the electrodes. A classical diffuse-double-layer model, which treats the capacitor’s separator as a dilute electrolytic solution, is augmented to include metal electrodes, modelled as electron gases. When accounted for in this way, the electrodes are found to impact the interfacial capacitance significantly, as well as exerting compressive stress on the electrolyte. Nonlinear and quadratically perturbed theories are explored, the former around a single plate and the latter around the entire capacitor. Perturbation reveals several mechanical scaling laws generally applicable to capacitive metal/electrolyte interfaces. The two-plate model rationalizes the exponential decay of disjoining pressure between voltage-biased plates as their separation distance grows, as well as retrieving the well-known properties of a dielectric capacitor when the plate separation is small. This was Paper 1964 presented at the Dallas, Texas, Meeting of the Society, May 26-May 30, 2019.

The Assessment of Elastic Follow-Up Effects on Cyclic Accumulation of Inelastic Strain Under Displacement-Control Loading

Assessment of strain accumulation due to nonlinear events like creep, plasticity or ratcheting phenomenon has gained importance, as it causes an increase in creep and fatigue damage in structures. Some factors such as the magnitude of loading, constitutive equations or the elastic regions around the nonlinear events have an effect on the rate of strain accumulation. The elastic follow-up can explain the mechanism of plastic strain accumulation. This phenomenon may occur when a mechanical structure with elastic manner is connected to nonlinear events. In cyclic loading with nonzero mean stress, the plastic strain may be accumulated. This behavior is known as ratcheting and usually takes place under cyclic load-control conditions. A new simplified method is proposed in this paper in order to assess the effects of elastic follow-up on the strain accumulation (ratcheting) behavior of two-plate model made up of AISI 1045 steel under displacement-control loading, and a set of experimental tests is conducted to verify this method. The tests were carried out by a servo-hydraulic Zwick–Roell machine. The test results confirm the accuracy of the proposed method and also reveal that in the presence of EFU in the system, the cyclic accumulation of plastic strain in addition to the load-control conditions may occur locally in the displacement-control conditions.

Incipient mantle delamination, active tectonics and crustal thickening in Northern Morocco: Insights from gravity data and numerical modeling

The Betic-Rif orocline surrounding the Alboran Sea, the westernmost tip of the Mediterranean Sea, accommodates the NW–SE convergence between the Nubia and Eurasia plates. Recent GPS observations indicate a ∼4 mm/yr SW motion of the Rif Mountains, relative to stable Nubia, incompatible with a simple two-plate model. New gravity data acquired in this study define a pronounced negative Bouguer anomaly south of the Rif, interpreted as a ∼40 km-thick crust in a state of non-isostatic equilibrium. We study the correlation between these present-day kinematic and geodynamic processes using a finite-element code to model in 2-D the first-order behavior of a lithosphere affected by a downward normal traction (representing the pull of a high-density body in the upper mantle). We show that intermediate viscosities for the lower crust and uppermost mantle (1021–1022Pas) allow an efficient coupling between the mantle and the base of the brittle crust, thus enabling (1) the conversion of vertical movement, resulting from the downward traction, to horizontal movement and (2) shortening in the brittle upper crust. Our results show that incipient delamination of the Nubian continental lithosphere, linked to slab pull, can explain the present-day abnormal tectonics, contribute to the gravity anomaly observed in northern Morocco, and give insight into recent tectonics in the Western Mediterranean region.

The investigation and modeling of two metals codeposition process

A codeposition of bismuth and lead from Bi3+/Bi2+/Bi+/Bi0 and Pb2+/Pb+/Pb0 systems in 0.5M KNO3 (pH=1) was investigated by cyclic voltammetry technique. The process was recognized as electrocatalytic and depicted by the two-plate model including Brunauer, Emmett and Teller (BET) adsorption expression. The model recreates all of the not resolved responses of two electronation/deelectronation couples. An alteration of electrode surface throughout electrode reaction is integrated with the model. It was proved that cyclic voltammetry (CV) method and two-plate approach is adequate to achieve a complete depiction of considered codeposition process. The estimated values of electrochemical kinetic parameters as well as the two-plate model with its BET adsorption expression were validated and discussed.

Microwave Dynamics of Superconducting Quantum Cell

We present an analysis of the microwave dynamics of the Superconducting Quantum Cell (SQC) in the microwave field performed by means of 3-D numerical simulations using a two-plate model. The simulations are necessary for the realization of active electrically small antennas (ESAs) based on Superconducting Quantum Arrays composed of SQCs. It was found that the incident wave mainly affects the SQC through its magnetic component in the same way as a low-frequency magnetic field does. We suggested possible improvements of the cell design by taking into account the current and field distributions in the plate intersection, as well as the size effects.

The description of the copper deposition/dissolution process in ammonia buffer with the application of mathematical two-plate model

The experimental Cu2+/Cu+/Cu0 system in ammonia buffer (pH=9.25) has been investigated by cyclic voltammetry method and described by the advanced two-plate model with BET adsorption equation. A change of electrode properties during electrode process is included into the applied model. The model reproduces four one-electron peaks of electronation/deelectronation process together with a characteristic loop on cathodic part of CV response and covers 0.1; 0.2, 0.5; 1; 2; 5; 10; 20; 50mM concentrations of Cu2+ at scan rate range 0.05–5V/s. The values of elementary kinetic parameters have been determined, validated and discussed. It has been proved that CV technique and two-plate model is adequate to cover complete description of the deposition process for the wide range of concentration. The parameters of applied BET adsorption model coupled with kinetic parameters of electrochemical process model have been extensively discussed.

The experimental verification of mathematical two-plate model describing the metal deposition/dissolution process

The advanced two-plate model with BET adsorption equation has been verified by the use of the experimental Cu2+/Cu0 system in 1 M NaClO4/pH 3 solution at different scan rates and at 5, 10, 25 mM concentrations of Cu2+. A change of electrode properties during electrode process was included into the applied model. The model reflects a characteristic loop on cathodic part of CV response. The values of elementary kinetic parameters have been determined and discussed.

The mathematical models of the stripping voltammetry metal deposition/dissolution process

Three mathematical models of electrochemical two-electron deposition/dissolution process have been presented and discussed. The advanced two-plate model with BET adsorption formula equation has been presented and verified by the use of the experimental Cu 2+/Cu +/Cu 0 system in 0.5 M HCl solution at different scan rates. A change of electrode properties during electrode process was included into applied model and discussed.

Stress modeling of tectonic blocks at Cape Kamchatka, Russia using principal stress proxies from high-resolution SAR: new evidence for the Komandorskiy Block

A new data set of 851 lineaments mapped from European Remote Sensing satellites 1 and 2 full resolution Synthetic Aperture Radar (SAR) data are interpreted as geological proxies for stresses resulting from plate and block collision near the Cape Kamchatka region of the Kamchatka Peninsula using a Geographical Information Systems-based analysis. Numerical Manifold Method (NMM) analysis is used to model the stress field within the Cape Kamchatka region resulting from the collision of lithospheric plates and blocks. Results of our NMM model, using different plate motion and plate configuration in the region, are compared with orientation data for the mapped set of lineaments. These data suggest that the lineaments observed in SAR cannot be fully explained by a simple two-plate model in this in the Cape Kamchatka region. As an alternative, we propose that the data can be explained by the existence of the previously proposed Komandorskiy Block. Recent Global Positioning Satellite measurements in the Aleutian Islands support our lineament-derived model and show that the near Islands/Komandorskiy Island block of the extreme western Aleutians is moving independently of the North American Plate.

Mantle dynamics with induced plate tectonics

Mantle circulation and plate tectonics can be described by means of two scalar fields. The poloidal field is related to horizontal divergence, i.e., to the vertical mass flux. The toroidal field expresses the shear deformation or the rotations within spherical shells. For the Earth, the surface kinetic energy is known to be equally distributed between the two fields. In recent years the lateral mantle density variations revealed by seismic tomography have been introduced in dynamic mantle models which have predicted the major features of both the geoid and the surface divergence. These models assumed a spherical symmetry of the rheological properties of the Earth. However, with this assumption, the Navier‐Stokes equation implies that mass heterogeneities cannot drive any toroidal motion. This prompted us to develop a new model which takes into account the existence of rigid and independent plates. These plates break the spherical symmetry assumed in all earlier models. They modify the mantle circulation and hence the predicted surface observables such as displacement and gravity. In this paper, we first explain by means of a very simple twoplate model, how the poloidal flow caused by mantle heterogeneities can be converted to surface toroidal motion. We then apply the model to the real Earth with its major plates and compare our predictions to those deduced from a more classical Earth model having a uniform free slip condition at the surface. Taking the seismic tomography pattern as a picture of the mantle mass heterogeneities, we achieve a highly satisfactory fit to the observed plate velocities. This new theoretical framework also improves the geoid prediction.

Gravity anomalies and deep structure of eastern Hudson bay

The Cape Smith and Belcher foldbelts of Lower Proterozoic (Aphebian) rocks form parts of the proposed Circum-Superior suture which separates the Superior and Churchill structural provinces of the Canadian Shield. Recent marine gravity surveys in eastern Hudson Bay (1976–1979) show that the distinctive linear gravity pattern of paired positive and negative anomalies along the Cape Smith foldbelt of northern Ungava extends southwards into Hudson Bay to the Belcher Islands. Interpretation of five gravity profiles across the Cape Smith and Belcher foldbelts suggests that the Churchill crust is thicker and denser than the Superior. The boundary between the two contrasting crustal blocks is interpreted as a collisional suture. The rocks of the foldbelts which are progressively more volcanic northwards are the source of a residual positive anomaly associated with the Cape Smith foldbelt and a series of discontinuous positive residual anomalies in the Bay. To the north the thicknesses of the foldbelt rocks are estimated to be between 4 and 9 km with a local maximum of 13 km in the northernmost profile. To the south in the Belcher Islands, where geological estimates of formation thickness and measured rock densities provide more constraints on the interpretation of the residual anomalies, the foldbelt rocks are generally 6–7 km thick with a local maximum thickness of about 9 km. One possible interpretation of paleomagnetic results for Belcher Islands rocks in terms of a two-plate model lends support to the collision hypothesis.

Paleomagnetism of igneous rocks from the Belcher Islands, Northwest Territories, Canada

Paleomagnetic results from igneous rock units on the Belcher Islands, Hudson Bay, are described. Fold tests for all units studied, as well as a contact test for the intrusive bodies, indicate that both primary (initial), and secondary (post-folding) magnetizations are present.The paleomagnetic pole position from primary directions of the oldest unit studied, the Eskimo volcanics, is situated at 40°S, 002°E (A95 = 12°) and is similar to that derived from equivalent volcanics on the mainland. The younger volcanic unit studied, the Flaherty volcanics, yielded a pole position from primary directions at 0°, 244°E (A95 = 7°). The Haig intrusions, associated with these younger volcanics, yields an almost identical pole position at 1°N, 247°E (A95 = 6°), being derived from directions which are shown to be not only pre–folding but also date from initial cooling. The Eskimo volcanics, which have been more deeply buried than the Flaherty (upper) volcanics, carry substantial components of secondary (post-folding) magnetization which yield a pole position at 19°N, 243°E (A95 = 15°), about 20° north of the pole positions derived from the youngest units.It is argued that the apparent polar wander path (APWP) constructed for the Belcher Islands is representative of the mainland Ungava Craton. Comparison with the equivalent APWP from elsewhere in North America shows that the two APWP's are at variance. Although a two-plate model could be advanced, perhaps a more conservative interpretation is to extend the existing North American APWP eastward to include the Belcher–Ungava APWP, that is, to favour a one-plate model.