Time-dependent Numerical Modeling Research Articles

On the design and fabrication of nanoliter-volume hanging drop networks

Hanging drop cultures provide a favorable environment for the gentle, gel-free formation of highly uniform three-dimensional cell cultures often used in drug screening applications. Initial cell numbers can be limited, as with primary cells provided by minimally invasive biopsies. Therefore, it can be beneficial to divide cells into miniaturized arrays of hanging drops to supply a larger number of samples. Here, we present a framework for the miniaturization of hanging drop networks to nanoliter volumes. The principles of a single hanging drop are described and used to construct the fundamental equations for a microfluidic system composed of multiple connected drops. Constitutive equations for the hanging drop as a nonlinear capacitive element are derived for application in the electronic-hydraulic analogy, forming the basis for more complex, time-dependent numerical modeling of hanging drop networks. This is supplemented by traditional computational fluid dynamics simulation to provide further information about flow conditions within the wells. A fabrication protocol is presented and demonstrated for creating transparent, microscale arrays of pinned hanging drops. A custom interface, pressure-based fluidic system, and environmental chamber have been developed to support the device. Finally, fluid flow on the chip is demonstrated to align with expected behavior based on the principles derived for hanging drop networks. Challenges with the system and potential areas for improvement are discussed. This paper expands on the limited body of hanging drop network literature and provides a framework for designing, fabricating, and operating these systems at the microscale.

Prospects for Detecting γ-Ray Bursts at Very High Energies with the HADAR Experiment

Recent ground-based observations of TeV photons have significantly deepened our understanding of the nature of gamma-ray bursts (GRBs). However, many fundamental problems remain unsolved concerning the physical mechanisms behind GRBs, necessitating the need for sufficient statistical data. The High Altitude Detection of Astronomical Radiation (HADAR) experiment utilizes a wide-angle water Cherenkov telescope, presenting a novel approach to measure the spectra and variability of GRBs from 10 GeV to 10 TeV energy ranges with unprecedented photon statistics and thereby break new ground in elucidating the physics of GRBs, which is still poorly understood. In this study, a time-dependent numerical modeling technique is utilized to simulate extensive light curves and spectral energy distributions of synthetic GRB afterglow emissions. By harnessing the remarkable capabilities of HADAR, we evaluate its potential in detecting GRB afterglow emissions at energies >10 GeV. Through our analysis, we unveil the prospect of detecting an estimated 5.8 GRBs annually, facilitating a systematic investigation into their reliance on model parameters. Future HADAR observations would offer valuable insights into the magnetic field and the environmental conditions surrounding GRBs.

Time-Dependent Numerical Modelling of Acoustic Cavitation in Liquid Metal Driven by Electromagnetic Induction

The numerically simulated method of using electromagnetic field from an alternating current is a patented method to create in liquid metal, under the conditions of resonance, acoustic waves of sufficient strength to cause cavitation and implosion of gas bubbles, leading to beneficial degassing and grain refinement. The modelling stages of electromagnetics are described below along with acoustics in liquids, bubble dynamics, and their interactions. Sample results are presented for a cylindrical container with liquid aluminium surrounded by an induction coil. The possibility of establishing acoustic resonance and sustaining the bubble oscillation at a useful level is demonstrated. Limitations of the time-dependent approach to this multi-physics modelling problem are also discussed.

The Southern African neutron monitor program: A regional network to study global cosmic ray modulation

Neutron monitor (NM) observations provide a unique, long-term record of galactic cosmic ray intensities, from which many valuable insights have been drawn as to the transport and modulation of these particles. In this paper, the African Neutron Monitor Network, which provides NM observations for broad range of cutoff rigidities, and spanning an exceptional period of time, is introduced. Aspects of these NM observations from this network are discussed, followed by a demonstration of time-dependent numerical cosmic ray modulation modelling done at the North-West University in South Africa, which hosts this network.

A Novel Method for Time-Dependent Numerical Modeling of Gastric Motility Directly from Magnetic Resonance Imaging.

Gastric motility has a critical role in disintegration and mixing of the ingested food inside the stomach. Several studies have been conducted to quantify and analyze the effect of the contractions of gastric musculature on the stomach contents. Despite the anatomical variation in stomach shape and motility patterns, previous numerical studies employed generalized geometries of the stomach as the computational domain for simulations. To model realistic gastric muscular contractions, the variation in stomach geometries need to be accounted for in numerical simulations. In the current study, a novel method was developed to utilize the recent advances in magnetic resonance imaging (MRI) technology and computational power expansion to build anatomically and physiologically realistic subject specific models of human gastric motility. In this method, MRI scans of the stomach were used to construct two and three dimensional geometry models of gastric motility. MRI was performed on 4 healthy participants. Using the developed method, dynamic numerical geometry models of gastric motility for each participant were constructed and related geometrical calculations were presented. Different combinations of solid and liquid test meals were consumed prior to the scans. The volume of the stomach ranged between 0.36 - 1.10 L in the fed state. The stomach models had an average length of 184 to 226 mm and a maximum diameter of 65 to 102 mm. Contraction propagation speed calculated from the models and MRI data were in good agreement, measuring around 2 mm/s.Clinical relevance- Clinicians can benefit from the proposed method for diagnostic purposes as the method is semi-automatic and can provide dynamic three-dimensional visualization of gastric motility of patients.

Time-dependent Numerical Modeling of Plain Concrete Columns Wrapped by FRP Sheets

The demand for strengthening structures becomes necessary when an increase in load is inevitable. For instance very little information is available on the time-dependent behaviour of strengthened concrete columns. Also, this is a primary factor hindering the widespread uses of FRP strengthening technologies in the construction implementations. This paper investigates the behaviour of strengthened concrete columns with FRP sheets subjected to long-term loading by non linear finite element analysis using ANSYS computer package. A three-dimensional finite element model has been used in this investigation. This study achieved a good agreement between numerical and experimental results, it was found that the percentage of error of specimens do not pass (5%) for creep strain. In addition, a parametric study was performed to study the effect of different factors on the behaviour of FRP strengthened concrete columns.

Computational Modeling on the Influence of the Schmidt Number on Second Phase Impurities SiC, Si2N2O and Si3N4 in Grown mc-Silicon for PV Applications

The influence of the Schmidt number on the incorporation of SiC, Si2N2O and Si3N4 precipitate formation during directional solidification of mc-silicon was investigated. SiC, Si2N2O and Si3N4 particles that precipitate in multi-crystalline silicon for PV application have detrimental effects on the wafer sawing process and solar cell performance. Time-dependent numerical modelling of the mass transport phenomena has been used with a diffusion model. There is still no study on the Schmidt number during the mc-silicon growth process. So, the numerical study has been investigated on the formation of second phase inclusions in mc-silicon for various Schmidt numbers. It may be used to control the precipitate of SiC, Si2N2O and Si3N4 in a mc-silicon ingot. In this paper, the second phase inclusions that precipitate in the mc-silicon ingot have been simulated and analyzed for three different Schmidt numbers Sc = 1, Sc = 10 and Sc = 100. From the obtained results, Schmidt number Sc = 1 is found to grow better quality mc-silicon crystals.

Compositional zonation of the shallow La Gloria pluton (Central Chile) by late-stage extraction/redistribution of residual melts by channelization: Numerical modeling

The origin of highly evolved magmas (e.g. rhyolites) has been a long-standing controversy in earth sciences. They are commonly thought to be generated in the upper crust by melt extraction from mush zones, but due to the rapid cooling of magma reservoirs in such shallow and typically cold environments, high magma emplacement rates of intermediate magmas are thought to be necessary to maintain large silicic mushes above the solidus long enough for the high-SiO2 melts extraction to occur. Late-stage redistribution of interstitial melts (i.e. heat and mass) by channels/dikes within those mushes has been invoked as a mechanism to preserve silicic mushes above their solidi for longer periods (i.e. delaying their final crystallization), but the nature of this process and its implications on plutons zonation are still poorly understood.Here, using time-dependent numerical modeling, we study the feasibility of late-stage interstitial melt extraction/redistribution by channels/dikes from a crystalline mush. Our model accounts for magma fluid dynamics, extraction of residual melts and thermal evolution of the crystallizing magma system and its hosting rocks, considering the thermal effect of the redistributing material. The model was applied to explain the anatomy of the well-documented La Gloria pluton (LGP, Central Chile), which exhibits increasing contents of SiO2 and abundant leucocratic dikes toward the margins, interpreted as trapped residual melts generated elsewhere in the magma chamber.Our results suggest that favorable conditions for extracting late-stage residual melts are reached at temperatures of ~750°C (60vol% crystallinity), at least for compositions similar to LGP dikes. Simulations correspond to 30kyr of reservoir cooling, when the concentric compositional zonation of LGP is reproduced after a short period of extraction (<15kyr) and outward redistribution of silicic melt, with an extracted mass fraction of up to 0.17. An inward growing crystal-dominated domain is the main source of interstitial melts. A total extracted melt volume of ~7.5km3 and a mean extraction rate of ~0.5km3/kyr were calculated for LGP conditions. For small magma reservoirs, the extracted rhyolitic melt could reach the upper levels of the magma chamber and the overlying host rock, but it seems unlikely that it can reach the surface to feed large rhyolitic eruptions, at least once recharges have stopped.

Efficient 58-GHz relativistic orotron with combined mode selection

This article presents time-dependent numerical modeling of V-band relativistic orotron: a high-power microwave generator with a TM03 oscillation mode in an oversized (D/λ ∼ 2.7) electrodynamic structure and diffractive output in the TM02 mode. Single-mode operation of the oscillator is ensured by the cyclotron selection of the working axisymmetric mode, with simultaneous depression of competing non-axisymmetric modes by means of cutting longitudinal slits in the wall of the slow-wave structure. The simulated output microwave power is 350 MW with a power conversion efficiency of 31% when using a 3.6 kA, 310 keV electron beam transported in the 3.9 T magnetic field. The simulation employed 2.5D axisymmetric and 3D Cartesian versions of the KARAT code.

Subduction initiation from a stagnant lid and global overturn: new insights from numerical models with a free surface

Subduction initiation is a key in understanding the dynamic evolution of the Earth and its fundamental difference to all other rocky planetary bodies in our solar system. Despite recent progress, the question about how a stiff, mostly stagnant planetary lid can break and become part in the global overturn of the mantle is still unresolved. Many mechanisms, externally or internally driven, are proposed in previous studies. Here, we present the results on subduction initiation obtained by dynamically self-consistent, time-dependent numerical modelling of mantle convection. We show that the stress distribution and resulting deformation of the lithosphere are strongly controlled by the top boundary formulation: A free surface enables surface topography and plate bending, increases gravitational sliding of the plates and leads to more realistic, lithosphere-scale shear zones. As a consequence, subduction initiation induced by regional mantle flow is demonstrably favoured by a free surface compared to the commonly applied, vertically fixed (i.e. free-slip) surface. In addition, we present global, three-dimensional mantle convection experiments that employ basal heating that leads to narrow mantle plumes. Narrow mantle plumes impinging on the base of the plate cause locally weak plate segments and a large topography at the lithosphere-asthenosphere boundary. Both are shown to be key to induce subduction initiation. Finally, our model self-consistently reproduces an episodic lid with a fast global overturn due to the hotter mantle developed below a former stagnant lid. We conclude that once in a stagnant-lid mode, a planet (like Venus) might preferentially evolve by temporally discrete, global overturn events rather than by a continuous recycling of lid and that this is something worth testing more rigorously in future studies.

Numerical Modelling on Industrial Scale Multi-Crystalline Silicon Growth Process at Critical Prandtl Number for PV Applications

Directional solidification (DS) is a very important technique for growing good quality multi-crystalline silicon at a large scale for photovoltaic (PV) solar cells. Time dependent numerical modelling of the temperature distribution, residual stress and dislocation density rate in multi-crystalline silicon ingots grown by directional solidification have been investigated for five growth stages using the finite volume method at the critical Prandtl number, Pr = 0.01. Impurity concentrations of O, C and SiC are calculated in the central region of grown crystal from bottom to top. The history of temperature distribution, stress generation, and dislocation multiplication are tracked in our modelling continuously considering the growth process from the beginning to the end of the solidification process. This paper reports an advanced understanding of the thermal and mechanical behaviour and generation of impurities in grown multi-crystalline ingots. The computational results show good agreement with experimental data for residual stress, dislocation density and impurities formation in grown ingots. From the obtained results, the crystal quality is evaluated under various solidification stages. We found that the above crystal properties undergo a sudden change at the final stage of the solidification process.

Time-dependent evolution of rock slopes by a multi-modelling approach

This paper presents a multi-modelling approach that incorporates contributions from morpho-evolutionary modelling, detailed engineering-geological modelling and time-dependent stress-strain numerical modelling to analyse the rheological evolution of a river valley slope over approximately 102kyr. The slope is located in a transient, tectonically active landscape in southwestern Tyrrhenian Calabria (Italy), where gravitational processes drive failures in rock slopes. Constraints on the valley profile development were provided by a morpho-evolutionary model based on the correlation of marine and river strath terraces. Rock mass classes were identified through geomechanical parameters that were derived from engineering-geological surveys and outputs of a multi-sensor slope monitoring system. The rock mass classes were associated to lithotechnical units to obtain a high-resolution engineering-geological model along a cross section of the valley. Time-dependent stress-strain numerical modelling reproduced the main morpho-evolutionary stages of the valley slopes. The findings demonstrate that a complex combination of eustatism, uplift and Mass Rock Creep (MRC) deformations can lead to first-time failures of rock slopes when unstable conditions are encountered up to the generation of stress-controlled shear zones. The multi-modelling approach enabled us to determine that such complex combinations may have been sufficient for the first-time failure of the S. Giovanni slope at approximately 140ka (MIS 7), even without invoking any trigger. Conversely, further reactivations of the landslide must be related to triggers such as earthquakes, rainfall and anthropogenic activities. This failure involved a portion of the slope where a plasticity zone resulted from mass rock creep that evolved with a maximum strain rate of 40% per thousand years, after the formation of a river strath terrace. This study demonstrates that the multi-modelling approach presented herein is a useful tool for estimating the progressive development of slope failures because it can highlight time-dependent continuous deformations as the major processes that drive rocky slopes to failure. This type of approach can be devoted to the best selection of risk mitigation strategies with respect to both human life and anthropic infrastructure.

Long-term time-dependent consolidation analysis by numerical modelling to determine subsidence effect area induced by longwall top coal caving method

Longwall top coal caving (LTCC) is one of the mining methods used in thick coal seams. Large subsidence occurs over the coal mines, where this method is utilised for production. The area affected by subsidence differs due to varying limit angles of the geological formations in the overburden. However, subsidence does not occur instantly, it is a phenomenon which progresses in time. It is especially important to perform time-dependent analyses of mines in the neighbourhood of residential areas, agricultural zones, or any kind of man-made structures. In this study, the long-term development of a subsidence due to production in an underground coal mine in Manisa-Soma-Eynez was examined using time-dependent numerical modelling technique. 750 days after the end of production, the effects of subsidence were examined in place, measurements were taken from the field and they were compared with the results of the time dependent numerical modelling analyses. [Received: November 15, 2014; Accepted: October 6, 2015]

Degradation of CdTe Solar Cells: Simulation and Experiment

Time-dependent numerical modeling is employed in conjunction with experimental data to investigate degradation mechanisms in cadmium telluride (CdTe) solar cells. Two mechanisms are tested against the data: 1) defect generation in the junction region caused by excess charge carriers and reactant defects and 2) back barrier increase. Junction effects result in stable $J_{{\rm sc}}$ with significant losses in $V_{{\rm oc}}$ and FF, in accordance with typical data for the type of light-soak stress conditions considered here. The back barrier increase causes additional FF loss. The results suggest that both mid-gap recombination centers and shallow acceptor-type defects form near the main junction as degradation proceeds. Our data reaffirm that the inclusion of copper in the back contact is associated with better initial performance and more rapid degradation. Correlations were observed between degradation rates and apparent doping hysteresis obtained from bidirectional capacitance–voltage (C–V) scans. Our time-resolved photoluminescence (PL) results show no correlation between light-soak-induced $V_{{\rm oc}}$ loss and PL lifetime.

Safety pillar design for main galleries in multi-slice longwall top coal caving method

Longwall top coal caving (LTCC) is one of the methods used in thick coal seams. In coal mines where this method is used, some coal is left in place to be retrieved later in order to prevent damage to the main galleries. Stresses and strains created by roof layer caving of the panels advancing towards each other may put pressure on the main galleries. The amount of this pressure increases with time-dependent consolidation of roof layers. Sizes of the safety pillars gain importance in order to prevent this pressure and thus avoid the damages on the supports of the main galleries. In this research, great deformations creating damages on the supports of the main galleries of an underground coal mines in Manisa, Soma-Eynez were examined. Time-dependent deformation amounts were investigated both in situ and with time-dependent numerical modelling analysis. The results obtained by this research provide the sizes of the safety pillars in the panels to be produced. [Received: September 24, 2014; Accepted: December 25, 2014]

Towards understanding junction degradation in cadmium telluride solar cells

A degradation mechanism in cadmium telluride (CdTe/CdS) solar cells is investigated using time-dependent numerical modeling to simulate various temperature, bias, and illumination stress conditions. The physical mechanism is based on defect generation rates that are proportional to nonequilibrium charge carrier concentrations. It is found that a commonly observed degradation mode for CdTe/CdS solar cells can be reproduced only if defects are allowed to form in a narrow region of the absorber layer close to the CdTe/CdS junction. A key aspect of this junction degradation is that both mid-gap donor and shallow acceptor-type defects must be generated simultaneously in response to photo-excitation or applied bias. The numerical approach employed here can be extended to study other mechanisms for any photovoltaic technology.

Numerical modeling of a high power terahertz source in Shanghai

On the basis of an energy-recovery linac, a terahertz source with a potential for kilowatts of average power is proposed in Shanghai, which will serve as an effective tool for material and biological sciences. In this paper, the physical design of two free electron laser (FEL) oscillators, in a frequency range of 2–10 THz and 0.5–2 THz respectively, are presented. By using three-dimensional, time-dependent numerical modeling of GENESIS in combination with a paraxial optical propagation code, the THz oscillator performance, the detuning effects, and the tolerance requirements on the electron beam, the undulator field and the cavity alignment are given.

THE DYNAMICS OF STELLAR CORONAE HARBORING HOT JUPITERS. I. A TIME-DEPENDENT MAGNETOHYDRODYNAMIC SIMULATION OF THE INTERPLANETARY ENVIRONMENT IN THE HD 189733 PLANETARY SYSTEM

We carry out the first time-dependent numerical MagnetoHydroDynamic modeling of an extrasolar planetary system to study the interaction of the stellar magnetic field and wind with the planetary magnetosphere and outflow. We base our model on the parameters of the HD 189733 system, which harbors a close-in giant planet. Our simulation reveals a highly structured stellar corona characterized by sectors with different plasma properties. The star-planet interaction varies in magnitude and complexity, depending on the planetary phase, planetary magnetic field strength, and the relative orientation of the stellar and planetary fields. It also reveals a long, comet-like tail which is a result of the wrapping of the planetary magnetospheric tail by its fast orbital motion. A reconnection event occurs at a specific orbital phase, causing mass loss from the planetary magnetosphere that can generate a hot spot on the stellar surface. The simulation also shows that the system has sufficient energy to produce hot-spots observed in Ca II lines in giant planet hosting stars. However, the short duration of the reconnection event suggests that such SPI cannot be observed persistently.

Time Dependence in Relativistic Collisionless Shocks: Theory of the Variable “Wisps” in the Crab Nebula

We describe results from time-dependent numerical modeling of the collisionless reverse shock terminating the pulsar wind in the Crab Nebula. We treat the upstream relativistic wind as composed of ions and electron-positron plasma embedded in a toroidal magnetic field, flowing radially outward from the pulsar in a sector around the rotational equator. The relativistic cyclotron instability of the ion gyrational orbit downstream of the leading shock in the electron-positron pairs launches outward-propagating magnetosonic waves. Because of the fresh supply of ions crossing the shock, this time-dependent process achieves a limit cycle, in which the waves are launched with periodicity on the order of the ion Larmor time. Compressions in the magnetic field and pair density associated with these waves, as well as their propagation speed, semiquantitatively reproduce the behavior of the wisp and ring features described in recent observations obtained using the Hubble Space Telescope and the Chandra X-Ray Observatory. By selecting the parameters of the ion orbits to fit the spatial separation of the wisps, we predict the period of time variability of the wisps that is consistent with the data. When coupled with a mechanism for nonthermal acceleration of the pairs, the compressions in the magnetic field and plasma density associated with the optical wisp structure naturally account for the location of X-ray features in the Crab. We also discuss the origin of the high-energy ions and their acceleration in the equatorial current sheet of the pulsar wind.

Time-variability of the Crab Nebula wisps

AbstractWe present results of time-dependent numerical modeling of the internal structure of the collisionless shock terminating the pulsar wind in Crab Nebula. We treat the equatorial relativistic wind as composed of ions and electron-positron plasma with an embedded toroidal magnetic field. Relativistic cyclotron instability of the ion ring downstream from the shock is found to launch outward propagating magnetosonic waves. Due to the fresh supply of ions crossing the shock, the time-dependent process achieves a limit-cycle pattern, in which the waves are launched with periodicity on the order of the ion Larmor time. Compressions in magnetic field and pair density associated with these waves as well as their propagation speed qualitatively reproduce the features observed in the wisps.