Model In Cartesian Coordinates Research Articles

Development and Validation of a 3-D Analytical Fluidic Model in Cartesian Coordinates for a Magnetic Refrigeration Application

This paper focuses on the development and validation of a three-dimensional (3-D) analytical model based on the formal resolution of the incompressible Navier-Stokes equations in Cartesian coordinates. This analytical fluidic model calculates the evolution of the fluid flow velocity for various pressure gradient shapes (i.e., square, trapezoidal, ramp, triangle, sinusoidal signals, etc.), with or without mean value, using Fourier series. The model can consider square and rectangular channels of any dimensions in terms of height, width, and depth. It allows for the study of different types of fluid flow and geometries. The introduction highlights the significance of analytical modeling, particularly in the context of Magnetic Refrigeration (MR) technologies. The model assumptions and governing equations are presented. The results obtained from the analytical model are validated and show good convergence with those obtained using the COMSOL Multiphysics® software. The comparison demonstrates a high level of agreement between the two models. The analytical model performs well in terms of computation time and accuracy. It will be coupled with an analytical thermic model and used to optimize Active Magnetic Regenerative Refrigeration (AMRR) cycles. The ultimate objective is to determine an optimal pressure gradient evolution in order to maximize heat exchange in a regenerator channel.

Development of a Regional Numerical Tidal Forecast Model Along the Coast of Bangladesh and Its Associated Tidal Height Estimation

A two-dimensional shallow water equation in the Cartesian coordinate model is developed to estimate the tide along the coast of Bangladesh. The model was developed and discretized by a finite difference method. The model equation was discretized by the Finite Difference Method (FDM) considering the forwarding of time and central in space. In our model, the coastal boundaries, islands, and some small rivers are approximated by an exact stair step representation and solved by a conditional stable semi-Implicit Finite Difference Technique in a Structured Arakawa C-Grid system. Ignoring the wind stress created stable tidal conditions along the southern open boundary of the ocean which was the astronomical M2 component. The desired results are obtained after running the model for a fixed period of time since the steady state. The model results give a reasonable agreement with the observed data. The root means square error of the mean also shows good reasonable agreement.

Gaussian processes based extended target tracking in polar coordinates with input uncertainty

Gaussian processes (GP) based extended target tracking (ETT) technique has attracted the attention of scientists since it can accurately estimate the kinematic states as well as the contour states of irregular-shape targets. Most traditional GP methods consider the ETT problem with a linear measurement model in Cartesian coordinates and ignore the input uncertainty of GP for simplicity. In many applications, however, measurements are generated with high-resolution sensors in polar coordinates. More importantly, the ignorance of input uncertainty in GP will exacerbate the tracking performance in these cases. In order to track an irregular-shape extended target in polar coordinates with input uncertainty, an improved GP-based probabilistic data association (IGP-PDA) algorithm is developed that includes the following enhancements: Firstly, a nonlinear measurement model is used and the unbiased converted measurement technique is invoked for the ETT problem. Secondly, the analytical form of statistical properties of the input uncertainty due to measurements noise and predicted error is derived. Thirdly, an IGP-PDA taking into account measurement origin uncertainty as well as input uncertainty is proposed, and three sub-optimal implementations are provided. Last, the posterior Cramer-Rao lower bound of ETT with input uncertainty is derived. Simulation results verify the effectiveness of the proposed method.

An Analysis of Track Effects on Storm Surge Simulation

This study investigates the effects of cyclone tracks on water levels during storm surges along the coast of Bangladesh. A numerical hydrodynamical model in Cartesian coordinates has been developed, where the developed equations are solved by a semi-implicit finite difference method. The boundary fitted grid technique is employed to rectangularized the physical domain. Along the north-east corner of the model, the Meghna River fresh water discharge is taken into account. A stable tidal regime over the region of interest is generated with the help of four major tidal constituents, namely M_2 (principal lunar semi diurnal), S_2 (principal solar semi diurnal), O_1 (principal lunar diurnal) and K_1 (principal lunar diurnal) along the southern open boundary of the outermost model. This previously generated tidal regime is used as the initial state of sea in order to obtain water levels due to the nonlinear interaction of tide and surge. Numerical experiments are made with the severe storm April 1991 and some hypothetical storm tracks. The simulated results with the real track are found to be in a good agreement with some observed and some reported data. The water levels are found to be greatly influenced by the hypothetical cyclone tracks.

Effect of Coriolis Force on the Numerical Estimation of Water Level Elevation Due to a Catastrophic Cyclone along the Coast of Bangladesh

A two-dimensional vertically integrated shallow water equation in the Cartesian coordinate model is used to estimate the water level considering the impact of Coriolis force. The shallow water model equation was discretized by a finite difference method (FDM). Consider the forwarding of time and central space as a moderator of this discretization. The model approximates coastal boundaries, small islands, small rivers and complex tributaries by an accurate stair step representation. The model equations are solved by a static semi-implicit finite difference technique where a structured Arakawa C-grid system is used as the condition. A one-way nested scheme technique is used to incorporate complex land-sea interfaces such as small offshore islands and water depths with sufficient accuracy as well as decreasing the computational cost. A stable tidal condition was created by applying M2 tidal forcing with the largest tide along the southern open boundary of the Bay of Bengal. The model uses the Coriolis force as an external force that can affect water buoyancy. The main task is to analyse the effect of Coriolis force on water buoyancy. The described model was applied to simulate sea-surface elevation associated with the severe cyclone in April 1991 that strike on the east coast of Bangladesh. We have found a significant impact of Coriolis force on surge height. However, the model gives an accurate numerical estimate of surge height.

Multiframe track-before-detect method based on velocity filtering in mixed coordinates

In this paper, a velocity filtering based track-before-detect algorithm in mixed coordinates is presented to address the problem of integration loss caused by inaccurate motion model in polar coordinate sensors. Since the motion of a constant velocity (CV) target is better modeled in Cartesian coordinates, the search of measurements for integration in polar sensor coordinates is carried out according to the CV model in Cartesian coordinates instead of an approximate model in polar sensor coordinates. The position of each cell is converted into Cartesian coordinates and predicted according to an assumed velocity. Then, the predicted Cartesian position is converted back to polar sensor coordinates for multiframe accumulation. The use of the correct model improves integration effectiveness and consequently improves algorithm performance. To handle the weak target with unknown velocity, a velocity filter bank in mixed coordinates is presented. The influence of velocity mismatch on the performance of filter bank is analyzed, and an efficient strategy for filter bank design is proposed. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.

A numerical estimate of water level elevation due to a cyclone associated with a different landfall angle

<p>Bangladesh is a disaster-prone riverine country in South Asia, most of them are cyclone-related. That's why research on cyclones in this region is very important. This study investigates the surge height associated with the changes of landfall angle due to climate change. The deflected angle of landfall was investigated from the data analysis of Bangladesh Meteorological Department (BMD), Joint typhoon warning center (JTWC), and Meteorological Research Institute- Atmospheric global circulation model (MRI-AGCM). A cyclone of future climate has been investigated from the Database for Policy Decision-Making for Future Climate Change (d4PDF) data under present and future climate conditions. To find the surge height, a vertically shallow water Cartesian coordinate model has been used to simulate the surge height. The shallow water model equations were discretized through finite difference technique with the Arakawa C grid system and solved by a conditionally stable semi-implicit manner. The fluctuated striking angle due to climate change was then applied to the known cyclone BOB 01 and the associated surge height was then investigated. We found that our simulated result and the observed result make a good agreement. We have also seen that different types of cyclones have a significant effect on the water level elevation due to their landfall angle</p>

A unified method based on pseudo-spectrum for track-before-detect of targets with motion model uncertainty

Track-before-detect (TBD) of weak targets with motion model uncertainty is of significance in practical applications, since targets may experience various motions. In this paper, a unified TBD framework is presented for multiframe detection of weak targets with constant velocity (CV) and coordinated turn (CT) motions. This enables detection and parameter estimation of weak CV and CT targets in a same state space. Firstly, according to common CT model in Cartesian coordinates, the state equation of the common model suitable for matched filtering based TBD is derived. In this equation, the speed, turn rate and initial heading are used to determine target motion. Secondly, a heading-speed-turn rate matched filter based on pseudo-spectrum in mixed coordinates is proposed for weak CT or CV target detection in sensor coordinates. The data search before multiframe integration is conducted according to the derived model in x-y plane by matching the constant target speed, turn rate and initial heading. Then, the echo energy is integrated based on the pseudo-spectrum in polar coordinates. This eliminates performance loss caused by model mismatch in sensor coordinates, and facilitates well-maintained target envelope. Thirdly, to deal with the problem that the target motion model may jump at any time during the processing batch, a joint motion parameter and jumping time matching based TBD in mixed coordinates is presented. The jumping time is considered as a matching parameter for multiframe integration in addition to speed, turn rate and heading. This method can supply complete information of the maneuvering target motion in the processing batch. Finally, simulations are conducted to demonstrate the effectiveness of the proposed methods.

Analysis of elastohydrodynamics and nutrient transport through deformable porous scaffold inside a hollow fiber membrane bioreactor

Hydrodynamics and nutrient transport in a hollow fiber membrane bioreactor is studied by developing a two-dimensional mathematical model in Cartesian coordinates. In a more realistic scenario, the scaffold is considered to be elastic and deformable, which undergoes deformation with the applied pore pressure. A mixture model is used to deal with the scaffold matrix, cells, and the fluid present in the scaffold region. The method of lubrication theory is incorporated when the aspect ratio of the lumen is small. The nutrient transport in the scaffold region is assumed to be governed by advection–diffusion–reaction mass balance due to the presence of cells and by advection–diffusion in the lumen and porous membrane. Analytical solution of the coupled system is presented for a short time scale where the cell growth, death, or differentiation is neglected. The results obtained focus on the effect of various parameters on the fluid flow, solid deformation, and consumption of nutrients due to different kinds of cells. It is observed that the deformation of the scaffold matrix increases monotonically with the flow rate supplied to the bioreactor. This behavior ensures that one can adjust the fluid flux to achieve optimum deformation in favor of cell growth and avoid damage of the scaffold. Moreover, a general criterion for the distribution of adequate nutrient concentration inside the bioreactor is developed to prevent the formation of the necrosis region inside the scaffold. Accordingly, the current investigation helps to arrive at suitable parameter combinations to monitor and control an ongoing experiment for optimum cell growth.

Combining the Magnetic Equivalent Circuit and Maxwell–Fourier Method for Eddy-Current Loss Calculation

In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series) is developed. This model coupling has been applied to a U-cored static electromagnetic device. The main objective is to compute the magnetic field behavior in massive conductive parts (e.g., aluminum, magnets, copper, iron) considering the skin effect (i.e., with the eddy-current reaction field) and to predict the eddy-current losses. The magnetic field distribution for various models is validated with 2-D and three-dimensional (3-D) finite-element analysis (FEA). The study is also focused on the discretization influence of 2-D generic MEC on the eddy-current loss calculation in conductive regions. Experimental tests and 3-D FEA have been compared with the proposed approach on massive conductive parts in aluminum. For an operating point, the computation time is divided by ~4.6 with respect to 3-D FEA.

Impact Assessment of a Major River Basin in Bangladesh on Storm Surge Simulation

A two-dimensional bay and river coupled numerical model in Cartesian coordinates was developed to find the impact of the river on the simulated water levels associated with a storm along the coast of Bangladesh. The shallow water models developed for both the bay and river were discretized by the finite difference method with forward in time and central in space. The boundaries for the coast and islands were approximated through proper stair steps representation and solved by a conditionally stable semi-implicit manner on a staggered Arakawa C-grid. A one-way nested scheme technique was used in the bay model to include coastal complexities as well as to save computational costs. A stable tidal condition was made by forcing the sea levels with the most energetic tidal constituent, M2, along with the southern open boundary of the bay model omitting wind stress. The developed model was then applied to foresee the sea-surface elevation associated with the catastrophic cyclone of 1991 and cyclone MORA. A comparative study of the water levels associated with a storm was made through model simulations with and without the inclusion of the river system. We found that the surge height in the bay-river junction area decreased by 20% and the surge height reduced by about 3–8% outside the junction area from this study. The obtained results were found to have a satisfactory similarity with some of the observed data.

Upward and Downward Catastrophes of Coronal Magnetic Flux Ropes in Quadrupolar Magnetic Fields

Abstract Coronal magnetic flux ropes are closely related to large-scale solar activities. Using a 2.5-dimensional time-dependent ideal magnetohydrodynamic model in Cartesian coordinates, we carry out numerical simulations to investigate the evolution of a magnetic system consisting of a flux rope embedded in a fully closed quadrupolar magnetic field with different photospheric flux distributions. It is found that when the photospheric flux is not concentrated too much toward the polarity inversion line and the constraint exerted by the background field is not too weak, the equilibrium states of the system are divided into two branches: the rope sticks to the photosphere for the lower branch and levitates in the corona for the upper branch. These two branches are connected by an upward catastrophe (from the lower branch to the upper) and a downward catastrophe (from the upper branch to the lower). Our simulations reveal that there exist both upward and downward catastrophes in quadrupolar fields, which may be either force-free or non-force-free. The existence and the properties of these two catastrophes are influenced by the photospheric flux distribution, and a downward catastrophe is always paired with an upward catastrophe. Comparing the decay indices in catastrophic and noncatastrophic cases, we infer that torus unstable may be a necessary but not sufficient condition for a catastrophic system.

Influence of Photospheric Magnetic Conditions on the Catastrophic Behaviors of Flux Ropes in Solar Active Regions

Since only the magnetic conditions at the photosphere can be routinely observed in current observations, it is of great significance to find out the influences of photospheric magnetic conditions on solar eruptive activities. Previous studies about catastrophe indicated that the magnetic system consisting of a flux rope in a partially open bipolar field is subject to catastrophe, but not if the bipolar field is completely closed under the same specified photospheric conditions. In order to investigate the influence of the photospheric magnetic conditions on the catastrophic behavior of this system, we expand upon the 2.5 dimensional ideal magnetohydrodynamic (MHD) model in Cartesian coordinates to simulate the evolution of the equilibrium states of the system under different photospheric flux distributions. Our simulation results reveal that a catastrophe occurs only when the photospheric flux is not concentrated too much toward the polarity inversion line and the source regions of the bipolar field are not too weak; otherwise no catastrophe occurs. As a result, under certain photospheric conditions, a catastrophe could take place in a completely closed configuration whereas it ceases to exist in a partially open configuration. This indicates that whether the background field is completely closed or partially open is not the only necessary condition for the existence of catastrophe, and that the photospheric conditions also play a crucial role in the catastrophic behavior of the flux rope system.

Lamb wave band gaps in one-dimensional radial phononic crystal slabs

In this paper, we theoretically investigate the band structures of Lamb wave in one-dimensional radial phononic crystal (PC) slabs composed of a series of alternating strips of epoxy and aluminum. The dispersion relations, the power transmission spectra and the displacement fields of the eigenmodes are calculated by using the finite element method based on two-dimensional axial symmetry models in cylindrical coordinates. The axial symmetry model is validated by three-dimensional finite element model in Cartesian coordinates. Numerical results show that the proposed radial PC slabs can yield several complete band gaps with a variable bandwidth exist for elastic waves. Furthermore, the effects of the filling fraction and the slab thickness on the band gaps are further explored numerically. It is worth observing that, with the increase of the filling fraction, both the lower and upper edges of the band gaps are simultaneously shifted to higher frequency, which results from the enhancement interaction between the rigid resonance of the scatterer and the matrix. The slab thickness is the key parameter for the existence and the width of complete band gaps in the radial PC slabs. These properties of Lamb waves in the radial PC plates can potentially be applied to optimize band gaps, generate filters and design acoustic devices in the rotary machines and structures.

Une formulation hybride du modèle de coque de Naghdi

We present a new version of the Naghdi model for shells with curvature discontinuities. The unknowns – the displacement and the rotation of the normal to the shell midsurface – are described respectively in Cartesian and local covariant or contravariant basis. Our purpose here is to consider a constraint-free formulation instead of the one introduced by Blouza et al. (Two finite element approximation of Naghdiʼs shell model in Cartesian coordinates, SIAM J. Numer. Anal. 44 (2) (2006) 636–654), where the tangency character of the rotation is enforced by penalization or by duality. This new version enables us, in particular, to approximate by conforming finite elements the solution with less degrees of freedom compared to the method of Blouza et al.

Tracking Control of Nonholonomic Wheeled Mobile Robot Based on New Sliding Surface with Approach Angle

This paper propose a method for designing the tracking control of nonholonomic wheeled mobile robots based on a new sliding surface with an approach angle. In order to remove the singular point problem at the origin, we consider the kinematic model in Cartesian coordinates. Also, we design a new sliding surface with an approach angle to solve the sliding surface constraints problem. Therefore, with the proposed controller, we derive the control input for arbitrary trajectories. We prove that the position tracking error converges to zero by using the Lyapunov stability theory. Finally, through computer simulations, we demonstrate the effectiveness of the proposed control system.

Research of Target Motion Model in Polar Coordinates Based on Dynamic Systems

Abstract:Aiming at the nonlinear observation problem of target motion model in Cartesian coordinates, a novel target motion model in polar coordinates is proposed based on dynamic systems with analysis of scientific data materials. This paper has done about the target motion model in polar coordinates corresponding to CV model and CA respectively and simulated with Monte Carlo. The experimental results indicate that the target motion model is all agreed with targets motion in fact and can be used to describe the targets motion. Simulations show that state estimation of the KF based on the target motion mode with analysis of dynamic systems is efficient.

Improvements in anisotropic models of single tree effects in Cartesian coordinates

For anisotropic density functions of e.g. fruit or leaf dispersal, most mathematical research is only done in polar coordinates. However, in software solutions aiming to derive inverse models for real world dispersal data, Cartesian coordinates may be preferred for several reasons. Thus, we introduce an anisotropic model in Cartesian coordinates following the approach in Wälder et al. (2009) with the von Mises approach. By introducing a correction factor, we thereby consider the fundamental attribute, that the integral over a density function with respect to the Cartesian coordinates has to be equal 1. It may have been overlooked so far that guaranteeing for this attribute needs different approaches whether working in polar or Cartesian coordinates. One result is that our approach can be used also for other anisotropic models rather than models from the von Mises approach.

Propagation of Cartesian beams in nonlocal nonlinear media

We introduce a very general self-trapped beam solution of the Snyder-Mitchell linear model in Cartesian coordinates. We name such a field a self-trapped Cartesian beam (CB) which is characterized by two parameters. The complex amplitude of the self-trapped CBs is described by the product of the parabolic cylinder functions and the Gaussian function. The self-trapped standard, elegant, and generalized Hermite-Gaussian beams can be obtained by treating them as the special cases of the self-trapped CBs.

Chromospheric magnetic reconnection caused by photospheric flux emergence: implications for jet-like events formation

Magnetic reconnection in the low atmosphere, e.g. chromosphere, is investigated in various physical environments. Its implications for the origination of explosive events (small--scale jets) are discussed. A 2.5-dimensional resistive magnetohydrodynamic (MHD) model in Cartesian coordinates is used. It is found that the temperature and velocity of the outflow jets as a result of magnetic reconnection are strongly dependent on the physical environments, e.g. the magnitude of the magnetic field strength and the plasma density. If the magnetic field strength is weak and the density is high, the temperature of the jets is very low (~10,000 K) as well as its velocity (~40 km/s). However, if environments with stronger magnetic field strength (20 G) and smaller density (electron density Ne=2x10^{10} cm^{-3}) are considered, the outflow jets reach higher temperatures of up to 600,000 K and a line-of-sight velocity of up to 130 km/s which is comparable with the observational values of jet-like events.