Search results for: elliptic PDEs

Authors: G. De Matteis, L. Martina, V. Turco

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The work is focused on determining and comparing special nonlinear static configurations in cholesteric liquid crystals (CLCs), confined between two parallel plates and in the presence of an external static electric/magnetic field. The solutions are stabilised by topological and non-topological conservation laws since they are described in terms of integrable or partially integrable nonlinear boundary value problems. In cholesteric liquid crystals which are subject to geometric frustration; anchoring conditions at boundaries, i.e., homeotropic conditions, are incompatible with the cholesteric twist. This aspect turns out to be essential in the admissible classes of solutions, allowing also for disclination type singularities. Within the framework of Frank-Oseen theory, we study the static configurations for CLCs. First, we find numerical solutions for isolated axisymmetric states in confined CLCs with weak homeotropic anchoring at the boundaries. These solutions describe 3-dimensional modulations, namely spherulites or cholesteric bubbles, actually observed in these systems, of standard baby skyrmions. Relations with well-known nonlinear integrable systems are found and are used to explore the asymptotic behavior of the solutions. Then we turn our attention to extended periodic static configurations called Helicoids or cholesteric fingers, described by an elliptic sine-Gordon model with appropriate boundary conditions, showing how their period and energies are determined by both the thickness of the cell and the intensity of the external electric/magnetic field. We explicitly show that helicoids with π or 2π of rotations of the molecular director are different in many aspects and are not simply algebraically related. The behaviour of the solutions, their energy and the properties of the associated disclinations are discussed in detail, both analytically and numerically.

Keywords: cholesteric liquid crystals, geometric frustration, helicoids, skyrmions

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Authors: Foad Hassaninejadafarahani, Scott Ormiston

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Reflux condensation occurs in a vertical channels and tubes when there is an upward core flow of vapor (or gas-vapor mixture) and a downward flow of the liquid film. The understanding of this condensation configuration is crucial in the design of reflux condensers, distillation columns, and in loss-of-coolant safety analyses in nuclear power plant steam generators. The unique feature of this flow is the upward flow of the vapor-gas mixture (or pure vapor) that retards the liquid flow via shear at the liquid-mixture interface. The present model solves the full, elliptic governing equations in both the film and the gas-vapor core flow. The computational mesh is non-orthogonal and adapts dynamically the phase interface, thus produces sharp and accurate interface. Shear forces and heat and mass transfer at the interface are accounted for fundamentally. This modeling is a big step ahead of current capabilities by removing the limitations of previous reflux condensation models which inherently cannot account for the detailed local balances of shear, mass, and heat transfer at the interface. Discretisation has been done based on a finite volume method and a co-located variable storage scheme. An in-house computer code was developed to implement the numerical solution scheme. Detailed results are presented for laminar reflux condensation from steam-air mixtures flowing in vertical parallel plate channels. The results include velocity and pressure profiles, as well as axial variations of film thickness, Nusselt number and interface gas mass fraction.

Keywords: Reflux, Condensation, CFD-Two Phase, Nusselt number

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Authors: N. Alias, W. Z. W. Muhammad, M. N. M. Ibrahim, M. Mohamed, H. F. S. Saipol, U. N. Z. Ariffin, N. A. Zakaria, M. S. Z. Suardi

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This paper presents the performance comparison of some computation software for solving the boundary element method (BEM). BEM formulation is the numerical technique and high potential for solving the advance mathematical modeling to predict the production of oil well in arbitrarily shaped based on multiple leases reservoir. The limitation of data validation for ensuring that a program meets the accuracy of the mathematical modeling is considered as the research motivation of this paper. Thus, based on this limitation, there are three steps involved to validate the accuracy of the oil production simulation process. In the first step, identify the mathematical modeling based on partial differential equation (PDE) with Poisson-elliptic type to perform the BEM discretization. In the second step, implement the simulation of the 2D BEM discretization using COMSOL Multiphysic and MATLAB programming languages. In the last step, analyze the numerical performance indicators for both programming languages by using the validation of Fortran programming. The performance comparisons of numerical analysis are investigated in terms of percentage error, comparison graph and 2D visualization of pressure on oil production of multiple leases reservoir. According to the performance comparison, the structured programming in Fortran programming is the alternative software for implementing the accurate numerical simulation of BEM. As a conclusion, high-level language for numerical computation and numerical performance evaluation are satisfied to prove that Fortran is well suited for capturing the visualization of the production of oil well in arbitrarily shaped.

Keywords: performance comparison, 2D visualization, COMSOL multiphysic, MATLAB, Fortran, modelling and simulation, boundary element method, reservoir pressure

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Authors: David Alejandro Lazo-Vasquez, Jorge Luis Balino

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In the petroleum industry, multiphase flow occurs when oil, gas, and water are transported in the same pipe through large pipeline systems. The flow can take different patterns depending on parameters like fluid velocities, pipe diameter, pipe inclination, and fluid properties. Mainly, intermittent flow is produced by the natural propagation of short and long waves, according to the Kelvin-Helmholtz Stability Theory. To model stratified flow and the onset of intermittent flow, it is crucial to have knowledge of short and long waves behavior. The two-fluid model, frequently employed for characterizing multiphase systems, becomes ill-posed for high liquid and gas velocities and large inclination angles, for short waves can develop infinite growth rates. We are interested in focusing attention on long-wave instability, which leads to the production of roll waves that may grow and result in the transition from stratified flow to intermittent flow. In this study, global and local linear stability analyses for dynamic and kinematic stability criteria predict the regions of stability of the flow for different pipe inclinations and fluid velocities in regularized and non-regularized systems, concurrently. It was possible to distinguish when: wave growth rates are absolutely bounded (stable stratified smooth flow), waves have finite growth rates (unstable stratified wavy flow), and when the equation system becomes elliptic and hyperbolization is needed. In order to bound short wave growth rates and regularize the equation system, we incorporated some lower and higher-order terms like interfacial drag and surface tension, respectively.

Keywords: linear stability analysis, multiphase flow, onset of slugging, two-fluid model regularization

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Authors: Davide Gotti, Milan Prodanovic, Sergio Pinilla, David Muñoz-Torrero

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Since its proposal, the Doyle-Fuller-Newman (DFN) lithium-ion battery model has gained popularity in the electrochemical field. In fact, this model provides the user with theoretical support for designing the lithium-ion battery parameters, such as the material particle or the diffusion coefficient adjustment direction. However, the model is mathematically complex as it is composed of several partial differential equations (PDEs) such as Fick’s law of diffusion, the MacInnes and Ohm’s equations, among other phenomena. Thus, to efficiently use the model in a time-domain simulation environment, the selection of the discretization technique is of a pivotal importance. There are several numerical methods available in the literature that can be used to carry out this task. In this study, a comparison between the explicit Euler, Crank-Nicolson, and Chebyshev discretization methods is proposed. These three methods are compared in terms of accuracy, stability, and computational times. Firstly, the explicit Euler discretization technique is analyzed. This method is straightforward to implement and is computationally fast. In this work, the accuracy of the method and its stability properties are shown for the electrolyte diffusion partial differential equation. Subsequently, the Crank-Nicolson method is considered. It represents a combination of the implicit and explicit Euler methods that has the advantage of being of the second order in time and is intrinsically stable, thus overcoming the disadvantages of the simpler Euler explicit method. As shown in the full paper, the Crank-Nicolson method provides accurate results when applied to the DFN model. Its stability does not depend on the integration time step, thus it is feasible for both short- and long-term tests. This last remark is particularly important as this discretization technique would allow the user to implement parameter estimation and optimization techniques such as system or genetic parameter identification methods using this model. Finally, the Chebyshev discretization technique is implemented in the DFN model. This discretization method features swift convergence properties and, as other spectral methods used to solve differential equations, achieves the same accuracy with a smaller number of discretization nodes. However, as shown in the literature, these methods are not suitable for handling sharp gradients, which are common during the first instants of the charge and discharge phases of the battery. The numerical results obtained and presented in this study aim to provide the guidelines on how to select the adequate discretization technique for the DFN model according to the type of application to be performed, highlighting the pros and cons of the three methods. Specifically, the non-eligibility of the simple Euler method for longterm tests will be presented. Afterwards, the Crank-Nicolson and the Chebyshev discretization methods will be compared in terms of accuracy and computational times under a wide range of battery operating scenarios. These include both long-term simulations for aging tests, and short- and mid-term battery charge/discharge cycles, typically relevant in battery applications like grid primary frequency and inertia control and electrical vehicle breaking and acceleration.

Keywords: Doyle-Fuller-Newman battery model, partial differential equations, discretization, numerical methods

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Authors: Donghyun Lee, Cam Nguyen

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Multi-band systems offer a great deal of benefit in modern communication and radar systems. In particular, multi-band antenna-array radar systems with their extended frequency diversity provide numerous advantages in detection, identification, locating and tracking a wide range of targets, including enhanced detection coverage, accurate target location, reduced survey time and cost, increased resolution, improved reliability and target information. An accurate calibration is a critical issue in antenna array systems. The amplitude and phase errors in multi-band and multi-polarization antenna array transceivers result in inaccurate target detection, deteriorated resolution and reduced reliability. Furthermore, the digital beam former without the RF domain phase-shifting is less immune to unfiltered interference signals, which can lead to receiver saturation in array systems. Therefore, implementing integrated front-end architecture, which can support calibration function with low insertion and filtering function from the farthest end of an array transceiver is of great interest. We report a dual K/Ka-band T/R/Calibration switch module with quasi-elliptic dual-bandpass filtering function implementing a Q-enhanced metamaterial transmission line. A unique dual-band frequency response is incorporated in the reception and calibration path of the proposed switch module utilizing the composite right/left-handed meta material transmission line coupled with a Colpitts-style negative generation circuit. The fabricated fully integrated T/R/Calibration switch module in 0.18-μm BiCMOS technology exhibits insertion loss of 4.9-12.3 dB and isolation of more than 45 dB in the reception, transmission and calibration mode of operation. In the reception and calibration mode, the dual-band frequency response centered at 24.5 and 35 GHz exhibits out-of-band rejection of more than 30 dB compared to the pass bands below 10.5 GHz and above 59.5 GHz. The rejection between the pass bands reaches more than 50 dB. In all modes of operation, the IP1-dB is between 4 and 11 dBm. Acknowledgement: This paper was made possible by NPRP grant # 6-241-2-102 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

Keywords: microwaves, millimeter waves, T/R switch, wireless communications, wireless communications

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Authors: O. B. Iskender, K. V. Ling, V. Dubanchet, L. Simonini

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This paper discusses the recent advances and future prospects of spacecraft position and attitude control using Model Predictive Control (MPC). First, the challenges of the space missions are summarized, in particular, taking into account the errors, uncertainties, and constraints imposed by the mission, spacecraft and, onboard processing capabilities. The summary of space mission errors and uncertainties provided in categories; initial condition errors, unmodeled disturbances, sensor, and actuator errors. These previous constraints are classified into two categories: physical and geometric constraints. Last, real-time implementation capability is discussed regarding the required computation time and the impact of sensor and actuator errors based on the Hardware-In-The-Loop (HIL) experiments. The rationales behind the scenarios’ are also presented in the scope of space applications as formation flying, attitude control, rendezvous and docking, rover steering, and precision landing. The objectives of these missions are explained, and the generic constrained MPC problem formulations are summarized. Three key design elements used in MPC design: the prediction model, the constraints formulation and the objective cost function are discussed. The prediction models can be linear time invariant or time varying depending on the geometry of the orbit, whether it is circular or elliptic. The constraints can be given as linear inequalities for input or output constraints, which can be written in the same form. Moreover, the recent convexification techniques for the non-convex geometrical constraints (i.e., plume impingement, Field-of-View (FOV)) are presented in detail. Next, different objectives are provided in a mathematical framework and explained accordingly. Thirdly, because MPC implementation relies on finding in real-time the solution to constrained optimization problems, computational aspects are also examined. In particular, high-speed implementation capabilities and HIL challenges are presented towards representative space avionics. This covers an analysis of future space processors as well as the requirements of sensors and actuators on the HIL experiments outputs. The HIL tests are investigated for kinematic and dynamic tests where robotic arms and floating robots are used respectively. Eventually, the proposed algorithms and experimental setups are introduced and compared with the authors' previous work and future plans. The paper concludes with a conjecture that MPC paradigm is a promising framework at the crossroads of space applications while could be further advanced based on the challenges mentioned throughout the paper and the unaddressed gap.

Keywords: convex optimization, model predictive control, rendezvous and docking, spacecraft autonomy

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Authors: S.I.Mukhin, S. Seidov, A. Mukherjee

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The Dicke model is a key tool for the description of correlated states of quantum atomic systems, excited by resonant photon absorption and subsequently emitting spontaneous coherent radiation in the superradiant state. The Dicke Hamiltonian (DH) is successfully used for the description of the dynamics of the Josephson Junction (JJ) array in a resonant cavity under applied current. In this work, we have investigated a generalized model, which is described by DH with a frustrating interaction term. This frustrating interaction term is explicitly the infinite coordinated interaction between all the spin half in the system. In this work, we consider an array of N superconducting islands, each divided into two sub-islands by a Josephson Junction, taken in a charged qubit / Cooper Pair Box (CPB) condition. The array is placed inside the resonant cavity. One important aspect of the problem lies in the dynamical nature of the physical observables involved in the system, such as condensed electric field and dipole moment. It is important to understand how these quantities behave with time to define the quantum phase of the system. The Dicke model without frustrating term is solved to find the dynamical solutions of the physical observables in analytic form. We have used Heisenberg’s dynamical equations for the operators and on applying newly developed Rotating Holstein Primakoff (HP) transformation and DH we have arrived at the four coupled nonlinear dynamical differential equations for the momentum and spin component operators. It is possible to solve the system analytically using two-time scales. The analytical solutions are expressed in terms of Jacobi's elliptic functions for the metastable ‘bound luminosity’ dynamic state with the periodic coherent beating of the dipoles that connect the two double degenerate dipolar ordered phases discovered previously. In this work, we have proceeded the analysis with the extended DH with a frustrating interaction term. Inclusion of the frustrating term involves complexity in the system of differential equations and it gets difficult to solve analytically. We have solved semi-classical dynamic equations using the perturbation technique for small values of Josephson energy EJ. Because the Hamiltonian contains parity symmetry, thus phase transition can be found if this symmetry is broken. Introducing spontaneous symmetry breaking term in the DH, we have derived the solutions which show the occurrence of finite condensate, showing quantum phase transition. Our obtained result matches with the existing results in this scientific field.

Keywords: Dicke Model, nonlinear dynamics, perturbation theory, superconductivity

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Authors: Dinara F. Gaynutdinova, Vladimir Ya Modorsky, Nikolay A. Shevelev

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The problem under research is that of unpredictable modes occurring in two-stage centrifugal hydraulic pump as a result of hydraulic processes caused by vibrations of structural components. Numerical, analytical and experimental approaches are considered. A hypothesis was developed that the problem of unpredictable pressure decrease at the second stage of centrifugal pumps is caused by cavitation effects occurring upon vibration. The problem has been studied experimentally and theoretically as of today. The theoretical study was conducted numerically and analytically. Hydroelastic processes in dynamic “liquid – deformed structure” system were numerically modelled and analysed. Using ANSYS CFX program engineering analysis complex and computing capacity of a supercomputer the cavitation parameters were established to depend on vibration parameters. An influence domain of amplitudes and vibration frequencies on concentration of cavitation bubbles was formulated. The obtained numerical solution was verified using CFM program package developed in PNRPU. The package is based on a differential equation system in hyperbolic and elliptic partial derivatives. The system is solved by using one of finite-difference method options – the particle-in-cell method. The method defines the problem solution algorithm. The obtained numerical solution was verified analytically by model problem calculations with the use of known analytical solutions of in-pipe piston movement and cantilever rod end face impact. An infrastructure consisting of an experimental fast hydro-dynamic processes research installation and a supercomputer connected by a high-speed network, was created to verify the obtained numerical solutions. Physical experiments included measurement, record, processing and analysis of data for fast processes research by using National Instrument signals measurement system and Lab View software. The model chamber end face oscillated during physical experiments and, thus, loaded the hydraulic volume. The loading frequency varied from 0 to 5 kHz. The length of the operating chamber varied from 0.4 to 1.0 m. Additional loads weighed from 2 to 10 kg. The liquid column varied from 0.4 to 1 m high. Liquid pressure history was registered. The experiment showed dependence of forced system oscillation amplitude on loading frequency at various values: operating chamber geometrical dimensions, liquid column height and structure weight. Maximum pressure oscillation (in the basic variant) amplitudes were discovered at loading frequencies of approximately 1,5 kHz. These results match the analytical and numerical solutions in ANSYS and CFM.

Keywords: computing experiment, hydroelasticity, physical experiment, vibration

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Authors: Yashas Bedre Raghavendra, Pim Vullers

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This study presents the design and implementation of an abstract cryptographic coprocessor, leveraging AMBA(Advanced Microcontroller Bus Architecture) protocols - APB (Advanced Peripheral Bus) and AHB (Advanced High-performance Bus), to enable seamless integration with the main CPU(Central processing unit) and enhance the coprocessor’s algorithm flexibility. The primary objective is to create a versatile coprocessor that can execute various cryptographic algorithms, including ECC(Elliptic-curve cryptography), RSA(Rivest–Shamir–Adleman), and AES (Advanced Encryption Standard) while providing a robust and secure solution for modern secure embedded systems. To achieve this goal, the coprocessor is equipped with a tightly coupled memory (TCM) for rapid data access during cryptographic operations. The TCM is placed within the coprocessor, ensuring quick retrieval of critical data and optimizing overall performance. Additionally, the program memory is positioned outside the coprocessor, allowing for easy updates and reconfiguration, which enhances adaptability to future algorithm implementations. Direct links are employed instead of DMA(Direct memory access) for data transfer, ensuring faster communication and reducing complexity. The AMBA-based communication architecture facilitates seamless interaction between the coprocessor and the main CPU, streamlining data flow and ensuring efficient utilization of system resources. The abstract nature of the coprocessor allows for easy integration of new cryptographic algorithms in the future. As the security landscape continues to evolve, the coprocessor can adapt and incorporate emerging algorithms, making it a future-proof solution for cryptographic processing. Furthermore, this study explores the addition of custom instructions into RISC-V ISE (Instruction Set Extension) to enhance cryptographic operations. By incorporating custom instructions specifically tailored for cryptographic algorithms, the coprocessor achieves higher efficiency and reduced cycles per instruction (CPI) compared to traditional instruction sets. The adoption of RISC-V 128-bit architecture significantly reduces the total number of instructions required for complex cryptographic tasks, leading to faster execution times and improved overall performance. Comparisons are made with 32-bit and 64-bit architectures, highlighting the advantages of the 128-bit architecture in terms of reduced instruction count and CPI. In conclusion, the abstract cryptographic coprocessor presented in this study offers significant advantages in terms of algorithm flexibility, security, and integration with the main CPU. By leveraging AMBA protocols and employing direct links for data transfer, the coprocessor achieves high-performance cryptographic operations without compromising system efficiency. With its TCM and external program memory, the coprocessor is capable of securely executing a wide range of cryptographic algorithms. This versatility and adaptability, coupled with the benefits of custom instructions and the 128-bit architecture, make it an invaluable asset for secure embedded systems, meeting the demands of modern cryptographic applications.

Keywords: abstract cryptographic coprocessor, AMBA protocols, ECC, RSA, AES, tightly coupled memory, secure embedded systems, RISC-V ISE, custom instructions, instruction count, cycles per instruction

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Authors: Mingqian Zhang

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Tip-enhanced Raman spectroscopy (TERS) is a scanning probe technique for individual objects and structured surfaces investigation that provides a wealth of enhanced spectral information with nanoscale spatial resolution and high detection sensitivity. It has become a powerful and promising chemical and physical information detection method in the nanometer scale. The TERS technique uses a sharp metallic tip regulated in the near-field of a sample surface, which is illuminated with a certain incident beam meeting the excitation conditions of the wave-vector matching. The local electric field, and, consequently, the Raman scattering, from the sample in the vicinity of the tip apex are both greatly tip-enhanced owning to the excitation of localized surface plasmons and the lightning-rod effect. Typically, a TERS setup is composed of a scanning probe microscope, excitation and collection optical configurations, and a Raman spectroscope. In the illumination configuration, an objective lens or a parabolic mirror is always used as the most important component, in order to focus the incident beam on the tip apex for excitation. In this research, a novel TERS setup was built up by introducing a plasmonic lens to the excitation optics as a focusing device. A plasmonic lens with symmetry breaking semi-annular slits corrugated on gold film was designed for the purpose of generating concentrated sub-wavelength light spots with strong longitudinal electric field. Compared to conventional far-field optical components, the designed plasmonic lens not only focuses an incident beam to a sub-wavelength light spot, but also realizes a strong z-component that dominants the electric field illumination, which is ideal for the excitation of tip-enhancement. Therefore, using a PL in the illumination configuration of TERS contributes to improve the detection sensitivity by both reducing the far-field background and effectively exciting the localized electric field enhancement. The FDTD method was employed to investigate the optical near-field distribution resulting from the light-nanostructure interaction. And the optical field distribution was characterized using an scattering-type scanning near-field optical microscope to demonstrate the focusing performance of the lens. The experimental result is in agreement with the theoretically calculated one. It verifies the focusing performance of the plasmonic lens. The optical field distribution shows a bright elliptic spot in the lens center and several arc-like side-lobes on both sides. After the focusing performance was experimentally verified, the designed plasmonic lens was used as a focusing component in the excitation configuration of TERS setup to concentrate incident energy and generate a longitudinal optical field. A collimated linearly polarized laser beam, with along x-axis polarization, was incident from the bottom glass side on the plasmonic lens. The incident light focused by the plasmonic lens interacted with the silver-coated tip apex and enhanced the Raman signal of the sample locally. The scattered Raman signal was gathered by a parabolic mirror and detected with a Raman spectroscopy. Then, the plasmonic lens based setup was employed to investigate carbon nanotubes and TERS experiment was performed. Experimental results indicate that the Raman signal is considerably enhanced which proves that the novel TERS configuration is feasible and promising.

Keywords: longitudinal electric field, plasmonics, raman spectroscopy, tip-enhancement

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