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Journal articles on the topic 'Hydrodynamic formulation'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Smith, Arlynn W., and Kevin F. Brennan. "Comparison of Non-Parabolic Hydrodynamic Models Based On Different Band Structure Models." VLSI Design 6, no. 1-4 (January 1, 1998): 177–80. http://dx.doi.org/10.1155/1998/71521.

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This paper presents two non-parabolic hydrodynamic model formulations suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship, (ℏk)2/2m = W(1+αW). The second formulation makes use of a power law, (ℏk)2/2m = xWy, for the dispersion relation. The non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation is limited. The power law formulation produces closed form coefficients similar to those under the parabolic band approximation but the carrier concentration can deviate. An extended power law dispersion relation is proposed to account for band structure effects, (ℏk)2/2m = xW1+yW. This dispersion relation closely matches the calculated band structure over a wide energy range and may lead to closed form coefficients for the hydrodynamic model.

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2

Avital, E. J., M. Alonso, and V. Supontisky. "Computational aeroacoustics: The low speed jet." Aeronautical Journal 112, no. 1133 (July 2008): 405–14. http://dx.doi.org/10.1017/s0001924000002360.

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AbstractLow speed circular, elliptic and planar jets are investigated computationally for basic sound generation and hydrodynamics. The jets are assumed to be incompressible and are simulated using the large eddy simulation (LES) approach. The emitted sound is calculated using Lighthill’s acoustic analogy. Two formulations are used, Lighthill’s stress tensor formulation and Powell’s vortex sound formulation. A new boundary correction for Powell’s formulation is developed in order to account for the finite size of the computational domain. Low to moderate Reynolds number jets are simulated. Good agreement with known hydrodynamic results is achieved. This includes the nature of the transition process, e.g. enhanced mixing and axis switching in the elliptic jet and in some statistical results. The new boundary correction for Powell’s formulation proves to be vital in order to achieve good agreement with Lighthill’s formulation. Some success in high frequency prediction at least for the circular and elliptic jets is achieved in terms of getting the expected asymptotic behaviour. Both formulations show that the elliptic jet noise level is mildly lower than the circular jet noise level. Good to very good agreement is achieved in terms of directivities and frequency spectra with known results for the various jets.

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3

Sorek, Shaul, and Vyacheslav Borisov. "Modified Eulerian–Lagrangian formulation for hydrodynamic modeling." Journal of Computational Physics 231, no. 8 (April 2012): 3083–100. http://dx.doi.org/10.1016/j.jcp.2011.12.005.

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4

Isaacson, Michael. "Earthquake-induced hydrodynamic forces on reservoir roofs." Canadian Journal of Civil Engineering 37, no. 8 (August 2010): 1107–15. http://dx.doi.org/10.1139/l10-049.

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The present paper describes the hydrodynamic loads on the roof of a water-filled reservoir or storage tank due to earthquake-induced sloshing. Initially, the paper summarizes available solutions for the water surface elevation in a rectangular reservoir subjected to harmonic and earthquake base motions, and as well an available formulation for the force on the roof of a rectangular reservoir. With this background, a new formulation for the force on the roof is developed, and selected results based on this are presented. A recommended design procedure is thereby proposed, and an example application is provided. The potential extension of the proposed formulation to other reservoir configurations is discussed. Although a validation of the proposed formulation based on laboratory test results is needed, it is suggested that in the interim the proposed formulation is adopted for design.

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5

Wang, Lian-Ping, Orlando Ayala, Scott E. Kasprzak, and Wojciech W. Grabowski. "Theoretical Formulation of Collision Rate and Collision Efficiency of Hydrodynamically Interacting Cloud Droplets in Turbulent Atmosphere." Journal of the Atmospheric Sciences 62, no. 7 (July 1, 2005): 2433–50. http://dx.doi.org/10.1175/jas3492.1.

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Abstract A methodology for conducting direct numerical simulations (DNSs) of hydrodynamically interacting droplets in the context of cloud microphysics has been developed and used to validate a new kinematic formulation capable of describing the collision rate and collision efficiency of cloud droplets in turbulent air. The theoretical formulation is formally the same as the formulation recently developed for geometrical collision rate of finite-inertia, nonsettling particles. It is shown that its application to hydrodynamically interacting droplets requires corrections because of a nonoverlap requirement. An approximate method for correcting the kinematic properties has been developed and validated against DNS data. The formulation presented here is more general and accurate than previously published formulations that, in most cases, are some extension to the description of hydrodynamic–gravitational collision. General dynamic and kinematic representations of the properly defined collision efficiency in a turbulent flow have been discussed. In addition to augmenting the geometric collision rate, air turbulence has been found to enhance the collision efficiency because, in a turbulent flow, hydrodynamic interactions become less effective in reducing the average relative radial velocity. The level of increase in the collision efficiency depends on the flow dissipation rate. For example, the collision efficiency between droplets of 20 and 25 μm in radii is increased by 59% and 10% by air turbulence at dissipation rates of 400 and 100 cm2 s−3, respectively. It is also shown that hydrodynamic interactions lead to higher droplet concentration fluctuations. The formulation presented here separates the effect of turbulence on collision efficiency from the previously observed effect of turbulence on the geometric collision rate.

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6

Kerr, Daniel C., Neil Goldsman, and Isaak D. Mayergoyz. "Three-Dimensional Hydrodynamic Modeling of MOSFET Devices." VLSI Design 6, no. 1-4 (January 1, 1998): 261–65. http://dx.doi.org/10.1155/1998/60859.

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The hydrodynamic (HD) model of semiconductor devices is solved numerically in three-dimensions (3-D) for the MOSFET device. The numerical instabilities of the HD model are analyzed to develop a stable discretization. The formulation is stabilized by using a new, higher-order discretization for the relaxation-time approximation (RTA) term of the energy-balance (EB) equation. The developed formulation is used to model the MOSFET.

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7

Burghardt, I., and L. S. Cederbaum. "Hydrodynamic equations for mixed quantum states. I. General formulation." Journal of Chemical Physics 115, no. 22 (2001): 10303. http://dx.doi.org/10.1063/1.1416493.

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8

Yang, Ciann-Dong. "A new hydrodynamic formulation of complex-valued quantum mechanics." Chaos, Solitons & Fractals 42, no. 1 (October 2009): 453–68. http://dx.doi.org/10.1016/j.chaos.2009.01.010.

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9

Lee, M., and Y. J. Cho. "On the migration of smooth particle hydrodynamic formulation in Cartesian coordinates to the axisymmetric formulation." Journal of Strain Analysis for Engineering Design 46, no. 8 (August 15, 2011): 879–86. http://dx.doi.org/10.1177/0309324711409656.

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The smooth particle hydrodynamic (SPH) method has been extended for application to large deformation problems such as high velocity impacts by including the effect of material strength. This paper presents a simple modification of the kernel function that allows the SPH formulation in Cartesian coordinates to be migrated into an axisymmetric formulation. The proposed procedure is first applied to analyse transient deformations of a cylindrical rod impacting a rigid wall (Taylor impact test). A good agreement with published experimental data for the deformed shape is obtained. A sensitivity study of the key parameters required in the SPH formulation is conducted to provide better insight into the SPH modelling approach. Impacts between two bodies at high speed have also been simulated using an axisymmetric SPH code.

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10

Intartaglia, Carmela, Leonardo Soria, and Maurizio Porfiri. "Hydrodynamic coupling of two sharp-edged beams vibrating in a viscous fluid." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2162 (February 8, 2014): 20130397. http://dx.doi.org/10.1098/rspa.2013.0397.

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In this paper, we study flexural vibrations of two thin beams that are coupled through an otherwise quiescent viscous fluid. While most of the research has focused on isolated beams immersed in placid fluids, inertial and viscous hydrodynamic coupling is ubiquitous across a multitude of engineering and natural systems comprising arrays of flexible structures. In these cases, the distributed hydrodynamic loading experienced by each oscillating structure is not only related to its absolute motion but is also influenced by its relative motion with respect to the neighbouring structures. Here, we focus on linear vibrations of two identical beams for low Knudsen, Keulegan–Carpenter and squeeze numbers. Thus, we describe the fluid flow using unsteady Stokes hydrodynamics and we propose a boundary integral formulation to compute pertinent hydrodynamic functions to study the fluid effect. We validate the proposed theoretical approach through experiments on centimetre-size compliant cantilevers that are subjected to underwater base-excitation. We consider different geometric arrangements, beam interdistances and excitation frequencies to ascertain the model accuracy in terms of the relevant non-dimensional parameters.

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11

Clift, Roland. "On the formulation of hydrodynamic stability criteria in fluidized beds." Powder Technology 72, no. 3 (November 1992): 199. http://dx.doi.org/10.1016/0032-5910(92)80037-w.

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12

Isayev, A. A., and S. V. Peletminsky. "On Hamiltonian formulation of hydrodynamic equations for superfluid 3He–A." Low Temperature Physics 23, no. 12 (December 1997): 955–61. http://dx.doi.org/10.1063/1.593503.

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13

Aluru, N. R., A. Raefsky, P. M. Pinsky, K. H. Law, R. J. G. Goossens, and R. W. Dutton. "A finite element formulation for the hydrodynamic semiconductor device equations." Computer Methods in Applied Mechanics and Engineering 107, no. 1-2 (August 1993): 269–98. http://dx.doi.org/10.1016/0045-7825(93)90180-6.

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14

SBRAGAGLIA, M., R. BENZI, L. BIFERALE, H. CHEN, X. SHAN, and S. SUCCI. "Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria." Journal of Fluid Mechanics 628 (June 1, 2009): 299–309. http://dx.doi.org/10.1017/s002211200900665x.

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Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria are placed within the framework of continuum kinetic theory. The mathematical treatment reveals that in order to be consistent with the correct thermo-hydrodynamical description, temperature must also be shifted, besides momentum. New perspectives for the formulation of thermo-hydrodynamic lattice kinetic models of non-ideal fluids are then envisaged. It is also shown that on the lattice, the definition of the macroscopic temperature requires the inclusion of new terms directly related to discrete effects. The theoretical treatment is tested against a controlled case with a non-ideal equation of state.

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15

Vorus, William S. "A Flat Cylinder Theory for Vessel Impact and Steady Planing Resistance." Journal of Ship Research 40, no. 02 (June 1, 1996): 89–106. http://dx.doi.org/10.5957/jsr.1996.40.2.89.

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This work has been motivated by the need for an alternative hydrodynamic theory to apply in analysis of impact loads on typical sections of vessels operating in waves, as well as for the closely analogous hydrodynamics of steady planing in calm water. A theory is needed which is computationally practical, but also physically sound, and incorporating the needed level of sensitivity to detail in the driving physical variables. A new theory believed to achieve this objective is proposed herewith. It can be viewed as a rational compromise between direct numerical inversion of the relatively exact governing equations, which is not presently possible to the needed level of generality, and the simple asymptotic theories evolved from the original work of Herbert Wagner (1932). The single solution field of the exact formulation is retained in the proposed theory; this is versus separate near and far fields of the asymptotic methods. The major reduction of the exact equations exercised here is the specification of uniform first-order geometric linearity; this is also an implicit characteristic of the Wagner class of asymptotic theories. All boundary conditions are satisfied on the horizontal axis in the limit of flatness. But the proposed theory retains the hydrodynamic nonlinearity of the exact formulation; the transverse flow perturbation is retained in the axis boundary conditions to consistent order. As contour flatness is approached and geometric linearity is more and more closely achieved, the transverse contour velocity becomes increasingly larger. The achievement of uniform geometric linearity in the flatness limit is therefore accompanied by uniform hydrodynamic nonlinearity. This is not recognized in the asymptotic theories, where the far field is linear both geometrically and hydrodynamically. The reduction of the exact formulation to an axis satisfaction of the boundary conditions allows much of the geometric inversion imbedded within the initial value problem to be performed analytically. Thus the outer numerical time integration of the system is in terms of stable algebraic formula, resulting in algorithms that are reliably computable on standard computing equipment. Discretization of the general theory for numerical analysis is proposed. The analysis procedure developed is applied to a number of cases of generalized flat cylinder impact. This is in the interest of demonstrating both its utility and its value in providing new insight into the very complex character of impact hydrodynamics.

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16

Sheng, Y. Peter, T. S. Wu, and P. F. Wang. "COASTAL AND ESTUARINE HYDRODYNAMIC MODELING IN CURVILINEAR GRIDS." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 197. http://dx.doi.org/10.9753/icce.v21.197.

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A time-dependent three-dimensional numerical model of coastal and estuarine circulation, which allows the use of generalized curvilinear grids to resolve the complex shoreline geometry and bathymetry, has been developed. Model formulation is briefly presented, followed by example model applications to such water bodies as Lake Okeechobee, James River and Chesapeake Bay.

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17

Liang, Wenchao, Daniel C. Kerr, Neil Goldsman, and Isaak D. Mayergoyz. "Hydrodynamic Device Simulation with New State Variables Specially Chosen for a Block Gummel Iterative Approach." VLSI Design 6, no. 1-4 (January 1, 1998): 191–95. http://dx.doi.org/10.1155/1998/32480.

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A new numerical formulation for solving the hydrodynamic model of semiconductor devices is presented. The method is based on using new variables to transform the conventional hydrodynamic equations into forms which facilitate numerical evaluation with a block Gummel approach. To demonstrate the new method, we apply it to model a 0.35 μm 2-D LDD MOSFET, where robust convergence properties are observed.

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18

Faria, Marco Tulio C., and Luis San Andre´s. "On the Numerical Modeling of High-Speed Hydrodynamic Gas Bearings." Journal of Tribology 122, no. 1 (March 8, 1999): 124–30. http://dx.doi.org/10.1115/1.555335.

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A numerical study of high-speed hydrodynamic gas bearing performance is presented using both finite element and finite difference methods. Efficient numerical procedures are developed to analyze diffusive-convective thin film gas flows in some simple geometries. A novel direct finite element formulation employing a new class of shape functions is specially devised to solve the Reynolds equation for compressible fluids. The formulation is as computationally efficient as the classical upwind finite element schemes without introducing artificial diffusion into the solution. Bearing load-capacity, static stiffness coefficients and frequency-dependent force coefficients are calculated for gas-lubricated plane and Rayleigh step slider bearings. [S0742-4787(00)01701-X]

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19

TROVATO, M., and L. REGGIANI. "A PROPER NONLOCAL FORMULATION OF QUANTUM MAXIMUM ENTROPY PRINCIPLE IN STATISTICAL MECHANICS." International Journal of Modern Physics B 26, no. 12 (May 8, 2012): 1241007. http://dx.doi.org/10.1142/s021797921241007x.

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By considering Wigner formalism, the quantum maximum entropy principle (QMEP) is here asserted as the fundamental principle of quantum statistical mechanics when it becomes necessary to treat systems in partially specified quantum states. From one hand, the main difficulty in QMEP is to define an appropriate quantum entropy that explicitly incorporates quantum statistics. From another hand, the availability of rigorous quantum hydrodynamic (QHD) models is a demanding issue for a variety of quantum systems. Relevant results of the present approach are: (i) The development of a generalized three-dimensional Wigner equation. (ii) The construction of extended quantum hydrodynamic models evaluated exactly to all orders of the reduced Planck constant ℏ. (iii) The definition of a generalized quantum entropy as global functional of the reduced density matrix. (iv) The formulation of a proper nonlocal QMEP obtained by determining an explicit functional form of the reduced density operator, which requires the consistent introduction of nonlocal quantum Lagrange multipliers. (v) The development of a quantum-closure procedure that includes nonlocal statistical effects in the corresponding quantum hydrodynamic system. (vi) The development of a closure condition for a set of relevant quantum regimes of Fermi and Bose gases both in thermodynamic equilibrium and nonequilibrium conditions.

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20

Dai, R. X., Q. Dong, and A. Z. Szeri. "Approximations in Hydrodynamic Lubrication." Journal of Tribology 114, no. 1 (January 1, 1992): 14–25. http://dx.doi.org/10.1115/1.2920853.

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In this numerical study of the approximations that led Reynolds to the formulation of classical Lubrication Theory, we compare results from (1) the full Navier-Stokes equations, (2) a lubrication theory relative to the “natural,” i.e., bipolar, coordinate system of the geometry that neglects fluid inertia, and (3) the classical Reynolds Lubrication Theory that neglects both fluid inertia and film curvature. By applying parametric continuation techniques, we then estimate the Reynolds number range of validity of the laminar flow assumption of classical theory. The study demonstrates that both the Navier-Stokes and the “bipolar lubrication” solutions converge monotonically to results from classical Lubrication Theory, one from below and the other from above. Furthermore the oil-film force is shown to be invariant with Reynolds number in the range 0 < R < Rc for conventional journal bearing geometry, where Rc is the critical value of the Reynolds number at first bifurcation. A similar conclusion also holds for the off-diagonal components of the bearing stiffness matrix, while the diagonal components are linear in the Reynolds number, in accordance with the small perturbation theory of DiPrima and Stuart.

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21

Pang, Hao, and Gracious Ngaile. "Formulation of SiO2/oil nanolubricant for metal forming using hydrodynamic cavitation." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 234, no. 12 (July 7, 2020): 1549–58. http://dx.doi.org/10.1177/0954405420933120.

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A novel hydrodynamic cavitation–based dispensing process was developed to disperse SiO2 nanoparticles into the base oil, and the effects of process parameters on dispersity and tribological properties of SiO2/oil nanolubricants were studied using the dynamic laser scattering and ring compression tests. With this process, nanolubricants with fine nanoparticles (139–1240 nm) were formulated. A mean particle size reduction of 78% was achieved in 60 min. This process can be scaled up for mass production with relative ease. The formulated SiO2/oil nanolubricants exhibited better tribological performance over that of base oil. Lubrication mechanisms of the SiO2/oil nanolubricant in metal forming were ascertained through analysis of the dispersity of nanolubricants and characterization of dents appearing on the surface of the deforming material. The study revealed the importance of formulating nanolubricants with specific particle size distribution that relate to the surface morphology of the deforming material. In this study, a nanolubricant with particle size of 3.6 μm exhibited better lubrication on ring samples with dent depth of 4.7 μm, implying that most nanoparticles were encapsulated in the dents facilitating hydrostatic lubrication.

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22

Shen, Min, Tongju Zhou, Ming-C. Cheng, and Robert M. Fithen. "Least-squares finite element formulation for hydrodynamic modeling of semiconductor devices." Computer Methods in Applied Mechanics and Engineering 190, no. 22-23 (February 2001): 2875–91. http://dx.doi.org/10.1016/s0045-7825(00)00350-9.

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23

Zholkovskiy, Emiliy K., Vladimir N. Shilov, Jacob H. Masliyah, and Mykola P. Bondarenko. "Hydrodynamic Cell Model: General Formulation and Comparative Analysis of Different Approaches." Canadian Journal of Chemical Engineering 85, no. 5 (May 19, 2008): 701–25. http://dx.doi.org/10.1002/cjce.5450850517.

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24

Brook, R. Glenn, Paul E. Oppenheimer, Charles A. Weatherford, Ioana Banicescu, and Jianping Zhu. "Solving the hydrodynamic formulation of quantum mechanics: A parallel MLS method." International Journal of Quantum Chemistry 85, no. 4-5 (2001): 263–71. http://dx.doi.org/10.1002/qua.1509.

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25

Burghardt, Irene, and Biman Bagchi. "On the non-adiabatic dynamics of solvation: A molecular hydrodynamic formulation." Chemical Physics 329, no. 1-3 (October 2006): 343–56. http://dx.doi.org/10.1016/j.chemphys.2006.07.014.

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26

Zalek, Steven F., Michael G. Parsons, and Robert F. Beck. "Naval Hull Form Multicriterion Hydrodynamic Optimization for the Conceptual Design Phase." Journal of Ship Research 53, no. 04 (December 1, 2009): 199–213. http://dx.doi.org/10.5957/jsr.2009.53.4.199.

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For a given set of ship design and operational criteria, there exists a trade-off between the ship's calm water powering performance and its seakeeping performance. Ship hulls that are designed for optimal powering performance can have poor seakeeping performance, and vice versa. It is typically not possible to obtain the global optimum for both of these objectives because of the competition between the powering and seakeeping performance functions and the design constraints. The set of globally nondominated solutions, or Pareto front, considering these competing criteria is searched for by navigating the multimodal search space using a multicriterion, population-based evolutionary algorithm optimization process. The optimization process uses a nontraditional objective function formulation that eliminates the need to tune the penalty function parameters for each new problem formulation and appears to provide a more thorough representation of the numerically approximated Pareto front. Results show that properly integrating this optimization process with the design criteria yields a set of hydrodynamically superior design solutions. The problem formulation and development is applicable to naval surface vessels and applied to a monohull frigate type example.

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27

Javanmardi, M., E. Jahanbakhsh, M. Seif, and H. Sayyaadi. "Hydrodynamic Analysis of Trimaran Vessels." Polish Maritime Research 15, no. 1 (January 1, 2008): 11–18. http://dx.doi.org/10.2478/v10012-007-0046-5.

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Hydrodynamic Analysis of Trimaran Vessels Trimaran vessels are developed for different applications and hydrodynamic behavior of such vessels is different than usual mono-hulls. In this paper hydrodynamic resistance and maneuvering of a trimaran with Wigley body form are investigated. The effects of outriggers position in four different longitudinal and two transverse locations are studied. For hydrodynamic simulations a CFD code has been developed and used. This code is capable for simulating three dimensional, time dependent, two phases, viscous flow coupled with rigid body motion. Formulation and solution algorithm are described in detail. Different case studies have been performance and numerical results have shown good agreement with experimental data. Based on resistance and maneuvering simulation of the trimaran vessels different conclusion are made. The results show that positions of outriggers have great effect on resistance and maneuverability of trimaran. The present method can be further employed to investigate other hydrodynamic qualities of trimaran vessels.

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28

Rudan, Massimo, and Giorgio Baccarani. "On the Structure and Closure-Condition of the Hydrodynamic Model." VLSI Design 3, no. 2 (January 1, 1995): 115–29. http://dx.doi.org/10.1155/1995/42492.

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Basing on a general formulation of the hydrodynamic model for semiconductor devices [1], a consistent approach to the solution of the model equations is proposed, along with a method for selezting the closure condition. The definition of the coefficients of the hydrodynamic and energy-transport models is then re-examined in order to make a comparison between them possible. Finally, the closure condition is discussed and compared with others proposed in the literature.

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29

Grimble, D. W., S. Theodossiades, H. Rahnejat, and M. Wilby. "Tribology of rough ultra-film contacts in drug delivery devices." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 11 (November 1, 2008): 2209–16. http://dx.doi.org/10.1243/09544062jmes1047.

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Elastomeric seals are extensively used in an assortment of drug delivery devices, such as syringes and pressurized metered dose inhalers. Although tribology of rubber seals and o-rings is reasonably well understood in engineering applications, the drug mixtures and formulations do not enjoy the required rheology to ensure coherent hydrodynamic action. In fact formation of uninterrupted hydrodynamic films is not actually sought in drug delivery devices, which often contain mixtures that are volatile when exposed to the environment. Furthermore, while engineering devices are often driven to overcome friction, many drug delivery systems are actuated manually and frequently by frail individuals. Therefore, the tribological problem is quite complex with many biological and environmental constraints. This paper highlights a parametric friction model for combined adhesive friction due to asperity interactions and non-Newtonian viscous action of the formulation. The model predicts the hysteretic behaviour of elastomeric seal contacts and conforms reasonably well to the experimental measurements of the same through actuation and release of inhaler valves.

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30

Wang, Lian-Ping, Orlando Ayala, and Wojciech W. Grabowski. "Improved Formulations of the Superposition Method." Journal of the Atmospheric Sciences 62, no. 4 (April 1, 2005): 1255–66. http://dx.doi.org/10.1175/jas3397.1.

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Abstract Two formulations of an improved superposition method are proposed for studying droplet–droplet hydrodynamic interactions. The formulations make explicit use of the boundary conditions on the surface of the two interacting droplets. The improved formulations are described through a consistent and rigorous consideration of the relationship between the drag force and representation of disturbance flows. It is demonstrated that the improved formulations are much more accurate than the original implementation of the superposition method. Specifically, for the case of Stokes disturbance flows, the relative errors on the drag force can be reduced by one order of magnitude using the improved formulations, when compared with the original formulation, for situations when the lubrication effect is not dominant. Using the improved superposition method, collision efficiencies of small cloud droplets falling in calm air are also computed and compared with previously published results.

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31

Bartolotti, Libero J. "The hydrodynamic formulation of time-dependent Kohn-Sham orbital density functional theory." Journal of Physical Chemistry 90, no. 22 (October 1986): 5518–23. http://dx.doi.org/10.1021/j100280a009.

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32

Bouaanani, N., P. Paultre, and J. Proulx. "A closed-form formulation for earthquake-induced hydrodynamic pressure on gravity dams." Journal of Sound and Vibration 261, no. 3 (March 2003): 573–82. http://dx.doi.org/10.1016/s0022-460x(02)01257-9.

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33

Tinawi, René, and Lotfi Guizani. "Formulation of hydrodynamic pressures in cracks due to earthquakes in concrete dams." Earthquake Engineering & Structural Dynamics 23, no. 7 (July 1994): 699–715. http://dx.doi.org/10.1002/eqe.4290230702.

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34

Banerjee, Supratik, and Sébastien Galtier. "An alternative formulation for exact scaling relations in hydrodynamic and magnetohydrodynamic turbulence." Journal of Physics A: Mathematical and Theoretical 50, no. 1 (November 30, 2016): 015501. http://dx.doi.org/10.1088/1751-8113/50/1/015501.

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35

Chiang-Sheng Yao, Jae-Gyung Ahn, Young-June Park, Hong-Shick Min, and R. W. Dutton. "Formulation of a tail electron hydrodynamic model based on Monte Carlo results." IEEE Electron Device Letters 16, no. 1 (January 1995): 26–29. http://dx.doi.org/10.1109/55.363210.

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36

Stewart, R. A., Liangxiu Ye, and J. N. Churchill. "Improved relaxation-time formulation of collision terms for two-band hydrodynamic models." Solid-State Electronics 32, no. 6 (June 1989): 497–502. http://dx.doi.org/10.1016/0038-1101(89)90033-6.

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37

Jeddi, L., M. El Khlifi, and D. Bonneau. "Thermohydrodynamic Analysis for a Hydrodynamic Journal Bearing Groove." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 219, no. 4 (April 1, 2005): 263–74. http://dx.doi.org/10.1243/135065005x33900.

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A numerical procedure is developed for the analysis of thermohydrodynamic behaviour of the hydrodynamic (HD) flow in the groove of a journal bearing. The Navier-Stokes and energy equations are written in terms of the primitive variables u, v, p, and T and solved simultaneously using the incremental load method and the finite element formulation. The numerical model is applied to the analysis of the velocities, the pressure, and the temperature patterns that characterize the lubricant flow in the HD groove. The effects of the runner velocity and the feeding pressure are investigated.

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38

Sunoqrot, Suhair, Malek Alfaraj, Ala’a M. Hammad, Violet Kasabri, Dana Shalabi, Ahmad A. Deeb, Lina Hasan Ibrahim, Khaldoun Shnewer, and Ismail Yousef. "Development of a Thymoquinone Polymeric Anticancer Nanomedicine through Optimization of Polymer Molecular Weight and Nanoparticle Architecture." Pharmaceutics 12, no. 9 (August 27, 2020): 811. http://dx.doi.org/10.3390/pharmaceutics12090811.

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Thymoquinone (TQ) is a water-insoluble natural compound isolated from Nigella sativa that has demonstrated promising chemotherapeutic activity. The purpose of this study was to develop a polymeric nanoscale formulation for TQ to circumvent its delivery challenges. TQ-encapsulated nanoparticles (NPs) were fabricated using methoxy poly(ethylene glycol)-b-poly(ε-caprolactone) (mPEG-PCL) copolymers by the nanoprecipitation technique. Formulation variables included PCL chain length and NP architecture (matrix-type nanospheres or reservoir-type nanocapsules). The formulations were characterized in terms of their particle size, polydispersity index (PDI), drug loading efficiency, and drug release. An optimized TQ NP formulation in the form of oil-filled nanocapsules (F2-NC) was obtained with a mean hydrodynamic diameter of 117 nm, PDI of 0.16, about 60% loading efficiency, and sustained in vitro drug release. The formulation was then tested in cultured human cancer cell lines to verify its antiproliferative efficacy as a potential anticancer nanomedicine. A pilot pharmacokinetic study was also carried out in healthy mice to evaluate the oral bioavailability of the optimized formulation, which revealed a significant increase in the maximum plasma concentration (Cmax) and a 1.3-fold increase in bioavailability compared to free TQ. Our findings demonstrate that the versatility of polymeric NPs can be effectively applied to design a nanoscale delivery platform for TQ that can overcome its biopharmaceutical limitations.

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39

Gavassino, Lorenzo, Marco Antonelli, and Brynmor Haskell. "Multifluid Modelling of Relativistic Radiation Hydrodynamics." Symmetry 12, no. 9 (September 18, 2020): 1543. http://dx.doi.org/10.3390/sym12091543.

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The formulation of a universal theory for bulk viscosity and heat conduction represents a theoretical challenge for our understanding of relativistic fluid dynamics. Recently, it was shown that the multifluid variational approach championed by Carter and collaborators has the potential to be a general and natural framework to derive (hyperbolic) hydrodynamic equations for relativistic dissipative systems. Furthermore, it also allows keeping direct contact with non-equilibrium thermodynamics, providing a clear microscopic interpretation of the elements of the theory. To provide an example of its universal applicability, in this paper we derive the fundamental equations of the radiation hydrodynamics directly in the context of Carter’s multifluid theory. This operation unveils a novel set of thermodynamic constraints that must be respected by any microscopic model. Then, we prove that the radiation hydrodynamics becomes a multifluid model for bulk viscosity or heat conduction in some appropriate physical limits.

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TORRES, Maycon de Paula Ribeiro, Rhuan Vínicius de Freitas ESPRENDOR, Solange Maria BONALDO, Elton Brito RIBEIRO, and Dênia Mendes de Sousa VALLADÃO. "Development, characterization and stability of microemulsionated formulations of bacaba, Oenocarpus bacaba oil." Acta Amazonica 49, no. 3 (September 2019): 246–55. http://dx.doi.org/10.1590/1809-4392201802702.

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ABSTRACT Advances in nanotechnology, combined with the use of natural products, represent a promissing research field. Brazil is a country of a rich biodiversity, especially in the Amazon forest. Fruits commonly used by local communities, such as bacaba (Oenocarpus bacaba), are potentially important for prospection of industrial applications of natural products. In nanotechnology, microemulsions stand out for providing a modified release to conveyed substances. This work aimed to develop microemulsionated formulations of bacaba oil, characterize them and evaluate their stability. We determined the HLB (hydrophile-lipophilic balance) of bacaba oil for formulation development. Six formulations were selected from pseudoternary diagrams, which indicated the proportions of surfactants, aqueous phase and bacaba oil. The viability of these formulations was evaluated through stability tests. We provided the rheological characterization of the formulations, evaluated their potential antioxidant activity through the DPPH (2,2-diphenyl-1-picrylhydrazyl) radical scavenging method, and determined the hydrodynamic diameter of the droplets. The microemulsions were stable throughout the test period. Droplet diameter was below 200 nm, and the microemulsions were characterized as newtonian fluids, presenting an increase in antioxidant activity when compared with the diluted oil. Our results confirm the potential of bacaba oil in microemulsionated formulation as a suitable carrier for active compounds.

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ROMATSCHKE, PAUL. "NEW DEVELOPMENTS IN RELATIVISTIC VISCOUS HYDRODYNAMICS." International Journal of Modern Physics E 19, no. 01 (January 2010): 1–53. http://dx.doi.org/10.1142/s0218301310014613.

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Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of applicability, and can be applied to both weakly and strongly coupled systems. In its modern formulation, relativistic viscous hydrodynamics can directly be solved numerically. This has been useful for the problem of ultrarelativistic heavy-ion collisions, and I will review the setup and results of a hydrodynamic description of experimental data for this case.

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Canalle, João Batista Garcia, Kinwah Wu, Mark Cropper, Gavin Ramsay, and Curtis J. Saxton. "Accretion Flow along a Dipolar Field: Application to Intermediate Polars." International Astronomical Union Colloquium 190 (2004): 208–14. http://dx.doi.org/10.1017/s0252921100002116.

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AbstractA hydrodynamic formulation for accretion flow channeled by a dipolar magnetic field is constructed using a curvi-linear coordinate system natural to the field structure. We solve the hydrodynamic equations and determine the velocity, density and temperature profiles of the post-shock accretion flow. The results are applied to accretion flows in intermediate polars. We have found that for systems with massive white dwarfs (~ 1 M⊙) the temperature profiles in the flow can differ significantly to those obtained from models in which the accretion column is assumed to be cylindrical.

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43

Imai, Satoya. "Effects of entanglement on vortex dynamics in the hydrodynamic representation of quantum mechanics." International Journal of Quantum Information 18, no. 06 (September 2020): 2050030. http://dx.doi.org/10.1142/s0219749920500306.

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The hydrodynamic representation of quantum mechanics describes virtual flow as if a quantum system were fluid in motion. This formulation illustrates pointlike vortices when the phase of a wavefunction becomes nonintegrable at nodal points. We study the dynamics of such pointlike vortices in the hydrodynamic representation for a two-particle wavefunction. In particular, we discuss how quantum entanglement influences vortex–vortex dynamics. For this purpose, we employ the time-dependent quantum variational principle combined with the Rayleigh–Ritz method. We analyze the vortex dynamics and establish connections with Dirac’s generalized Hamiltonian formalism.

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Saint-Raymond, Laure. "Entropy inequality and hydrodynamic limits for the Boltzmann equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 2005 (December 28, 2013): 20120350. http://dx.doi.org/10.1098/rsta.2012.0350.

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Boltzmann brought a fundamental contribution to the understanding of the notion of entropy, by giving a microscopic formulation of the second principle of thermodynamics. His ingenious idea, motivated by the works of his contemporaries on the atomic nature of matter, consists of describing gases as huge systems of identical and indistinguishable elementary particles. The state of a gas can therefore be described in a statistical way. The evolution, which introduces couplings, loses part of the information, which is expressed by the decay of the so-called mathematical entropy (the opposite of physical entropy!).

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Boudreau, Paul, Michel Leclerc, and Guy R. Fortin. "Modélisation hydrodynamique du lac Saint-Pierre, fleuve Saint-Laurent : l'influence de la végétation aquatique." Canadian Journal of Civil Engineering 21, no. 3 (June 1, 1994): 471–89. http://dx.doi.org/10.1139/l94-051.

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The macrophytes (aquatic plants) can have a substantial effect on the hydrodynamics of some watercourses. A mathematical formulation for the resistance effect of macrophytes on the current is inserted in a two-dimensional finite element hydrodynamic model. The method introduced herein allows to take into account the morphology, the density, and the growth curve of the different species of macrophytes present in the river. The Lake Saint-Pierre between Sorel and Trois-Rivières (Québec, Canada) in the St. Lawrence River is used to demonstrate the approach. The mathematical aspect of the model is first briefly presented. The field surveys of macrophytes and some other data sets used with the model are then analyzed. Finally, after the calibration–validation step, which insures the good behavior of the model, some results are presented to show the effect of the macrophytes on the flow structure. Key words: hydrodynamics, aquatic plants, St. Lawrence River, Lake Saint-Pierre, two-dimensional modelling, simulation, finite element method, Manning's coefficient.

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Oh, Kong Ping. "The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem." Journal of Tribology 108, no. 4 (October 1, 1986): 598–603. http://dx.doi.org/10.1115/1.3261274.

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The mixed-lubrication problem is formulated as a nonlinear generalized complementarity problem in which the pressure acting on the load-bearing surface is taken as the unknown, and the lubricant flow and the gap between the surfaces are taken as its complements. An iterative method was developed to find the solution, which satisfies the complementarity condition that at each point on the load-bearing surface, the pressure or at least one of its complements, is zero at all times. Moreover, the pressure and its complements satisfy non-negativity constraints. The solution intrinsically decomposes the load-bearing surface into three distinct subregions: solid-to-solid contact, hydrodynamically lubricated contact, and no contact (or cavitation). It is shown that the mixed-lubrication formulation degenerates into the special cases of hydrodynamic or solid-to-solid contacts under appropriate load and speed conditions. A journal bearing with elastic support is analyzed to illustrate the method of solution. The transition of the lubrication mode from pure hydrodynamic contact to mixed contact is demonstrated.

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Favacho, B. I., J. R. P. Vaz, and A. L. A. Mesquita. "CONTRIBUTIONS TO THE MARINE PROPELLERS HYDRODYNAMIC DESIGN." Revista de Engenharia Térmica 13, no. 2 (December 31, 2014): 41. http://dx.doi.org/10.5380/reterm.v13i2.62093.

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The navigation in Amazon region is very important due to the length of navigable rivers and the lack of alternative road network, as well as being a form of transportation costless for the flow of agricultural and manufacturing production. This kind of transportation present social, economic and technological importance for this region. Thus, this work objective to develop a mathematical approach for the marine propellers design, using a formulation for chord and pitch angle optimization, taken into account the equations of mass, energy and momentum balance for the theoretical calculation of thrust and torque relationships on an annular control volume, ie, the mathematical model is based in the Blade Element Momentum (BEM) theory. The proposed hydrodynamic model present low computational cost and it is easy to implement. The results are compared with classical Glauert's theory and the experimental data of the Wageningen B3-50 propeller, presenting good agreement.

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Hsiao, C. H., and D. L. Young. "Calculation of Hydrodynamic Forces for Unsteady Stokes Flows by Singularity Integral Equations Based on Fundamental Solutions." Journal of Mechanics 30, no. 2 (August 8, 2013): 129–36. http://dx.doi.org/10.1017/jmech.2013.56.

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ABSTRACTThe attractive feature of the singularity method for steady Stokes flows is that the hydrodynamic forces acting on the particle can be calculated by the total strength of distributed singularities. For unsteady Stokes flows, however we have to derive hydrodynamic forces acting on a solid body in terms of the strengths of both unsteady Stokeslets as well as unsteady potential dipoles if mass and force sources are both taken into consideration. Since the hydrodynamic force formulation results in a Volterra integral equation of the first kind, and the strengths are numerically approximated by means of the Lubich convolution quadrature method (CQM) in this study. As far as the numerical solutions of time-domain integral formulations of the unsteady Stokes equations are concerned, this paper requires only the Laplace-domain instead of the time- domain fundamental solutions of the governing equations. The stability and accuracy of the proposed method are verified through some well selected numerical examples. In total we include two examples presenting the accuracy of Lubich CQM, and another two examples for calculating general hydrody-namic forces of a sphere in oscillating or non-oscillating unsteady Stokes flows. It is concluded that this study is able to extend the unsteady Stokes flow theory to more general transient motions instead to limit to the oscillating flow assumption.

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Moskowitz, Shaye I., James Liu, and Ajit A. Krishnaney. "Postoperative Complications Associated with Dural Substitutes in Suboccipital Craniotomies." Operative Neurosurgery 64, suppl_1 (March 1, 2009): ONS28—ONS34. http://dx.doi.org/10.1227/01.neu.0000334414.79963.59.

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Abstract Objective: Dural replacements are used in cranial surgery when primary closure of native dura is not possible. The goal is to recreate a watertight barrier to prevent cerebrospinal fluid leakage with few associated complications. We reviewed a single-institution experience with a variety of dural substitutes in posterior fossa neurosurgery, for which higher complication rates are well described. Methods: Patients were screened for suboccipital posterior fossa neurosurgery between November 2005 and April 2007. Surgical logs were reviewed for diagnosis, procedure, and use of dural replacement. Clinical courses were reviewed for hydrodynamic complications, including delayed hydrocephalus, clinically significant pseudomeningocele, aseptic meningitis, and persistent cerebrospinal leakage. Results: One hundred twenty-eight patients were included, and a dural replacement was used in 106. Overall, the complication rate was 21.9% (28 patients). Complications were seen for acellular human dermis in 33.3%, for collagen matrix in the original formulation in 18.2%, for the reformulation in 16.9%, for the suturable formulation in 50%, for nonautologous materials in 24%, and for no dural replacement in 16.7%. Univariate and multivariate analysis demonstrated that hydrodynamic complications were associated with use of the suturable collagen matrix (odds ratio, 10.8; 95% confidence interval, 2.5–46.1; P = 0.0014) and trended with use of acellular human dermis (odds ratio, 4.6; 95% confidence interval, 0.9–23.1; P = 0.06). Conclusion: The increased risk of hydrodynamic complications associated with suboccipital neurosurgery is modified by choice of dural replacement. Similar complication rates were seen for most materials with a variety of primary abnormalities, with the exception of suturable bovine collagen matrix, with hydrodynamic complications in 50% of patients.

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Simakov, Andrei N., and Kim Molvig. "Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation." Physics of Plasmas 23, no. 3 (March 2016): 032115. http://dx.doi.org/10.1063/1.4943894.

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