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N. H. March - One of the best experts on this subject based on the ideXlab platform.
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The role of the von Weizsäcker Kinetic Energy gradient term in independent harmonically confined fermions for arbitrary two-dimensional closed-shell occupancy
Journal of Physics A: Mathematical and Theoretical, 2010Co-Authors: I.a. Howard, N. H. MarchAbstract:The search for the single-Particle Kinetic Energy functional TS[n] continues to be of major interest for density functional theory. Since it is expected to be generally applicable, exactly solvable models are of obvious interest. Here we focus on one, which is also of interest experimentally in magnetic trapping of ultracold fermion vapours. This is the model of independent harmonically trapped fermions in two dimensions. Here, the role of the von Weizsacker inhomogeneity Kinetic Energy is a focal point, prompted also by the work of Delle Site (2005 J. Phys. A: Math. Gen. 38 7893).
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Density-potential relation via the single-Particle Kinetic Energy density for one-dimensional two-level fermion systems with application to Be-like atomic ions in the (1s)2(2s)2 configuration
Physical Review A, 2006Co-Authors: I.a. Howard, N. H. MarchAbstract:Using the Dawson-March transformation of two-level wave functions in terms of density amplitude and phase, a differential equation is constructed relating the single-Particle Kinetic Energy to the fermion density. Employing then the differential form of the virial theorem derived by March and Young [Nucl. Phys. 12, 237 (1959)], a nonlinear electron-density-one-body potential relation emerges. Application to the Be-like atomic ions is briefly considered.
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Single-Particle Kinetic Energy in density-functional theory: Harmonic confinement in two and three dimensions
Physical Review A, 2006Co-Authors: N. H. MarchAbstract:Using the known perturbation series for the idempotent Dirac density matrix in powers of a given one-body potential V(r), Stoddart and March (SM) generated a corresponding series for the Kinetic Energy density. While the general term of the SM series is known, a summation has not been achieved to date. A contribution to solve this problem is made here by exhibiting an explicit form of the above Kinetic Energy density for Fermions filling an arbitrary number of closed shells, when the confinement is harmonic. This example is of considerable current interest because of ongoing experiments on ultracold atomic gases of Fermions.
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dirac density matrix and the legendre transform of the Kinetic Energy generated by one dimensional model potentials
Journal of Physics A, 2006Co-Authors: I.a. Howard, N. H. MarchAbstract:In density functional theory, the single-Particle Kinetic Energy is still not known in an orbital-free form. The natural tool to calculate such Kinetic Energy for a given one-body potential V is the Dirac density matrix y. Here, by first taking solvable one-dimensional examples, and in particular the sech 2 (x) potential, forms for the Dirac density matrix are exhibited in terms of the potential.This in turn generates the Legendre transform of the single-Particle Kinetic Energy. Finally, one-dimensional perturbation theory for the Kinetic Energy density, summed to all orders in V, is presented in the appendix.
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electrostatic interpretation of the force vxc r connected with the exchange correlation potential direct relation to single Particle Kinetic Energy density in be atom
Physics Letters A, 2004Co-Authors: N. H. March, Paul Geerlings, K D SenAbstract:Abstract In a recent study by one of us [Phys. Rev. A 65 (2002) 034501], an electrostatic interpretation has been proposed for the force − ∂V xc / ∂r associated with the exchange-correlation potential Energy V xc ( r ) in a spherical atom such as Be or Ne. Here, this proposal is employed to relate − ∂V xc / ∂r directly to (a) the exact ground-state density ρ ( r ) (e.g., from diffraction experiments or quantum Monte Carlo simulation) and its low-order derivatives, and (b) the single-Particle Kinetic Energy density t s ( r ), calculated again from the exact ρ ( r ), for the example of the Be-atom. It would, of course, be important if this type of relation could be extended beyond a (1s) 2 (2s) 2 two-level single-Particle configuration.
Jan K. Spelt - One of the best experts on this subject based on the ideXlab platform.
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erosion modeling in abrasive slurry jet micro machining of brittle materials
Journal of Manufacturing Processes, 2015Co-Authors: Haj Mohammad R Jafar, Jan K. Spelt, H Nouraei, M Emamifar, M PapiniAbstract:Abstract Abrasive slurry jet micro-machining (ASJM) uses a relatively low pressure jet of abrasive slurry to machine features such as holes and channels. This study investigated the effect of alumina Particle Kinetic Energy and jet impact angle on the roughness and erosion rate of channels machined in borosilicate glass using ASJM. A computational fluid dynamics model was used to calculate the local Particle impact velocities and angles, and thus the Kinetic energies of Particles striking the surface. Consistent with earlier work on air-driven abrasive jets, the roughness and erosion rate of the channels machined at perpendicular incidence depended only on the Kinetic Energy of Particles above the apparent cracking threshold of the glass target. Slurry jets of higher Kinetic Energy produced rougher channels and higher erosion rates since the impacting Particles caused larger lateral cracks to form, and thus removed larger chips. The measured erosion rate at various impact angles, and the observed damage due to individual alumina Particle impacts, indicated that the dominant mode of material removal was brittle erosion. Two similar analytical brittle-erosion models derived for air-driven abrasive jet micromachining (AJM), were found to predict reasonably well the roughness and the erosion rate of ASJM channels, despite the large differences in the fluid media, flow patterns, and Particle trajectories in AJM and ASJM. A key requirement was that the average Particle Kinetic Energy was calculated using the CFD model. With only minor modifications, the models predicted the channel erosion rate and centreline roughness with average errors of 12% and 17%, respectively. In addition, a numerical simulation, previously developed to predict the erosion in AJM of brittle materials, was used to predict the centreline average roughness, shape parameters and depth of ASJM channels for various machining conditions.
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abrasive enhanced electrochemical slurry jet micro machining comparative experiments and synergistic effects
Journal of Materials Processing Technology, 2014Co-Authors: H Nouraei, Jan K. Spelt, M PapiniAbstract:Abstract Abrasive enhanced electrochemical slurry-jet machining (ESJM) is presented as a new approach to the micro-machining of metals using a combination of abrasive slurry-jet machining (ASJM) and electrochemical jet machining (ECJM). A novel ESJM prototype was developed to generate a charged slurry jet consisting of a mixture of Al2O3 abrasive Particles and an electrolytic solution of NaCl and NaNO3. A DC potential of 30 V was applied between the nozzle and specimen. A series of micro-channels were machined in Stellite 12 using ASJM, ECJM and ESJM processes to investigate the relative effects of erosion and anodic dissolution on the material removal rate and surface finish in the combined process of ESJM. The results illustrated that the ESJM process results in significantly greater target mass loss rate than the separate erosion and corrosion processes. The magnitude of the synergistic effect on the rate of mass loss was found to vary from positive to negative as the erosion component increased with increasing Particle Kinetic Energy (jet pressure) and Particle concentration. The roughness of the channels machined using ESJM was between that obtained with ASJM and ECJM. The roughness decreased as the erosion component of the total mass loss increased.
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Blast cleaning of gas turbine components: deposit removal and substrate deformation
Wear, 2001Co-Authors: A. Raykowski, Mahmoud Al-hader, B. Maragno, Jan K. SpeltAbstract:Abstract The effectiveness of glass and stainless steel spheres in the blast cleaning of stationary gas turbine components was evaluated as a function of Particle size, speed, impact angle, and standoff distance. The overall objective was to maximize the rate of deposit removal while minimizing substrate deformation. It was found that deposit erosion and substrate deformation were strong functions of Particle stream power, Particle Kinetic Energy, and impact angle. The erosion of deposits on compressor and turbine stage components exhibited brittle characteristics, while substrate deformation was ductile. For this reason, an impact angle of 90° to the surface was optimal. Substrate deformation increased with average Particle Kinetic Energy, independent of stream power. Deposit removal with glass media increased with stream power. Blasting with the stainless steel media, which was softer than the substrate, prevented deformation while still removing deposits.
Fengzhou Fang - One of the best experts on this subject based on the ideXlab platform.
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theoretical study on Particle velocity in micro abrasive jet machining
Powder Technology, 2019Co-Authors: Ruslan Melentiev, Fengzhou FangAbstract:Abstract Micro-abrasive jet machining (AJM) is an advanced subtractive machining technology with ample opportunities to form regular micro-patterns on freeform surfaces. AJM removes material mainly through erosion and abrasion, which transform Kinetic Energy to fracture and deform substrates. The Kinetic Energy of a solid Particle is tightly connected to its velocity, which is the most significant source of error in precise prediction of a machined feature. The present study involves both theoretical analysis and two-dimensional axisymmetric numerical simulation of Particle velocity fields at the lower end of the micro-scale. The developed model represents the finest Particles in a cylindrical nozzle down to an inner diameter of 100 μm. The computed results agree well with the experimental data. It is shown that, due to viscous friction, such nozzles are significantly less efficient in terms of Particle saturation with Kinetic Energy. The study highlights the effects of nozzle diameter and length, air pressure, Particle size and density on Particle velocity development through the jet field. Finally, practical recommendations and multiple regression models of maximum Particle velocity, location from the nozzle exit and simplex velocity profile approximation are offered for management of Particle Kinetic Energy.
M Papini - One of the best experts on this subject based on the ideXlab platform.
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erosion modeling in abrasive slurry jet micro machining of brittle materials
Journal of Manufacturing Processes, 2015Co-Authors: Haj Mohammad R Jafar, Jan K. Spelt, H Nouraei, M Emamifar, M PapiniAbstract:Abstract Abrasive slurry jet micro-machining (ASJM) uses a relatively low pressure jet of abrasive slurry to machine features such as holes and channels. This study investigated the effect of alumina Particle Kinetic Energy and jet impact angle on the roughness and erosion rate of channels machined in borosilicate glass using ASJM. A computational fluid dynamics model was used to calculate the local Particle impact velocities and angles, and thus the Kinetic energies of Particles striking the surface. Consistent with earlier work on air-driven abrasive jets, the roughness and erosion rate of the channels machined at perpendicular incidence depended only on the Kinetic Energy of Particles above the apparent cracking threshold of the glass target. Slurry jets of higher Kinetic Energy produced rougher channels and higher erosion rates since the impacting Particles caused larger lateral cracks to form, and thus removed larger chips. The measured erosion rate at various impact angles, and the observed damage due to individual alumina Particle impacts, indicated that the dominant mode of material removal was brittle erosion. Two similar analytical brittle-erosion models derived for air-driven abrasive jet micromachining (AJM), were found to predict reasonably well the roughness and the erosion rate of ASJM channels, despite the large differences in the fluid media, flow patterns, and Particle trajectories in AJM and ASJM. A key requirement was that the average Particle Kinetic Energy was calculated using the CFD model. With only minor modifications, the models predicted the channel erosion rate and centreline roughness with average errors of 12% and 17%, respectively. In addition, a numerical simulation, previously developed to predict the erosion in AJM of brittle materials, was used to predict the centreline average roughness, shape parameters and depth of ASJM channels for various machining conditions.
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abrasive enhanced electrochemical slurry jet micro machining comparative experiments and synergistic effects
Journal of Materials Processing Technology, 2014Co-Authors: H Nouraei, Jan K. Spelt, M PapiniAbstract:Abstract Abrasive enhanced electrochemical slurry-jet machining (ESJM) is presented as a new approach to the micro-machining of metals using a combination of abrasive slurry-jet machining (ASJM) and electrochemical jet machining (ECJM). A novel ESJM prototype was developed to generate a charged slurry jet consisting of a mixture of Al2O3 abrasive Particles and an electrolytic solution of NaCl and NaNO3. A DC potential of 30 V was applied between the nozzle and specimen. A series of micro-channels were machined in Stellite 12 using ASJM, ECJM and ESJM processes to investigate the relative effects of erosion and anodic dissolution on the material removal rate and surface finish in the combined process of ESJM. The results illustrated that the ESJM process results in significantly greater target mass loss rate than the separate erosion and corrosion processes. The magnitude of the synergistic effect on the rate of mass loss was found to vary from positive to negative as the erosion component increased with increasing Particle Kinetic Energy (jet pressure) and Particle concentration. The roughness of the channels machined using ESJM was between that obtained with ASJM and ECJM. The roughness decreased as the erosion component of the total mass loss increased.
Norman H. March - One of the best experts on this subject based on the ideXlab platform.
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A form of the single-Particle Kinetic Energy density of an inhomogeneous electron liquid from a combination of one-body potential and ground-state electron density
Physics and Chemistry of Liquids, 2011Co-Authors: Claudio Amovilli, Norman H. MarchAbstract:Gal and March have recently proposed a form of the single-Particle Kinetic Energy density in density functional theory in terms of the one-body potential V(r) and the ground-state electron density n(r) generated thereby. Here, with a minor modification of the GM form, examples are given for (a) harmonic trapping and (b) a bare Coulomb potential. The case of the He atom is also considered, via the Chandrasekhar variational wave function. Finally, the use of the semiempirical fine-tuned Hartree–Fock n(r) for spherical atoms due to Cordero et al. is briefly referred to.
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Towards an exact orbital-free single-Particle Kinetic Energy density for the inhomogeneous electron liquid in the Be atom
arXiv: Chemical Physics, 2010Co-Authors: Alisa Krishtal, Norman H. March, Christian Van AlsenoyAbstract:Holas and March (Phys. Rev. A51, 2040 (1995)) wrote the gradient of the one-body potential V(r) in terms of low-order derivatives of the idempotent Dirac density matrix built from a single Slater determinant of Kohn-Sham orbitals. Here, this is first combined with the study of Dawson and March (J. Chem. Phys. 81, 5850 (1984)) to express the single-Particle Kinetic Energy density of the Be atom ground-state in terms of both the electron density n(r) and potential V(r). While this is the more compact formulation, we then, by removing V(r), demonstrate that the ratio t(r)/n(r) depends, though non-locally, only on the single variable n'(r)/n(r), no high-order gradients entering for the spherical Be atom.
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Pauli potential in terms of Kinetic Energy density and electron density in the leading Coulombic term of the nonrelativistic 1/Z expansion of spherical atomic ions
Physical Review A, 2010Co-Authors: Norman H. March, Ágnes NagyAbstract:The Pauli potential V{sub P} in density functional theory is known to be the difference between the functional derivative of the single-Particle Kinetic Energy T{sub s}[n] with respect to the electron density n and its von Weizsaecker counterpart. For the leading Coulombic term in the 1/Z expansion for spherical atomic ions, V{sub P}[n] is written in terms of the Kinetic Energy density plus n(r) and its low-order derivatives. For comparison, the example of an arbitrary number of closed shells with purely harmonic confinement is also treated.
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Relation between single-Particle Kinetic Energy and exchange Energy in DFT for the inhomogeneous electron liquid in the Be atom
Physics and Chemistry of Liquids, 2010Co-Authors: Ferenc Bogár, Ferenc Bartha, Norman H. MarchAbstract:In a recent study, the authors have used the semi empirical fine-tuned Hartree–Fock ground-state electron density n(r) of Cordero et al. [Phys. Rev. A 75, 052502 (2007)] for the Be atom to calculate the phase θ(r) from a non-linear pendulum-like equation. Since the density amplitude n(r)1/2 plus θ(r) determine, in turn, the idempotent Dirac density matrix γ(r, r′), we use n(r) and θ(r) first of all to calculate the exchange Energy density e X (r) of the density functional theory (DFT). This enables us to obtain the Slater (Sl) approximation to the exchange-only potential. A comparison can then be made, by integrating the earlier predicted exchange-correlation force −∂V XC (r)/∂r, of V XC (r) with . Relationship to the Becke semiempirical density gradient approximation for exchange is also established. Some brief discussion of the Perdew–Burke–Ernzerhof density functional is added.
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Differential equation for the electron density in large molecules
International Journal of Quantum Chemistry, 2009Co-Authors: Norman H. MarchAbstract:Developments in density functional theory involve, almost inevitably, the knowledge of the single-Particle Kinetic Energy Ts[p] as a functional of the electron density p(r). Here, the possibilities of approximating this quantity through a one-body potential inserted in a Schrodinger equation for the density amplitude {p(r)}1/2 are explored in both finite and extended inhomogeneous electron gases. Nonlocal theory relating the contribution VPauli(r) of the one-body potential arising from the Fermi statistics obeyed by electrons is contemplated and some examples given.
