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Nanoparticle Production by Spark Ablation: Principle, Configurations, and Basic Steps toward Application
Published in Andreas Schmidt-Ott, Spark Ablation, 2019
Maurits F. J. Boeije, George Biskos, Bibianne E. van der Maesen, Tobias V. Pfeiffer, Aaike W. van Vugt, Bernardus Zijlstra, A. Schmidt-Ott
The coagulation kernel in the continuum limit is given by () βCo(v,v′)=2kT3η(v13+v′13)(C(v)v13+C(v′)v′13),
Aerosols
Published in Efstathios E. Michaelides, Clayton T. Crowe, John D. Schwarzkopf, Multiphase Flow Handbook, 2016
Yannis Drossinos, Christos Housiadas
Equations 20.74 and 20.75 show, as initially postulated by Dahneke (1973) and discussed extensively by ajudeen et al. (2012), that the adjusted-sphere radius becomes a geometric descriptor of an aggregate: it depends solely on the morphology of the aggregate. For an aggregate, it depends on the radius of gyration, the number of monomers, and the monomer radius, all geometric quantities. For a straight chain, it depends on the number of monomers and the monomer radius. Given the adjusted-sphere radius, it is easy to calculate the friction coe cient of fractal-like aggregates via the de ning equation of the adjusted-sphere radius and the expression for the single-sphere slip correction factor. It is instructive to reconsider the limiting behavior of Equation 20.66. We obtain, in the continuum limit Kng, Knadj 0,
Controlled Electronic Transfer in Molecular Chains and Segments
Published in Günter Mahler, Volkhard May, Michael Schreiber, Molecular Electronics, 2020
Hanspeter Knoll, Michael Mehring
In the continuum limit the energy dispersion curve is readily obtained as ϵk=4t02cos2k+Δ02sin2kwith−π/2<k<π/2
Some comments on unitary qubit lattice algorithms for classical problems
Published in Radiation Effects and Defects in Solids, 2023
Paul Anderson, Lillian Finegold-Sachs, George Vahala, Linda Vahala, Abhay K. Ram, Min Soe, Efstratios Koukoutsis, Kyriakos Hizandis
Since the equation is a scalar equation for the real function one need only to employ 2 qubits / lattice site. First we shall reconsider the QLA for KdV with the use of an external potential to model the nonlinear term in KdV [1]. The collision operator is nothing but Equation (1). We denote the operator to be the streaming operator that translates the qubit one lattice unit in the -direction. To eliminate the 2nd order spatial derivative one must choose the interleaved sequence of collision-stream unitary operators carefully. In particular the following sequence will generate a second order QLA for the KdV equation where the unitary collision operator C is nothing but the maximally entangling operator, Equation (1), with . . The external potential is the Hermitian matrix In the continuum limit, one recovers on defining . With the choice of we have a second order accurate QLA for KdV. Note that the QLA of Equation (26) is not fully unitary because of the non-unitary property of the external potential operator .
Quantum theory of light in a dispersive structured linear dielectric: a macroscopic Hamiltonian tutorial treatment
Published in Journal of Modern Optics, 2020
In the continuum limit, , we replace , , and . Then Choose , so . Then the displacement field operator becomes (using to label the band):
Quantum lattice representation for the curl equations of Maxwell equations
Published in Radiation Effects and Defects in Solids, 2022
George Vahala, John Hawthorne, Linda Vahala, Abhay K. Ram, Min Soe
It is convenient to introduce the qubits as just the Riemann–Silberstein–Weber vectors, Equation (2). With that choice, we now proceed to determine the required form of the collision, scattering and potential operators that will recover the two curl equations of Maxwell in the continuum limit. As details are presented in our earlier papers [1–5], we just summarize the results here. Since we are considering 1D propagation in the x-direction, we automatically have . This reduces the number of qubits/lattice site to 4: since . An appropriate collision matrix acting on the 4-spinor is the unitary matrix and the interleaved non-commuting sequence of collide-stream operators where streams qubits and one lattice unit to the right while not streaming qubits and . is the adjoint of the unitary matrix C. To perturbatively recover the two curl equations of Maxwell, one will need to introduce the potential operators and and the rotation angles and . The perturbation parameter ϵ will turn out to be the speed of light in that medium. The QLA time evolution of the 4-qubits is then determined by In the continuum limit the above QLA reduces, to , From Equations (3) and (4), it is readily shown that the continuum Equation (10) is nothing but the two curl equations of Maxwell for both polarizations.