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  • American Institute of Physics (AIP)  (8)
  • Geological Society of America (GSA)  (5)
  • 1
    Electronic Resource
    Electronic Resource
    Generalization of the Darboux transform (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 966-975 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This article presents a generalization of the standard Darboux transform applied to Sturm–Liouville differential equations. This is achieved with the aid of an ansatz as a particular solution for the Riccati relationship involved, which in turn led us to obtain its generalized Darboux solution that contains, as a particular case, the standard Darboux transform. The proposed generalized Darboux transform (GDT), applied to the quantum mechanical field, gives the opportunity to prove the existence of standard and generalized Darboux potentials that match with the so-called isospectral potentials. This is exemplified by obtaining, through the GDT, a set of standard and generalized Darboux potentials that form the partner of the one-dimensional harmonic oscillator model for any quantum principal number. The worked example indicates how the GDT can be used to obtain the isospectral potentials associated to any known specific potential. We consider also the application of our method as proposed to the theory of solitons in order to show why the GDT will be important in other fields of application where the standard Darboux transform is usually concerned. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1334904
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  • 2
    Electronic Resource
    Electronic Resource
    Electron nuclear dynamics of proton collisions with methane at 30 eV (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 6146-6155 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The reactive collisions of protons with methane molecules at 30 eV in the laboratory frame are studied with the electron nuclear dynamics (END). The results from this theoretical approach, which does not invoke the Born–Oppenheimer approximation and does not impose any constraints on the nuclear dynamics, are compared to the results from time-of-flight measurements. Total differential cross sections and integral cross sections as well as fragmentation ratios and energy loss spectra are discussed.© 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.474343
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  • 3
    Electronic Resource
    Electronic Resource
    Hypervirial theorem and parameter differentiation: Closed formulation for harmonic oscillator integrals (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1032-1035 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple method has been developed to generate a closed formula for the calculation of matrix elements of arbitrary functions f(x) in the representation of the harmonic oscillator. The proposed algebraic procedure is based on the combined use of the hypervirial theorem with and without the second quantization formalism along with the parameter differentiation technique. The closed formula thus obtained is given in terms of a sum involving the jth derivative of f(x) evaluated at zero.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527543
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  • 4
    Electronic Resource
    Electronic Resource
    Recurrence relations for two-center harmonic oscillator integrals (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2966-2972 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: General recurrence relations for the calculation of two-center harmonic oscillator (HO) integrals are obtained by means of a hypervirial-like-theorem commutator algebra procedure, combined with a second quantization formalism. The method is based on a linear transformation between the creation and annihilation operators of two displaced HO with different frequencies. Ansbacher's recurrence relations for the calculation of Franck–Condon factors are obtained straightforwardly from the proposed general recurrence relations. The application to polynomial, exponential, and Gaussian operator integrals is shown and new recurrence relations are given. In all cases, the proposed recurrence relations reduce, as particular cases, to the corresponding formulas for the calculation of one-center integrals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527277
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  • 5
    Electronic Resource
    Electronic Resource
    The generalization of the binomial theorem (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 393-397 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: As is well known, the binomial theorem is a classical mathematical relation that can be straightforwardly proved by induction or through a Taylor expansion, albeit it remains valid as long as [A,B]=0. In order to generalize such an important equation to cases where [A,B]≠0, an algebraic approach based on Cauchy's integral theorem in conjunction with the Baker–Campbell–Hausdorff series is presented that allows a partial extension of the binomial theorem when the commutator [A,B]=c, where c is a constant. Some useful applications of the new proposed generalized binomial formula, such as energy eigenvalues and matrix elements of power, exponential, Gaussian, and arbitrary f(xˆ) functions in the one-dimensional harmonic oscillator representation are given. The results here obtained prove to be consistent in comparison to other analytical methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528457
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  • 6
    Electronic Resource
    Electronic Resource
    Two new potentials for the free particle model (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5555-5564 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this work, is proposed a very simple method for obtaining the generalized potential associated with a known standard potential. The procedure is straightforward because it only uses two Ricatti-type relationships as enough condition to find a generalized potential; one particular equation is needed to identify the specific potential under study and one general Ricatti relationship is used to find the corresponding generalized potential. Moreover, the method is completely general due to the fact that an arbitrary potential has been considered in its development for which the procedure can also be used to find new potentials which could be needed in the modeling of important quantum interactions. The usefulness of the proposed approach, is shown with the treatment of the three- and one-dimensional potential for the free particle model. This work example leads to two new potentials whose Hamiltonians are isospectral when they are compared with the former Hamiltonian. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533045
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  • 7
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    Agricultural activity shapes the communication and migration patterns in Senegal (2016)
    American Institute of Physics (AIP)
    In: Chaos
    Details
    Publication Date: 2016-06-08
    Description: The communication and migration patterns of a country are shaped by its socioeconomic processes. The economy of Senegal is predominantly rural, as agriculture employs over 70% of the labor force. In this paper, we use mobile phone records to explore the impact of agricultural activity on the communication and mobility patterns of the inhabitants of Senegal. We find two peaks of phone calls activity emerging during the growing season. Moreover, during the harvest period, we detect an increase in the migration flows throughout the country. However, religious holidays also shape the mobility patterns of the Senegalese people. Hence, in the light of our results, agricultural activity and religious holidays are the primary drivers of mobility inside the country.
    Print ISSN: 1054-1500
    Electronic ISSN: 1089-7682
    Topics: Physics
    Published by American Institute of Physics (AIP)
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  • 8
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    Delamination in the Betic Range: Deep structure, seismicity, and GPS motion (2013)
    Geological Society of America (GSA)
    In: Geology
    Details
    Publication Date: 2013-02-20
    Description: Subduction comes to an end when all oceanic lithosphere is consumed and continental or transitional crust, with positive buoyancy, becomes involved. During continental collision, the final stage of subduction may be characterized by slab breakoff, limited continental subduction, and delamination below the fold-and-thrust belt. We report receiver function images, constructed from a dense array of seismic broadband stations, that reveal the underthrusting of Iberia beneath the Alboran plate. The underthrusted crust is delaminating beneath part of the Betic mountain range, still connected to the foreland lithosphere on one side, and interrupted discontinuously along the other side. Intermediate deep earthquakes associated with the delamination process do not respond to downdip stresses like subduction earthquakes. The GPS velocity field and source mechanisms for shallow earthquakes demonstrate ongoing active shortening on top of the hinge of delamination, and localized perpendicular extension on top of the edge of delamination, introducing independent motion of the overriding crustal block. Delamination beneath the Betic Range drives seismicity by inducing fundamental changes in deformation patterns within the collision orogen.
    Print ISSN: 0091-7613
    Electronic ISSN: 1943-2682
    Topics: Geosciences
    Published by Geological Society of America (GSA)
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  • 9
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    Three-dimensional gyrokinetic simulation of the relaxation of a magnetized temperature filament (2015)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2015-10-08
    Description: An electromagnetic, 3D gyrokinetic particle code is used to study the relaxation of a magnetized electron temperature filament embedded in a large, uniform plasma of lower temperature. The study provides insight into the role played by unstable drift-Alfvén waves observed in a basic electron heat transport experiment [D. C. Pace et al ., Phys. Plasmas 15 , 122304 (2008)] in which anomalous cross-field transport has been documented. The simulation exhibits the early growth of temperature-gradient-driven, drift-Alfvén fluctuations that closely match the eigenmodes predicted by linear theory. At the onset of saturation, the unstable fluctuations display a spiral spatial pattern, similar to that observed in the laboratory, which causes the rearrangement of the temperature profile. After saturation of the linear instability, the system exhibits a markedly different behavior depending on the inclusion in the computation of modes without variation along the magnetic field, i.e., k z  = 0. In their absence, the initial filament evolves into a broadened temperature profile, self-consistent with undamped, finite amplitude drift-Alfvén waves. But the inclusion of k z  = 0 modes causes the destruction of the filament and damping of the drift-Alfvén modes leading to a final state consisting of undamped convective cells and multiple, smaller-scale filaments.
    Print ISSN: 1070-664X
    Electronic ISSN: 1089-7674
    Topics: Physics
    Published by American Institute of Physics (AIP)
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  • 10
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    Connection between the Jurassic oceanic lithosphere of the Gulf of Cádiz and the Alboran slab imaged by Sp receiver functions (2019)
    Geological Society of America (GSA)
    In: Geology
    Details
    Publication Date: 2019
    Description: 〈span〉〈div〉Abstract〈/div〉We investigate the lithospheric structure beneath the Gibraltar arc (western Mediterranean) using S-wave receiver functions (SRFs). From a dense network deployed in the Ibero-Maghrebian region during different seismic surveys, we calculated ∼11,000 SRFs that sample the upper mantle detecting the lithosphere-asthenosphere boundary (LAB). The observed seismic LAB belongs to different lithospheric domains: Iberian and African forelands, Alboran domain, and Atlantic Ocean. Common conversion point (CCP) migrated profiles show the geometrical relation among them. Under the Strait of Gibraltar, we observe a deep LAB (∼150 km). It can be associated with Jurassic-age lithosphere of ∼120 km thickness, one of the thickest ever reported in oceanic environments. There is an abrupt offset between the oceanic LAB and the shallow (80-km-deep) continental LAB of the Iberian foreland, suggesting displacement along a former transform fault. The northwestern African continental LAB is 90–100 km deep. The oceanic LAB under the Gibraltar arc continues to ∼180 km depth beneath the Alboran Sea, showing the connection between the Alboran slab and the oceanic lithosphere in the central Gulf of Cádiz. This geometry agrees with an ∼200-km-wide corridor of oceanic lithosphere between the central Atlantic and the Alpine Tethys, developed during the Middle–Late Jurassic. Our results support the proposed westward rollback of an oceanic east-dipping slab, which has continuity at least to the central Gulf of Cádiz.〈/span〉
    Print ISSN: 0091-7613
    Electronic ISSN: 1943-2682
    Topics: Geosciences
    Published by Geological Society of America (GSA)
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