“…Our results, supported by numerically integrating the nonlinear rate equations and performing linear stability analysis, reveals the following: (1) In principle a second threshold exists after which single mode operation becomes unstable, signaling multimode oscillatory dynamics, (2) For a wide range of design parameters, single mode operation of PT lasers having relatively large free spectral range (FSR) can be robust even at higher gain values, (3) PT symmetric photonic molecule lasers are more robust than their counterpart structures made of single microresonators; and (4) Extending the concept of single longitudinal mode operation based on PT symmetry in millimeter long edge emitting lasers having smaller FSR can be challenging due to instabilities induced by nonlinear modal interactions. …”
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“…The equations of motion from the finite element (FE) model of an overhung rotor system with a breathing crack are numerically integrated to obtain the whirl response. The transient whirl responses with different bearing conditions are thoroughly investigated for excitation of Po-BW. …”
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“…The algorithms we devise are orders of magnitude more accurate and efficient than stepping towards the steady-state using a standard numerical integrator. We seek to enhance a given network's nonlinear behavior by altering the eigenvalues of the graph Laplacian, i.e., the resonances of the linearized system. …”
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“…We found that both substrates with and without roughening pretreatment exhibited a coarse surface, whereas the roughening pretreatment could remove the original machined surface of the substrate and thus make the near surface with numerous integrated crystalline grains become the new topmost surface. …”
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“…The central fringe of (−1,−1) magnetically sensitive Ramsey transition can be predicted by using a numerical integrating of the magnetic field “map”. Comparing the predicted central fringe with that identified by Ramsey method, the frequency difference between these two is, at most, a fringe width of 0.3. …”
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“…Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.…”
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“…A particularly powerful approach uses data that consist of bi-allelic markers (e.g. single nucleotide polymorphism data) and allows for exact likelihood computations of phylogenetic networks while numerically integrating over all possible gene trees per marker. …”
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“…The AAL values were calculated here by numerically integrating loss-exceedance probability distributions to represent economic annual flood risk to the building, contents, and use. …”
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“…In computational neuroscience, hypotheses are often formulated as bottom-up mechanistic models of the systems in question, consisting of differential equations that can be numerically integrated forward in time. Candidate models can then be validated by comparison against experimental data. …”
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“…The resulting set of ordinary differential equations was numerically integrated to describe the time evolution of each cell subpopulation and the overall tumor growth. …”
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“…In addition, fiber tracts were created by numerically integrating the primary eigenvector field in the heart into coherent streamlines. …”
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“…The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Image: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Image: see text] , where [Image: see text] is the replica order. …”
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“…Caenorhabditis elegans and related Caenorhabditis spp. contain LTR retrotransposons and, as described here, numerous integrated viral genes including viral envelope genes that are part of LTR retrotransposons. …”
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“…These results confirm the peak detection capability of the proposed algorithm that satisfactorily predicts thermal peaks in the FRDM-KL26Z board as modeled with a finite element thermal analysis tool (the Numerical Integrated elements for System Analysis (NISA) tool), to gauge the level of local thermomechanical stresses that may be induced. …”
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“…In particular, we recorded numerous integrated solutions for EHR from the area of free and open-source software. …”
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“…The non-linearity that emerged from the convective terms was then treated using the Newton-Raphson method, while the numerical integrals were computed using a Gaussian quadrature rule with six quadrature points. …”
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“…How novel phenotypes evolve is challenging to imagine because traits are often underlain by numerous integrated phenotypic components, and changes to any one form can disrupt the function of the entire module. …”
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“…Generation of these tools has become increasingly efficient with the advent of numerous integration methods including transposon, CRISPR and recombinase-mediated integration. …”
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“…The greatest genetic variation among these strains is attributed to numerous integrated prophage and prophage-like elements, encoding several virulence factors. …”
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“…Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. …”
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