Journal articles: 'WKB Model'

1

Brink, D. M., and S. Klarsfeld. "WKB treatment of a simple two-dimensional fission model." Physical Review C 32, no. 5 (November 1, 1985): 1781–83. http://dx.doi.org/10.1103/physrevc.32.1781.

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Bokes, Pavol. "Heavy-tailed distributions in a stochastic gene autoregulation model." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (November 1, 2021): 113403. http://dx.doi.org/10.1088/1742-5468/ac2edb.

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Abstract Synthesis of gene products in bursts of multiple molecular copies is an important source of gene expression variability. This paper studies large deviations in a Markovian drift-jump process that combines exponentially distributed bursts with deterministic degradation. Large deviations occur as a cumulative effect of many bursts (as in diffusion) or, if the model includes negative feedback in burst size, in a single big jump. The latter possibility requires a modification in the WKB solution in the tail region. The main result of the paper is the construction, via a modified WKB scheme, of matched asymptotic approximations to the stationary distribution of the drift-jump process. The stationary distribution possesses a heavier tail than predicted by a routine application of the scheme.

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Mathur, Manikandan, Glenn S. Carter, and Thomas Peacock. "Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?" Journal of Physical Oceanography 46, no. 7 (July 2016): 2157–68. http://dx.doi.org/10.1175/jpo-d-15-0145.1.

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AbstractAn established analytical technique for modeling internal tide generation by barotropic flow over bottom topography in the ocean is the Green function–based approach. To date, however, for realistic ocean studies this method has relied on the WKB approximation. In this paper, the complete Green function method, without the WKB approximation, is developed and tested, and in the process, the accuracy of the WKB approximation for realistic ridge geometries and ocean stratifications is considered. For isolated Gaussian topography, the complete Green function approach is shown to be accurate via close agreement with the results of numerical simulations for a wide range of height ratios and criticality; in contrast, the WKB approach is found to be inaccurate for small height ratios in the subcritical regime and all tall topography that impinges on the pycnocline. Two ocean systems are studied, the Kaena and Wyville Thomson Ridges, for which there is again excellent agreement between the complete Green function approach and numerical simulations, and the WKB approximate solutions have substantial errors. This study concludes that the complete Green function approach, which is typically only modestly more computationally expensive than the WKB approach, should be the go-to analytical method to model internal tide generation for realistic ocean ridge scenarios.

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BOUCHERES, T., T. COLIN, B. NKONGA, B. TEXIER, and A. BOURGEADE. "STUDY OF A MATHEMATICAL MODEL FOR STIMULATED RAMAN SCATTERING." Mathematical Models and Methods in Applied Sciences 14, no. 02 (February 2004): 217–52. http://dx.doi.org/10.1142/s0218202504003222.

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We study a semiclassical modelization of the interaction of a laser with a mono-atomic gas. The Maxwell equations are coupled with a three-level version of the Bloch equations. Taking into account the specificities of the laser pulse and of the gas, we introduce small parameters and a dimensionless form of the equations. To describe stimulated Raman scattering, we perform a three-scale WKB expansion in the weakly nonlinear regime of geometric optics. The limit system is of Schrödinger–Bloch type. We prove a global existence result for this system and the convergence of its solution toward the solution of the initial Maxwell–Bloch equations, as the parameter of the WKB expansion goes to 0. We put in evidence Raman instability in the one-dimensional case, both theoretically and numerically.

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NAKAMURA, TAKASHI, and SHIN TAKAGI. "MACROSCOPIC QUANTUM NUCLEATION: WKB ANALYSIS OF 3+2−3 MODEL." Modern Physics Letters B 09, no. 10 (April 30, 1995): 591–99. http://dx.doi.org/10.1142/s0217984995000541.

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The Lifshitz–Kagan model of macroscopic quantum nucleation is re-examined. The nucleation rate originally proposed by Lifshitz and Kagan is shown to be inapplicable to ordinary laboratory experiments. This problem is circumvented by removing some of the unnecessary assumptions within the WKB approximation. It is also shown that fairly tight bounds on relevant physical parameters may be established without substantial assumptions.

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Nankali, Amir. "Application of the WKB method for an active cochlear model." Journal of the Acoustical Society of America 137, no. 4 (April 2015): 2205. http://dx.doi.org/10.1121/1.4920022.

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Nielsen, Rasmus, and Sergey Sorokin. "The WKB approximation for analysis of wave propagation in curved rods of slowly varying diameter." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2167 (July 8, 2014): 20130718. http://dx.doi.org/10.1098/rspa.2013.0718.

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The Wentzel–Kramers–Brillouin (WKB) approximation is applied for asymptotic analysis of time-harmonic dynamics of corrugated elastic rods. A hierarchy of three models, namely, the Rayleigh and Timoshenko models of a straight beam and the Timoshenko model of a curved rod is considered. In the latter two cases, the WKB approximation is applied for solving systems of two and three linear differential equations with varying coefficients, whereas the former case is concerned with a single equation of the same type. For each model, explicit formulations of wavenumbers and amplitudes are given. The equivalence between the formal derivation of the amplitude and the conservation of energy flux is demonstrated. A criterion of the validity range of the WKB approximation is proposed and its applicability is proved by inspection of eigenfrequencies of beams of finite length with clamped–clamped and clamped-free boundary conditions. It is shown that there is an appreciable overlap between the validity ranges of the Timoshenko beam/rod models and the WKB approximation.

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Demić, Aleksandar, Vitomir Milanović, Jelena Radovanović, and Milenko Musić. "WKB method for potentials unbounded from below." Modern Physics Letters B 30, no. 03 (January 28, 2016): 1650003. http://dx.doi.org/10.1142/s0217984916500032.

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Bound states degenerated in energy (and differing in parity) may form in one-dimensional quantum mechanics if the potential is unbounded from below. We focus on symmetric potential and present quasi-exactly solvable (QES) model based on WKB method. The application of this method is limited on slow-changing potentials. We consider the overlap integral of WKB wave functions [Formula: see text] and [Formula: see text] which correspond to energies [Formula: see text] and [Formula: see text], and by setting [Formula: see text], we determine the type of spectrum depending on parameter [Formula: see text] which arises from this method. For finite value [Formula: see text], we show that the entire spectrum will consist of degenerated bound states.

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Schenk, Andreas. "1D analytical model of the metal-semiconductor contact beyond the WKB approximation." Solid-State Electronics 37, no. 9 (September 1994): 1633–47. http://dx.doi.org/10.1016/0038-1101(94)90046-9.

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10

Wang, B. B., G. P. Zank, L. Adhikari, and L. L. Zhao. "On the Conservation of Turbulence Energy in Turbulence Transport Models." Astrophysical Journal 928, no. 2 (April 1, 2022): 176. http://dx.doi.org/10.3847/1538-4357/ac596e.

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Abstract Zank et al. developed models describing the transport of low-frequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Elsässar variables and then taking “moments” subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large, of order unity, or small. Here, we show explicitly that the three sets of turbulence transport models admit a conservation representation that resembles the well-known WKB transport equation for Alfvén wave energy density after introducing appropriate definitions of the “pressure” associated with the turbulent fluctuations. This includes introducing a distinct turbulent pressure tensor for 3D incompressible turbulence (the large plasma beta limit) and pressure tensors for quasi-2D and slab turbulence (the plasma beta order-unity or small regimes) that generalize the form of the WKB pressure tensor. Various limits of the different turbulent pressure tensors are discussed. However, the analogy between the conservation form of the turbulence transport models and the WKB model is not close for multiple reasons, including that the turbulence models express fully nonlinear physical processes unlike the strictly linear WKB description. The analysis presented here both serves as a check on the validity and correctness of the turbulence transport models and also provides greater transparency of the energy dissipation term and the “turbulent pressure” in our models, which is important for many practical applications.

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Dashevskaya, Elena I., Evgeny E. Nikitin, and Hans-Jürgen Troe. "Uniform Airy Approximation for Nonadiabatic Transitions in a Curve-Crossing Weak-Coupling Case." Zeitschrift für Physikalische Chemie 232, no. 3 (March 28, 2018): 311–23. http://dx.doi.org/10.1515/zpch-2017-1025.

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AbstractThis work suggests a connection between Landau-Zener transition probabilities between two crossing potentials in the classically accessible WKB regime and Landau-Lifshitz transition probabilities in the classically inaccessible WKB regime. It is based on the uniform Airy (UAi) approximation which represents a generalization of quantum transition probabilities for linear crossing potentials with constant coupling. The performance of the UAi approximation is tested by comparison with distorted-wave probabilities for an exponential potential model and illustrated for potentials that determine the intersection of twoab initiovibronic potential surfaces of the NO-Ar system.

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Krishnaswami, Govind S., and T. R. Vishnu. "Quantum Rajeev–Ranken model as an anharmonic oscillator." Journal of Mathematical Physics 63, no. 3 (March 1, 2022): 032101. http://dx.doi.org/10.1063/5.0079269.

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The Rajeev–Ranken (RR) model is a Hamiltonian system describing screw-type nonlinear waves of wavenumber k in a scalar field theory pseudodual to the 1 + 1D SU(2) principal chiral model. Classically, the RR model is Liouville integrable. Here, we interpret the model as a novel 3D cylindrically symmetric quartic oscillator with an additional rotational energy. The quantum theory has two dimensionless parameters. Upon separating variables in the Schrödinger equation, we find that the radial equation has a four-term recurrence relation. It is of type [0, 1, 16] and lies beyond the ellipsoidal Lamé and Heun equations in Ince’s classification. At strong coupling λ, the energies of highly excited states are shown to depend on the scaling variable λk. The energy spectrum at weak coupling and its dependence on k in a double-scaling strong coupling limit are obtained. The semi-classical Wentzel-Kramers-Brillouin (WKB) quantization condition is expressed in terms of elliptic integrals. Numerical inversion enables us to establish a ( λk)2/3 dispersion relation for highly energetic quantized “screwons” at moderate and strong coupling. We also suggest a mapping between our radial equation and the one of Zinn-Justin and Jentschura that could facilitate a resurgent WKB expansion for energy levels. In another direction, we show that the equations of motion of the RR model can also be viewed as Euler equations for a step-3 nilpotent Lie algebra. We use our canonical quantization to uncover an infinite dimensional reducible unitary representation of this nilpotent algebra, which is then decomposed using its Casimir operators.

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Rabei, Eqab M., and Mohammed Al Horani. "Quantization of fractional singular Lagrangian systems using WKB approximation." International Journal of Modern Physics A 33, no. 36 (December 30, 2018): 1850222. http://dx.doi.org/10.1142/s0217751x18502226.

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In this paper, the fractional singular Lagrangian system is studied. The Hamilton–Jacobi treatment is developed to be applicable for fractional singular Lagrangian system. The equations of motion are obtained for the fractional singular systems and the Hamilton–Jacobi partial differential equations are obtained and solved to determine the action integral. Then the wave function for fractional singular system is obtained. Besides, to demonstrate this theory, the fractional Christ-Lee model is discussed and quantized using the WKB approximation.

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Lim, Kian-Meng, and Charles R. Steele. "A three-dimensional nonlinear active cochlear model analyzed by the WKB-numeric method." Hearing Research 170, no. 1-2 (August 2002): 190–205. http://dx.doi.org/10.1016/s0378-5955(02)00491-4.

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TAILLEUX, RÉMI, and JAMES C. McWILLIAMS. "Energy propagation of long extratropical Rossby waves over slowly varying zonal topography." Journal of Fluid Mechanics 473 (December 10, 2002): 295–319. http://dx.doi.org/10.1017/s0022112002002422.

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In classical WKB theory the only way wave energy density, as a surrogate for wave action density, can increase or decrease along a ray is as a result of the ray focusing or widening. This occurs when the group velocity is divergent. There are particular regions, however, where the wave can resonantly exchange action with another wave mode with approximately the same wavenumbers; a situation known as Landau–Zener transition, mode conversion, linear (adiabatic) resonance, etc. This effect invalidates locally the underlying assumption of WKB theory that no scattering of energy occurs between WKB wave modes. In this paper this effect is investigated theoretically for free long baroclinic Rossby waves in a two-layer planetary geostrophic model of the ocean with a purely zonal topography, here taken as a Gaussian ridge. The waves are excited along the east coast by an unspecified wavemaker at a fixed frequency ω. In the computation considered, mode conversion is found to occur principally near the ridge’s top and on the eastern flank. The predictions of mode conversion theory are tested against the results of direct numerical simulations. This shows excellent agreement, both for the locations of mode conversion points, and for the amplitude of the transmitted and converted WKB wave modes.

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16

Gorman, Arthur D. "Dispersive waves and caustics." International Journal of Mathematics and Mathematical Sciences 8, no. 1 (1985): 93–107. http://dx.doi.org/10.1155/s0161171285000084.

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The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of linear, non-dispersive wave equations at turning points. The formalism is adapted to include those equations which model dispersive waves.

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Usmanov, Arcadi V., Melvyn L. Goldstein, Bruno P. Besser, and Johannes M. Fritzer. "A global MHD solar wind model with WKB Alfvén waves: Comparison with Ulysses data." Journal of Geophysical Research: Space Physics 105, A6 (June 1, 2000): 12675–95. http://dx.doi.org/10.1029/1999ja000233.

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PREMA, P., S. MAHADEVAN, C. S. SHASTRY, A. BHAGWAT, and Y. K. GAMBHIR. "STUDY OF ALPHA DECAY OF SUPER HEAVY ELEMENTS USING S-MATRIX AND WKB METHODS." International Journal of Modern Physics E 17, no. 04 (April 2008): 611–29. http://dx.doi.org/10.1142/s0218301308010039.

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A comparative study of the S-matrix and the WKB methods for the calculation of the half widths of alpha decay of super heavy elements is presented. The extent of the reliability of the WKB methods is demonstrated through simple illustrative examples. Detailed calculations have been carried out using the microscopic alpha-daughter potentials generated in the framework of the double-folding model using densities obtained in the relativistic mean field theories. We consider alpha-nucleus systems appearing in the decay chains of super heavy parent elements having A = 277, Z = 112 and A = 269, Z = 110. For negative and small positive log τ1/2 values the results from both methods are similar even though the S-matrix results should be considered to be more accurate. However, when log τ1/2 values are large and positive, the width associated with such state is infinitesimally small and hence calculation of such width by the S-matrix pole search method becomes a numerically difficult problem. We find that overall, the WKB method is reliable for the calculation of half lives of alpha decay from heavy nuclei.

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Maniccia, Giulia, Mariaveronica De Angelis, and Giovanni Montani. "WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings." Universe 8, no. 11 (October 25, 2022): 556. http://dx.doi.org/10.3390/universe8110556.

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In this review, we analyse different aspects concerning the possibility to separate a gravity-matter system into a part which lives close to a quasi-classical state and a “small” quantum subset. The considered approaches are all relying on a WKB expansion of the dynamics by an order parameter and the natural arena consists of the Bianchi universe minisuperspace. We first discuss how, limiting the WKB expansion to the first order of approximation, it is possible to recover for the quantum subsystem a Schrödinger equation, as written on the classical gravitational background. Then, after having tested the validity of the approximation scheme for the Bianchi I model, we give some applications for the quantum subsystem in the so-called “corner” configuration of the Bianchi IX model. We individualize the quantum variable in the small one of the two anisotropy degrees of freedom. The most surprising result is the possibility to obtain a non-singular Bianchi IX cosmology when the scenario is extrapolated backwards in time. In this respect, we provide some basic hints on the extension of this result to the generic cosmological solution. In the last part of the review, we consider the same scheme to the next order of approximation identifying the quantum subset as made of matter variables only. This way, we are considering the very fundamental problem of non-unitary morphology of the quantum gravity corrections to quantum field theory discussing some proposed reformulations. Instead of constructing the time dependence via that one of the classical gravitational variables on the label time as in previous works, we analyse a recent proposal to construct time by fixing a reference frame. This scheme can be reached both introducing the so-called “kinematical action”, as well as by the well-known Kuchar–Torre formulation. In both cases, the Schrödinger equation, amended for quantum gravity corrections, has the same morphology and we provide a cosmological implementation of the model, to elucidate its possible predictions.

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Snamina, Jacek. "Self-Excited Travelling Waves as a Model of Cable Galloping." Solid State Phenomena 177 (July 2011): 135–42. http://dx.doi.org/10.4028/www.scientific.net/ssp.177.135.

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In the paper the galloping phenomenon is modelled by self-excited waves travelling along the cable. The critical conditions of air flow and corresponding changes in the lift coefficient are presented. The motion of the cable was described in relation to equilibrium configuration. Since the wavelengths are small with reference to considered distances and additionally the tension and curvature of equilibrium line of the cable are slowly varying functions of the arc co-ordinate, the problems concerning the travelling waves can be solved using the Wentzel-Kramers-Brillouin (WKB) method. Using this method the equations describing wave numbers and amplitudes of waves were derived. The results of the calculations of amplitudes are presented in the form of plots.

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LI, GU-QIANG. "WKB APPROXIMATION AND EFFECT OF SPIN ON THE BLACK HOLE ENTROPY." International Journal of Modern Physics A 22, no. 28 (November 10, 2007): 5229–35. http://dx.doi.org/10.1142/s0217751x07037305.

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The black hole entropy due to spin fields are calculated by using brick-wall model. The appearance of the logarithmic terms is demonstrated and we specially deal with the subleading logarithmic term which exists for any spin fields. It is shown that the subleading logarithmic term is related to the use of WKB approximation but it usually includes not only a quadratic term and a linear term of the spin but also a zero-power term of the spin.

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Koyuncu, F., A. Soylu, and O. Bayrak. "Binary cluster model calculations for 20Ne and 44Ti nuclei." Modern Physics Letters A 32, no. 09 (March 20, 2017): 1750050. http://dx.doi.org/10.1142/s021773231750050x.

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The elastic scattering data of [Formula: see text] and [Formula: see text] systems at [Formula: see text] = 32.2–146 MeV and [Formula: see text] = 24.1–49.5 MeV energies have been analyzed with double-folding (DF) potential in optical model formalism in order to investigate the cluster structures of [Formula: see text]Ne and [Formula: see text]Ti nuclei. The deduced DF potentials between [Formula: see text] and [Formula: see text]O as well as [Formula: see text] and [Formula: see text]Ca have been used for obtaining the excitation energies and [Formula: see text]-decay widths of [Formula: see text]Ne and [Formula: see text]Ti in Gamow code, but the reasonable results could not be obtained. Thus, the real parts of DF potentials which are in the best agreement with experimental data have been fitted with the squared-Woods–Saxon (WS2) potential parameters to calculate the [Formula: see text]-decay widths of [Formula: see text]Ne and [Formula: see text]Ti with Wentzel–Kramers–Brillouin (WKB) approach. The nuclear potential sets obtained in WKB calculations are also used for Gamow code calculations. We take into account the deformation and orientation of [Formula: see text]Ca nucleus to examine their influence on both the excitation energies and decay widths of [Formula: see text]Ti. Besides, by using the binary cluster model the rotational band energies and electromagnetic transition probabilities (BE2)s according to angles are also reproduced for both nuclei. The obtained results showed that the binary cluster model is very useful to understand the observables of [Formula: see text]Ne and [Formula: see text]Ti nuclei. Although only spherical calculations are made for [Formula: see text]Ne ([Formula: see text] + [Formula: see text]O), the deformation in [Formula: see text]Ca would be important for the understanding of [Formula: see text]Ti ([Formula: see text] + [Formula: see text]Ca) cluster structure. The mechanism presented here would also be applied to understand the cluster structures in heavy nuclei.

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Ohkuwa, Y., and T. Kitazoe. "Wave Packet in Quantum Cosmology and Definition of Semiclassical Time." International Journal of Modern Physics A 12, no. 05 (February 20, 1997): 859–71. http://dx.doi.org/10.1142/s0217751x97000657.

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We consider a quantum cosmology with a massless background scalar field ϕB and adopt a wave packet as the wave function. This wave packet is a superposition of the WKB form wave functions, each of which has a definite momentum of the scalar field ϕB. In this model it is shown that to trace the formalism of the WKB time is seriously difficult without introducing a complex value for a time. We define a semiclassical real time variable TP from the phase of the wave packet and calculate it explicitly. We find that, when a quantum matter field ϕQ is coupled to the system, an approximate Schrödinger equation for ϕQ holds with respect to TP in a region where the size a of the universe is large and |ϕB| is small.

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Bokes, Pavol, Alessandro Borri, Pasquale Palumbo, and Abhyudai Singh. "Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach." Journal of Mathematical Biology 81, no. 1 (June 24, 2020): 343–67. http://dx.doi.org/10.1007/s00285-020-01512-y.

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Övgün, Ali, Wajiha Javed, and Riasat Ali. "Tunneling Glashow-Weinberg-Salam Model Particles from Black Hole Solutions in Rastall Theory." Advances in High Energy Physics 2018 (July 18, 2018): 1–11. http://dx.doi.org/10.1155/2018/3131620.

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Using the semiclassical WKB approximation and Hamilton-Jacobi method, we solve an equation of motion for the Glashow-Weinberg-Salam model, which is important for understanding the unified gauge-theory of weak and electromagnetic interactions. We calculate the tunneling rate of the massive charged W-bosons in a background of electromagnetic field to investigate the Hawking temperature of black holes surrounded by perfect fluid in Rastall theory. Then, we study the quantum gravity effects on the generalized Proca equation with generalized uncertainty principle (GUP) on this background. We show that quantum gravity effects leave the remnants on the Hawking temperature and the Hawking radiation becomes nonthermal.

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Ardani, Samira, and James M. Kaihatu. "A MODEL IN FREQUENCY DOMAIN FOR TRANSFORMATION OF FULLY DISPERSIVE NONLINEAR WAVES." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 60. http://dx.doi.org/10.9753/icce.v36.papers.60.

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In this study, mathematical derivation and numerical verification of a wave transformation model in frequency domain is discussed. This wave model is fully dispersive and nonlinear; and is derived based on the WKB assumptions. Transforming the problem into the frequency domain and using multiple scale analysis in space and perturbation theory, the model is expanded up to second order in wave steepness. This fully dispersive nonlinear wave model is a set of evolution equations which explicitly contains quadratic near-resonant interactions. The comparison between the presented model, the existing fully dispersive model and a nearshore model with different set of laboratory and field data shows that the presented model provides significant improvements particularly at higher frequencies.

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Miller, C. E. "VLFEM Analysis of a Two-Dimensional Cochlear Model." Journal of Applied Mechanics 52, no. 4 (December 1, 1985): 743–51. http://dx.doi.org/10.1115/1.3169140.

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A hybrid technique named here the Very Large Finite Element Method (VLFEM) is developed to analyze a two-dimensional model of the cochlea of the inner ear. In this method, the domain is divided into elements of constant material properties and the exact solution to the model equations obtained in each element. This involves two forms of eigenexpansion, allowing a one-dimensional instead of two-dimensional discretization. The discretization is related to the rate of change of the wavenumber of traveling waves on the elastic partition, producing an optimal mesh spacing. A full characterization of the multiple complex wavenumbers is obtained. The results of this analysis for partition (basilar membrane) amplitude and phase exactly correspond to those from previous finite difference and finite element analyses, but less computing effort is required for the same accuracy of results. Reflected waves, abrupt changes in material properties, and arbitrary boundary conditions pose no difficulties for VLFEM analysis, an advantage over the WKB (or LG) technique used previously on this problem.

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Sakurai, T., O. Kitayama, and J. Ma. "Analytical model of the phase mixing phenomena by the use of the wkb method of solution." Geophysical & Astrophysical Fluid Dynamics 79, no. 1-4 (August 1995): 277–87. http://dx.doi.org/10.1080/03091929508229001.

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Wirth, Volkmar. "Waveguidability of idealized midlatitude jets and the limitations of ray tracing theory." Weather and Climate Dynamics 1, no. 1 (April 2, 2020): 111–25. http://dx.doi.org/10.5194/wcd-1-111-2020.

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Abstract. Ray paths of stationary Rossby waves emanating from a local midlatitude source are usually refracted equatorward. However, this general tendency for equatorward propagation is mitigated by the presence of a midlatitude jet that acts as a zonal waveguide. This opens up the possibility of circum-global teleconnections and quasi-resonance, which suggests that the ability to guide a wave in the zonal direction is an important jet property. This paper investigates waveguidability of idealized midlatitude jets in a barotropic model on the sphere. A forced-dissipative model configuration with a local source for Rossby waves is used in order to quantify waveguidability by diagnosing the latitudinal distribution of waviness in a longitudinal sector far downstream of the forcing. Systematic sensitivity experiments show that waveguidability increases smoothly with increasing jet amplitude and with decreasing jet width. This result is contrasted with the predictions from two idealized theoretical concepts based on (1) ray tracing as derived from Wentzel–Kramers–Brillouin (WKB) theory and (2) a sharp jet with a zonally oriented front of potential vorticity. The existence of two so-called turning latitudes, which is the key diagnostic for a zonal waveguide according to ray tracing theory, turns out to be a poor predictor for the dependence of waveguidability on jet amplitude and jet width obtained in the numerical simulations. By contrast, the meridional gradient of potential vorticity correlates fairly well with the diagnosed waveguidability. The poor predictions from ray tracing are not surprising, because the underlying WKB assumptions are not satisfied in the current context. The failure of WKB is traced back to the properties of the underlying equations, and a heuristic argument is presented to elucidate the potential of the potential vorticity (PV) gradient to act as a proxy for waveguidability.

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Novikov, Oleg. "Inhomogeneous perturbations in the pseudo-Hermitian quantum cosmology." EPJ Web of Conferences 191 (2018): 07005. http://dx.doi.org/10.1051/epjconf/201819107005.

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We consider the quantum cosmology of the phantom fields within the Wheeler-DeWitt approach using the classically equivalent model with complex potential. The Born-Oppenheimer approximation is used to study the behaviour of the inhomogeneous perturbations over the minisuperspace background. The evolution Hamiltonian is treated as a pseudo-Hermitian one and the conserved inner product is constructed within WKB approximation of the homogeneous wavefunction.

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Saidi, F., M. R. Oudih, M. Fellah, and N. H. Allal. "Cluster decay investigation within a modified Woods–Saxon potential." Modern Physics Letters A 30, no. 30 (September 7, 2015): 1550150. http://dx.doi.org/10.1142/s0217732315501503.

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The cluster decay process is studied in the WKB approximation based on the unified fission model. The cluster is considered to be emitted by tunneling through a potential barrier taken as the sum of the Coulomb potential, the centrifugal potential and the modified Woods–Saxon (MWS) nuclear potential. The results of our calculations are compared to those obtained by other theoretical models as well as experimental data. It is shown that the unified fission model with the MWS nuclear potential can be successfully used to evaluate the cluster decay half-lives of heavy nuclei.

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Manjunatha, H. C., G. R. Sridhar, N. Sowmya, P. S. Damodara Gupta, and H. B. Ramalingam. "A systematic study of alpha decay in actinide nuclei using modified generalized liquid drop model." International Journal of Modern Physics E 30, no. 02 (February 2021): 2150013. http://dx.doi.org/10.1142/s0218301321500130.

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The alpha decay half-lives of actinides within modified generalized liquid drop model (MGLDM) are investigated by the Wentzel–Kramers–Brillouin (WKB) barrier penetration probability. The potential barrier was studied taking in to account of nuclear proximity, coulomb interaction and centrifugal potential with the inclusion of angular momentum. This work predicts the alpha decay half-lives of unknown actinide nuclei such as [Formula: see text]Am, [Formula: see text]Cm, [Formula: see text]Bk, [Formula: see text]Es and [Formula: see text]No. The calculated alpha decay half-lives reproduce accurately the experimental data. The predictions provided for the alpha decay half-lives within the MGLDM may be helpful for identifying the new isotopes in this field.

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Samelson, R. M., and J. Pedlosky. "Local baroclinic instability of flow over variable topography." Journal of Fluid Mechanics 221 (December 1990): 411–36. http://dx.doi.org/10.1017/s0022112090003615.

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Local baroclinic instability is studied in a two-layer quasi-geostrophic model. Variable meridional bottom slope controls the local supercriticality of a uniform zonal flow. Solutions are found by matching pressure, velocity, and upper-layer vorticity across longitudes where the bottom slope changes abruptly so as to destabilize the flow in a central interval of limited zonal extent. In contrast to previous results from heuristic models, an infinite number of modes exist for arbitrarily short intervals. For long intervals, modal growth rates and frequencies approach the numerical and WKB results for the most unstable mode. For intervals of length comparable to and smaller than the wavelengths of unstable waves in the homogeneous problem, the WKB results lose accuracy. The modes retain large growth rates (about half maximum) for intervals as short as the internal deformation radius. Evidently, the deformation radius and not the homogeneous instability determines the fundamental scale for local instability. Maximum amplitudes occur near the downstream edge of the unstable interval. Lower-layer amplitudes decay downstream more rapidly than upper-layer amplitudes. For short intervals, the instability couples motions with widely disparate horizontal scales in the upper and lower layers. Heat flux is more strictly confined than amplitude. Growth rates increase linearly with weak supercriticality.

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Sahu, Sanjeev Anand, Juhi Baroi, A. Chattopadhyay, and Sonal Nirwal. "Characterization of Polarized Shear Waves in FGPM Composite Structure with Imperfect Boundary: WKB Method." International Journal of Applied Mechanics 11, no. 09 (November 2019): 1950083. http://dx.doi.org/10.1142/s1758825119500832.

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Propagation behavior of horizontally polarized shear waves (SH-waves) in a piezo-composite structure is discussed, using the Wentzel–Kramers–Brillouin (WKB) method. The considered model is made by combining the Functionally Graded Piezoelectric Material (FGPM) layer and piezoelectric orthotropic substrate. The linear form spring model is considered to delineate the imperfection of interface. Moreover, the material properties of FGPM layer are varying linearly along the thickness direction. Dispersion relation is obtained for both electrically open and short cases. Numerical example and graphical representation have been provided to illustrate the effect of different parameters on the phase velocity of SH-waves. As a special case, dispersion relation has been obtained when the boundary is perfect. Results are compared for different orthotropic materials to add more specific observations. Finally, the outcome of this study is validated by matching it with classical Love wave result. Observations will be helpful in optimization of Love wave sensors and Surface Acoustic Wave (SAW) devices.

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Syahroni, Edy, A. Suparmi, and C. Cari. "The Determination of the Spectrum Energy on the model of DNA-protein interactions using WKB approximation method." Journal of Physics: Conference Series 795 (January 2017): 012027. http://dx.doi.org/10.1088/1742-6596/795/1/012027.

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NEC, YANA. "Explicitly solvable eigenvalue problem and bifurcation delay in sub-diffusive Gierer–Meinhardt model." European Journal of Applied Mathematics 27, no. 5 (January 29, 2016): 699–725. http://dx.doi.org/10.1017/s0956792516000012.

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A spike solution is constructed on the infinite line for a sub-diffusive version of the Gierer–Meinhardt reaction – diffusion model. A non-local eigenvalue problem governs the spike's stability and is explicitly solvable for a certain choice of the kinetic parameters. Its solution generalises former results for the Gierer–Meinhardt model with regular diffusion, and the normal and anomalous systems' properties are juxtaposed. It is shown that a Hopf bifurcation occurs in the sub-diffusive system for larger values of the time parameter τo as compared to the normal counterpart, rendering the anomalous system more stable. Asymptotic solutions are obtained near important values of the diffusion anomaly index γ and collectively shown to be valid over most of the applicable range 0 < γ < 1. A bifurcation delay scenario is described for the sub-diffusive system, and the WKB exponent is computed analytically.

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Ebert, Marcelo Rempel, and Michael Reissig. "Theory of damped wave models with integrable and decaying in time speed of propagation." Journal of Hyperbolic Differential Equations 13, no. 02 (June 2016): 417–39. http://dx.doi.org/10.1142/s0219891616500132.

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We study the Cauchy problem for damped wave equations with a time-dependent propagation speed and dissipation. The model of interest is [Formula: see text] We assume [Formula: see text]. Then we propose a classification of dissipation terms in non-effective and effective. In each case we derive estimates for kinetic and elastic type energies by developing a suitable WKB analysis. Moreover, we show optimality of results by the aid of scale-invariant models. Finally, we explain by an example that in some estimates a loss of regularity appears.

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Zhao, Liang, Wei Min Bao, and Chun Ye Gong. "An Overview of the Research of Plasma Sheath." Advanced Materials Research 1049-1050 (October 2014): 1518–21. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.1518.

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The plasma sheath can be regarded as a model of a phenomenon of spacecraft reentry or hypersonic vehicles and causes so called radio blackout, which interferes with radio signals. This paper gives a survey on several aspects of plasma sheath, including the characteristic of plasma sheath, experiments to deal with the blackout and numerical solutions. The numerical methods includes WKB, finite-difference time-domain method, particle-in-cell method, CFD based method and Monte Carlo method. Some discussions are also presented.

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ERICH ORMAND, W. "NUCLEAR PHYSICS WITH STATISTICS." International Journal of Modern Physics E 14, no. 01 (February 2005): 67–74. http://dx.doi.org/10.1142/s0218301305002783.

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Properties of shell model Hamiltonians, and in particular the tri-diagonal matrices obtained with the Lanczos procedure are exploited to determine the density of states and to estimate the ground-state energies. It will be shown that with a few parameters that are adjusted to the moments up to fourth order of the Hamiltonian, one can model the resultant tri-diagonal matrices. An estimate of the ground state energy can quickly be obtained from the modeled matrices, and the density of states for the full matrix can quickly be obtained using the WKB approximation. The accuracy of the ground state is dependent on high moments, six and greater.

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CHUNG, S. G. "SOLITON THEORY FOR CLASSICAL STATISTICAL MECHANICS OF THE MASSIVE-THIRRING-SINE-GORDON MODEL." International Journal of Modern Physics B 08, no. 18 (August 15, 1994): 2447–88. http://dx.doi.org/10.1142/s0217979294000981.

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This paper reviews soliton theories for classical statistical mechanics of the massive-Thirring-sine-Gordon model. These theories attempt not only to reproduce the classical transfer matrix method result but also to provide thermodynamic information about exact nonlinear excitations of the model. Three theories are discussed. Firstly, the soliton–gas phenomenology which is successful in the Toda lattice is shown to be not even approximately correct for the sine-Gordon model. This breakdown is due to the incorrect counting of the number of degrees of freedom. Secondly, the soliton–phonon theory which reproduces the WKB result is also shown to be not exact. This non-exactness is ascribed to the fact that the nonlinear phonons are not exact elementary excitations in the model. Thirdly, a non-gas phenomenological soliton–breather theory is derived as a classical limit of quantum statistical mechanics of the model. The exactness of the last theory is demonstrated through an accurate numerical analysis of its basic equations.

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Shigaki, Takahiro. "Exact WKB Analysis of Eigenvalue Problems for an Ordinary Differential Equation Arising from the Mathematical Model of Mesons." Funkcialaj Ekvacioj 66, no. 2 (August 15, 2023): 125–57. http://dx.doi.org/10.1619/fesi.66.125.

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Ijichi, Takashi, and Toshiyuki Hibiya. "Eikonal Calculations for Energy Transfer in the Deep-Ocean Internal Wave Field near Mixing Hotspots." Journal of Physical Oceanography 47, no. 1 (January 2017): 199–210. http://dx.doi.org/10.1175/jpo-d-16-0093.1.

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AbstractIn the proximity of mixing hotspots in the deep ocean, the observed internal wave spectra are usually distorted from the Garrett–Munk (GM) spectrum and are characterized by the high energy level E as well as a shear–strain ratio Rω quite different from that of the GM spectrum. On the basis of the eikonal theoretical model, Ijichi and Hibiya (IH) recently proposed the revised finescale parameterization of turbulent dissipation rates in the distorted internal wave field, although the vertical velocity associated with background internal waves and the strict WKB scale separation, for example, were not taken into account. To see the effects of such simplifying assumptions on the revised parameterization, this study carries out a series of eikonal calculations for energy transfer through various internal wave spectra distorted from the GM. Although the background vertical velocity and the strict WKB scale separation somewhat affect the calculated energy transfer rates, their parameter dependence is confirmed as expected; the calculated energy transfer rates ε follow the basic scaling ε ∝ E2N2f with the local buoyancy frequency N and the local inertial frequency f and exhibit strong Rω dependence quite similar to that predicted by IH.

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Shojaei, Mohammad Reza, Maryam Amini, and Niloufar Zoghi-Foumani. "A New Approach for Parameters of Nucleon-Nucleon Scattering at Low Energies in One and Two Dimensions." International Frontier Science Letters 3 (January 2015): 1–10. http://dx.doi.org/10.18052/www.scipress.com/ifsl.3.1.

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Many of the important properties of multi-nucleon systems can be found by studying the nucleon- nucleon interactions. In this work, a suitable central and an appropriate noncentral potential have been used to study nucleon- nucleon scattering in one and two dimensions. The phase shift, scattering cross section, length and amplitude are calculated using the Nikiforov-Uvarov (NU) method and WKB approximation. Comparison between the results of the suggested model in this article and the experimental reported values indicates that there is a good consistency between them.

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Iurov, Andrii, Liubov Zhemchuzhna, Godfrey Gumbs, and Danhong Huang. "Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene." Applied Sciences 13, no. 10 (May 16, 2023): 6095. http://dx.doi.org/10.3390/app13106095.

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In this paper, we have constructed a WKB approximation for graphene having a Y-shaped Kekulé lattice distortion and a special folding of the K and K′ valleys, which leads to very specific linear energy dispersions with two non-equivalent pairs of subbands. These obtained semi-classical results, which include the action, electron momentum and wave functions, are utilized to analyze the dynamics of electron tunneling through non-square potential barriers. In particular, we explore resonant scattering of an electron by a potential barrier built on Kekulé-distorted graphene. Mathematically, a group of consecutive equations for a semi-classical action have been solved by following a perturbation approach under the condition of small strain-induced coupling parameter Δ0≪1 (a good fit to its actual value Δ0∽ 0.1). Specifically, we consider a generalized model for Kek-Y graphene with two arbitrary Fermi velocities. The dependence of the electron transmission amplitude on the potential profile V(x) and band parameters of Kekulé-patterned graphene has been explored and analyzed in detail.

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Li, Ping, Rui Jiang, Jian Lv, and Xianghua Zhai. "Scalar Perturbations of Black Holes in the f(R)=R−2αR Model." Universe 8, no. 1 (January 12, 2022): 47. http://dx.doi.org/10.3390/universe8010047.

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In this paper, we study the perturbations of the charged static spherically symmetric black holes in the f(R)=R−2αR model by a scalar field. We analyze the quasinormal modes spectrum, superradiant modes, and superradiant instability of the black holes. The frequency of the quasinormal modes is calculated in the frequency domain by the third-order WKB method, and in the time domain by the finite difference method. The results by the two methods are consistent and show that the black hole stabilizes quicker for larger α satisfying the horizon condition. We then analyze the superradiant modes when the massive charged scalar field is scattered by the black hole. The frequency of the superradiant wave satisfies ω∈(μ2,ωc), where μ is the mass of the scalar field, and ωc is the critical frequency of the superradiance. The amplification factor is also calculated by numerical method. Furthermore, the superradiant instability of the black hole is studied analytically, and the results show that there is no superradiant instability for such a system.

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Soylu, A. "Semi-classical calculations of the α decay half-lives for even–even nuclei." International Journal of Modern Physics E 28, no. 06 (June 2019): 1950042. http://dx.doi.org/10.1142/s0218301319500423.

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The half-lives of the [Formula: see text] decay for even–even nuclei having [Formula: see text] (164 nuclei) have been calculated by using the Wentzel–Kramers–Brillouin (WKB) method together Bohr–Sommerfeld (BS) quantization condition for cosh potential in two-different forms with and without the isospin effects for six different parameter sets. By comparing the obtained results with the experimental values, the rms deviations have been computed. It is obtained that when the cosh potential is used in 2 different type forms, the rms values are also changed and the better one for obtaining the half-lives is cosh-2 form. Even if the isospin-dependent potential does not have so much effect on rms values in this sort of WKB with BS calculations with cosh potential forms, considering the isospin effect together the isospin-dependent nuclear diffuseness parameter have a strong influence on the rms values. New hindrance factor formula based on liquid drop model was used in order to show the influence of hindrance factor on the [Formula: see text] decay half-lives. It is pointed out that this new function of the hindrance factor does not depend on the magic numbers, it contains fewer free parameters and using of this improves the calculations positively. New estimates by using present model have also been made for even–even nuclei having with [Formula: see text] which do not have the measured [Formula: see text] decay half-lives yet and they have been compared the results of the ImSahu model. The present results would provide useful information and knowledge for the explanation of half-lives of [Formula: see text] decay of nuclei and future possible experimental studies.

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Anacleto, M. A., F. A. Brito, S. S. Cruz, and E. Passos. "Noncommutative correction to the entropy of Schwarzschild black hole with GUP." International Journal of Modern Physics A 36, no. 03 (January 29, 2021): 2150028. http://dx.doi.org/10.1142/s0217751x21500287.

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In this paper we study through tunneling formalism, the effect of noncommutativity to Hawking radiation and the entropy of the noncommutative Schwarzschild black hole. In our model we have considered the noncommutativity implemented via the Lorentzian distribution. We obtain noncommutative corrections to the Hawking temperature using the Hamilton–Jacobi method and the Wentzel–Kramers–Brillouin (WKB) approximation. In addition, we found corrections of the logarithmic and other types due to noncommutativity and quantum corrections from the generalized uncertainty principle (GUP) for the entropy of the Schwarzschild black hole.

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BOGOJEVIĆ, A. R. "SYMMETRY BREAKING AS A CONSEQUENCE OF STABILIZATION OF A BOTTOMLESS THEORY." Modern Physics Letters A 06, no. 22 (July 20, 1991): 2009–18. http://dx.doi.org/10.1142/s0217732391002177.

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The Greensite–Halpern stabilization technique is applied to d = 0 Euclidean field theories. The effective action is calculated using WKB as well as a variational approach. For a set of free theories with non-trivial measure the effective action is computed exactly, and a comparison is made with the results of approximate techniques. The effect of stabilization on the measure is to bring in a "centrifugal barrier" term that breaks parity invariance. A model with quartic interaction of wrong sign is also analyzed in the limit of large coupling.

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Chen, Wenhui, and Yan Liu. "Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I." Journal of Mathematical Physics 64, no. 2 (February 1, 2023): 021504. http://dx.doi.org/10.1063/5.0099622.

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In this paper, we are interested in the Cauchy problem for the viscoelastic damped wave equation with memory of type I. By applying the WKB analysis and the Fourier analysis, we explain the memory’s influence on dissipative structures and asymptotic profiles of solutions to the model with additionally weighted L1 initial data. Furthermore, concerning standard energy and the solution itself, we establish the singular limit between the dissipative Moore–Gibson–Thompson equation with memory and the viscoelastic damped wave equation with memory, where a crucial compatibility condition of the initial datum is found.

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Alarcón, Tomás, and Karen M. Page. "Mathematical models of the VEGF receptor and its role in cancer therapy." Journal of The Royal Society Interface 4, no. 13 (November 21, 2006): 283–304. http://dx.doi.org/10.1098/rsif.2006.0170.

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We present an analysis of a stochastic model of the vascular endothelial growth factor (VEGF) receptor. This analysis addresses the contribution of ligand-binding-induced oligomerization, activation of src-homology 2 domain-carrying kinases and receptor internalization in the overall behaviour of the VEGF/VEGF receptor (VEGFR) system. The analysis is based upon a generalization of a Wentzel–Kramers–Brillouin (WKB) approximation of the solution of the corresponding master equation. We predict that tumour-mediated overexpression of VEGFRs in the endothelial cells (ECs) of tumour-engulfed vessels leads to an increased sensitivity of the ECs to low concentrations of VEGF, thus endowing the tumour with increased resistance to anti-angiogenic treatment.

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Journal articles on the topic 'WKB Model'

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