The Experts below are selected from a list of 33216 Experts worldwide ranked by ideXlab platform
Jiqiang Zheng - One of the best experts on this subject based on the ideXlab platform.
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focusing nls with Inverse Square potential
Journal of Mathematical Physics, 2018Co-Authors: Jiqiang ZhengAbstract:In this paper, we utilize Dodson-Murphy’s method to establish the radial scattering result for the focusing nonlinear Schrodinger equation with Inverse Square potential i∂tu−Lau=−|u|p−1u in the energy space Ha1(Rd) in dimensions d ≥ 3, which extends our previous result to higher dimensional cases but with radial initial data. The new ingredient is to establish the dispersive estimate for radial functions and overcome the weak dispersive estimate when a < 0.
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focusing nls with Inverse Square potential
arXiv: Analysis of PDEs, 2018Co-Authors: Jiqiang ZhengAbstract:In this paper, we utilize the method in Dodson-Murphy [4] to establish the radial scattering result for the focusing nonlinear Schrodinger equation with Inverse Square potential $i\pa_tu-\la u=-|u|^{p-1}u$ in the energy space $H^1_a(\R^d)$ in dimensions $d\geq3$, which extends the result of [10,11] to higher dimensions cases but with radial initial data. The new ingredient is to establish the dispersive estimate for radial function and overcome the weak dispersive estimate when $a<0$.
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sobolev spaces adapted to the schrodinger operator with Inverse Square potential
Mathematische Zeitschrift, 2018Co-Authors: Rowan Killip, Changxing Miao, Junyong Zhang, Monica Visan, Jiqiang ZhengAbstract:We study the $$L^p$$ -theory for the Schrodinger operator $$\mathcal L_a$$ with Inverse-Square potential $$a|x|^{-2}$$ . Our main result describes when $$L^p$$ -based Sobolev spaces defined in terms of the operator $$(\mathcal L_a)^{s/2}$$ agree with those defined via $$(-\Delta )^{s/2}$$ . We consider all regularities $$0
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the energy critical nls with Inverse Square potential
Discrete and Continuous Dynamical Systems, 2017Co-Authors: Rowan Killip, Changxing Miao, Junyong Zhang, Monica Visan, Jiqiang ZhengAbstract:We consider the defocusing energy-critical nonlinear Schrodinger equation with Inverse-Square potential \begin{document}$iu_t = -Δ u + a|x|^{-2}u + |u|^4u$\end{document} in three space dimensions. We prove global well-posedness and scattering for \begin{document}$a > - \frac{1}{4} + \frac{1}{{25}}$\end{document} . We also carry out the variational analysis needed to treat the focusing case.
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the focusing cubic nls with Inverse Square potential in three space dimensions
Differential and Integral Equations, 2017Co-Authors: Rowan Killip, Monica Visan, Jason Murphy, Jiqiang ZhengAbstract:We consider the focusing cubic nonlinear Schrodinger equation with Inverse-Square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts, Holmer, and Roudenko for the standard focusing cubic NLS [7, 11]. We also prove failure of uniform space-time bounds at the
Dmitry S. Shkirmanov - One of the best experts on this subject based on the ideXlab platform.
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Extended Grimus-Stockinger theorem and Inverse Square law violation in quantum field theory
The European Physical Journal C, 2013Co-Authors: Vadim A. Naumov, Dmitry S. ShkirmanovAbstract:We study higher-order corrections to the Grimus-Stockinger theorem dealing with the large-distance asymptotic behavior of the wave-packet modified neutrino propagator within the framework of field-theoretical description of the neutrino oscillation phenomenon. We discuss the possibility that these corrections are responsible for breakdown of the classical Inverse-Square law (ISL) at the macroscopic distances. In particular the ISL violation can be an explanation of the well-known reactor antineutrino anomaly.
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extended grimus stockinger theorem and Inverse Square law violation in quantum field theory
European Physical Journal C, 2013Co-Authors: Vadim A. Naumov, Dmitry S. ShkirmanovAbstract:We study corrections to the Grimus–Stockinger theorem dealing with the large-distance asymptotic behavior of the external wave-packet modified neutrino propagator within the framework of a field-theoretical description of the neutrino-oscillation phenomenon. The possibility is discussed that these corrections, responsible for breakdown of the classical Inverse-Square law (ISL), can lead to measurable effects at small but macroscopic distances accessible in the SBL (anti)neutrino experiments and in particular can provide an explanation of the well-known reactor antineutrino anomaly.
Raphael Voituriez - One of the best experts on this subject based on the ideXlab platform.
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reply to comment on Inverse Square levy walks are not optimal search strategies for d 2
Physical Review Letters, 2021Co-Authors: Nicolas Levernier, O Benichou, Johannes Textor, Raphael VoituriezAbstract:We refute here the concernes raised in the Comment of our letter. This reply states clearly the validity range of our results and shows that the optimality of Inverse-Square Levy walks at the basis of the Levy flight foraging hypothesis is generically unfounded. We also give the precise set of conditions for which Inverse-levy Square Levy walks turn to be optimal, conditions which are unlikely to be verified biologically.
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Inverse Square levy walks are not optimal search strategies for d 2
Physical Review Letters, 2020Co-Authors: Nicolas Levernier, O Benichou, Johannes Textor, Raphael VoituriezAbstract:The Levy hypothesis states that Inverse Square Levy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets. It has served as a theoretical basis to interpret a wealth of experimental data at various scales, from molecular motors to animals looking for resources, putting forward the conclusion that many living organisms perform Levy walks to explore space because of their optimal efficiency. Here we provide analytically the dependence on target density of the encounter rate of Levy walks for any space dimension d; in particular, this scaling is shown to be independent of the Levy exponent α for the biologically relevant case d≥2, which proves that the founding result of the Levy hypothesis is incorrect. As a consequence, we show that optimizing the encounter rate with respect to α is irrelevant: it does not change the scaling with density and can lead virtually to any optimal value of α depending on system dependent modeling choices. The conclusion that observed Inverse Square Levy patterns are the result of a common selection process based purely on the kinetics of the search behavior is therefore unfounded.
Vadim A. Naumov - One of the best experts on this subject based on the ideXlab platform.
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Extended Grimus-Stockinger theorem and Inverse Square law violation in quantum field theory
The European Physical Journal C, 2013Co-Authors: Vadim A. Naumov, Dmitry S. ShkirmanovAbstract:We study higher-order corrections to the Grimus-Stockinger theorem dealing with the large-distance asymptotic behavior of the wave-packet modified neutrino propagator within the framework of field-theoretical description of the neutrino oscillation phenomenon. We discuss the possibility that these corrections are responsible for breakdown of the classical Inverse-Square law (ISL) at the macroscopic distances. In particular the ISL violation can be an explanation of the well-known reactor antineutrino anomaly.
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extended grimus stockinger theorem and Inverse Square law violation in quantum field theory
European Physical Journal C, 2013Co-Authors: Vadim A. Naumov, Dmitry S. ShkirmanovAbstract:We study corrections to the Grimus–Stockinger theorem dealing with the large-distance asymptotic behavior of the external wave-packet modified neutrino propagator within the framework of a field-theoretical description of the neutrino-oscillation phenomenon. The possibility is discussed that these corrections, responsible for breakdown of the classical Inverse-Square law (ISL), can lead to measurable effects at small but macroscopic distances accessible in the SBL (anti)neutrino experiments and in particular can provide an explanation of the well-known reactor antineutrino anomaly.
Nicolas Levernier - One of the best experts on this subject based on the ideXlab platform.
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reply to comment on Inverse Square levy walks are not optimal search strategies for d 2
Physical Review Letters, 2021Co-Authors: Nicolas Levernier, O Benichou, Johannes Textor, Raphael VoituriezAbstract:We refute here the concernes raised in the Comment of our letter. This reply states clearly the validity range of our results and shows that the optimality of Inverse-Square Levy walks at the basis of the Levy flight foraging hypothesis is generically unfounded. We also give the precise set of conditions for which Inverse-levy Square Levy walks turn to be optimal, conditions which are unlikely to be verified biologically.
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Inverse Square levy walks are not optimal search strategies for d 2
Physical Review Letters, 2020Co-Authors: Nicolas Levernier, O Benichou, Johannes Textor, Raphael VoituriezAbstract:The Levy hypothesis states that Inverse Square Levy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets. It has served as a theoretical basis to interpret a wealth of experimental data at various scales, from molecular motors to animals looking for resources, putting forward the conclusion that many living organisms perform Levy walks to explore space because of their optimal efficiency. Here we provide analytically the dependence on target density of the encounter rate of Levy walks for any space dimension d; in particular, this scaling is shown to be independent of the Levy exponent α for the biologically relevant case d≥2, which proves that the founding result of the Levy hypothesis is incorrect. As a consequence, we show that optimizing the encounter rate with respect to α is irrelevant: it does not change the scaling with density and can lead virtually to any optimal value of α depending on system dependent modeling choices. The conclusion that observed Inverse Square Levy patterns are the result of a common selection process based purely on the kinetics of the search behavior is therefore unfounded.
