Hopf-Cole Transformation

Liu, Tai-Ping

doi:10.21915/bimas.2017103

Cited by 8 publications

(5 citation statements)

References 33 publications

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“…The life-history data for M. dirhodum were analyzed based on the age-stage, two-sex life table approach (Chi and Liu, 1985;Chi, 1988;Chi and Su, 2006) utilizing the TWOSEX-MSChart computer program (Chi, 2020). Age-stage-specific survival rate (s xj ) (x = age in days; j = stage), the age-stage-specific fecundity ( f xj ), the age-specific survival rate (l x ), the age-specific fecundity (m x ), and the population parameters [the intrinsic rate of increase (r m ), the finite rate of increase (λ), the net reproductive rate (R 0 ), the mean generation time (T ), the age-stage-specific life expectancy (e xj ), and the age-stage-specific reproductive value (v xj )] were calculated accordingly.…”

Section: Discussionmentioning

confidence: 99%

Effects of drought stress and plant cultivar type on demographic characteristics of the rose-grain aphid, Metopolophium dirhodum (Hemiptera: Aphididae)

Akhbari

Zahediannezhad²,

Minaei³

et al. 2022

Bull. Entomol. Res.

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Drought is a substantial threat to cereal production under global climatic change scenarios, albeit its aftermath on arthropod pests is yet contentious. To address this issue, demographic characteristics of Metopolophium dirhodum (Walker, 1849) (Hemiptera: Aphididae) were studied on one drought-susceptible wheat cultivar and one drought-tolerant wheat cultivar under different water treatments. Some physiological and biochemical features of wheat cultivars including leaf soluble sugar and proline contents and antioxidant enzymes activities were also investigated. Significant differences occurred in the developmental period, survival, and fecundity of M. dirhodum between wheat cultivars under various water treatments. The impact of intermediate and severe water stress on M. dirhodum was neutral and negative for the tolerant cultivar and negative for the water-susceptible cultivar, respectively. Under severe water stress, on both wheat cultivars, the aphids had low net reproductive rates and finite and intrinsic rates of increase in comparison with those reared on unstressed plants. In total, drought resulted in lower growth of population and reduced survival of aphids. Hence, in the context of projected climatic changes, acute water deficiency could probably result in reducing the abundance and menace of outburst of M. dirhodum. However, it should be noted that the potential likelihood of M. dirhodum eruptions can be drastically affected by the degree of drought intensity and host plant cultivar.

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Section: Discussionmentioning

confidence: 99%

Effects of drought stress and plant cultivar type on demographic characteristics of the rose-grain aphid, Metopolophium dirhodum (Hemiptera: Aphididae)

Akhbari

Zahediannezhad²,

Minaei³

et al. 2022

Bull. Entomol. Res.

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“…Let's make the Hopf-Cole transform [75] ψ(x, t) = e and taking the partial derivative with respect to x, we get the Burgers equation for u(x, t):…”

Section: Appendix C Accelerated Reference Frame and Gravity In Classi...mentioning

confidence: 99%

Free fall in KvN mechanics and Einstein's principle of equivalence

Sen,

Dhasmana,

Silagadze

2020

Preprint

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The implementation of Einstein's principle of equivalence in Koopman-von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because KvN mechanics provides a Hilbert space formulation of classical mechanics that is very similar to the quantum mechanical formalism.Both in KvN mechanics and quantum mechanics, a propagator in a homogeneous gravitational field is simply related with a free propagator. As a result, the wave function in a homogeneous gravitational field in a freely falling reference frame differs from the free wave function only in phase.Fisher information, which quantifies our ability to estimate mass from coordinate measurements, does not depend on the magnitude of the homogeneous gravitational field, and this fact constitutes the formulation of Einstein's principle of equivalence, which is valid both in quantum mechanics and KvN mechanics.

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“…The Burgers' equation thus takes center stage among a few analytically solved NPDEs with a stipulated set of arbitrary initial functions and boundary restrictions. In 1950, Hopf-Cole [3] showed how to use a nonlinear transform to change Burgers' equation into a linear diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

Revisiting (2+1)-dimensional Burgers’ dynamical equations: analytical approach and Reynolds number examination

et al. 2023

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Classical Burgers’ equation is an indispensable dynamical evolution equation that is autonomously devised by Burgers and Harry Bateman in 1915 and 1948, respectively. This important model is featured through a nonlinear partial diﬀerential equation (NPDE). Furthermore, the model plays a crucial role in many areas of mathematical physics, including, for instance, ﬂuid dynamics, traﬃc ﬂow, nonlinear acoustics, turbulence phenomena, and linking convection and diﬀusion processes to state a few. Thus, in the present study, an eﬃcient analytical approach by the name “generalized Riccati equation approach” is adopted to securitize the class of (2 + 1)-dimensional Burgers’ equations by revealing yet another set of analytical structures to the governing single and vector-coupled Burgers’ equations. In fact, the besieged method of the solution has been proven to divulge various sets of hyperbolic, periodic, and other forms of exact solutions. Moreover, the method ﬁrst begins by transforming the targeted NPDE to a nonlinear ordinary diﬀerential equation (NODE), and subsequently to a set of an algebraic system of equations; where the algebraic system is then solved simultaneously to obtain the solution possibilities. Lastly, certain graphical illustrations in 2- and 3-dimensional plots are set to be depicted - featuring the evolutional nature of the resulting structures, and thereafter, analyze the inﬂuence of the Reynolds number Ra on the respective wave proﬁles.

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Hopf-Cole Transformation

Cited by 8 publications

References 33 publications

Effects of drought stress and plant cultivar type on demographic characteristics of the rose-grain aphid, Metopolophium dirhodum (Hemiptera: Aphididae)

Effects of drought stress and plant cultivar type on demographic characteristics of the rose-grain aphid, Metopolophium dirhodum (Hemiptera: Aphididae)

Free fall in KvN mechanics and Einstein's principle of equivalence

Revisiting (2+1)-dimensional Burgers’ dynamical equations: analytical approach and Reynolds number examination

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