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Journal articles on the topic 'Diffusion Equivalence'

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Author: Grafiati

Published: 27 July 2024

Last updated: 29 July 2024

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1

Derbez, Patrick, and Marie Euler. "Equivalence of Generalised Feistel Networks." IACR Transactions on Symmetric Cryptology 2024, no. 1 (March 1, 2024): 412–40. http://dx.doi.org/10.46586/tosc.v2024.i1.412-440.

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This paper focuses on equivalences between Generalised Feistel Networks (GFN) of type-II. We introduce a new definition of equivalence which captures the concept that two GFNs are identical up to re-labelling of the inputs/outputs, and give a procedure to test this equivalence relation. Such two GFNs are therefore cryptographically equivalent for several classes of attacks. It induces a reduction o the space of possible GFNs: the set of the (k!)2 possible even-odd GFNs with 2k branches can be partitioned into k! different classes.This result can be very useful when looking for an optimal GFN regarding specific computationally intensive properties, such as the minimal number of active S-boxes in a differential trail. We also show that in several previous papers, many GFN candidates are redundant as they belong to only a few classes. Because of this reduction of candidates, we are also able to suggest better permutations than the one of WARP: they reach 64 active S-boxes in one round less and still have the same diffusion round that WARP. Finally, we also point out a new family of permutations with good diffusion properties.

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2

Goldberg, Maxim J., and Seonja Kim. "Equivalence of $$L_p$$ diffusion approximation and a function’s diffusion smoothness." Semigroup Forum 100, no. 3 (May 28, 2019): 837–49. http://dx.doi.org/10.1007/s00233-019-10030-3.

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3

Harkola, Julia, and Arent Greve. "DIFFUSION OF TECHNOLOGY: COHESION OR STRUCTURAL EQUIVALENCE?" Academy of Management Proceedings 1995, no. 1 (August 1995): 422–26. http://dx.doi.org/10.5465/ambpp.1995.17536702.

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4

Malham, David G. "Toward Reality Equivalence in Spatial Sound Diffusion." Computer Music Journal 25, no. 4 (December 2001): 31–38. http://dx.doi.org/10.1162/01489260152815279.

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5

Iagar, Razvan Gabriel, Guillermo Reyes, and Ariel Sánchez. "Radial Equivalence of Nonhomogeneous Nonlinear Diffusion Equations." Acta Applicandae Mathematicae 123, no. 1 (June 6, 2012): 53–72. http://dx.doi.org/10.1007/s10440-012-9714-2.

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6

Yairi, Micah B., and David A. B. Miller. "Equivalence of diffusive conduction and giant ambipolar diffusion." Journal of Applied Physics 91, no. 7 (April 2002): 4374–81. http://dx.doi.org/10.1063/1.1453508.

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7

Popovych, Roman O., and Nataliya M. Ivanova. "Potential equivalence transformations for nonlinear diffusion–convection equations." Journal of Physics A: Mathematical and General 38, no. 14 (March 22, 2005): 3145–55. http://dx.doi.org/10.1088/0305-4470/38/14/006.

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8

Skal, Asya S. "Equivalence in Mapping of Conductivity, Elasticity and Diffusion Equations Appears or Disappears." Modern Physics Letters B 12, no. 29n30 (December 30, 1998): 1227–35. http://dx.doi.org/10.1142/s0217984998001451.

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Equivalence in mapping of diffusion and conductivity equations appears when diffusion and conductivity belong to the same universality class and disappears in the opposite case. For asymptotic long-time behavior one exponent of regular diffusion coefficient above the threshold [Formula: see text] and two below the threshold [Formula: see text] and [Formula: see text] are introduced, using the conductivity critical exponent (μ and s) and the Hall coeffcient critical exponent Re(p-pc)-g if R2/R1→1 and Re(p-pc)2s if R2/R1→1 and p<pc. In the first two cases equivalence between the diffusion and conductivity problems are disappear. A problem with this analogy lies in an intrinsic property that for percolation lattice the diffusion coeffcient is not a self-averaging quantity unlike the conductivity. Analogy between conductivity and elasticity appears for scalar forces and disappears for vector forces. The latter leads to new equivalence between elasticity and conductivity in a magnetic field. The new formulae for a real part of dielectric constant in the static limit for p>pc and the low-frequency ac conductivity are determined due to the new critical exponent for regular diffusion.

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9

Kim, Heeyoun, and Juyoung Byun. "Development of HLB3-002 (recombinant human PH20 stand-alone) and its applicability as an anticancer diffusion agent." Journal of Clinical Oncology 42, no. 16_suppl (June 1, 2024): e15195-e15195. http://dx.doi.org/10.1200/jco.2024.42.16_suppl.e15195.

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e15195 Background: HLB3-002 is a standalone of Halozyme's rHuPH20 (Original) and has the same amino acid sequence. HLB3-002 is being developed as a drug diffusion agent that decomposes subcutaneous hyaluronan, allowing substances such as anticancer drugs to be administered subcutaneously. This study was conducted to compare the in vivo efficacy and PK of original and HLB3-002 to confirm equivalence and thereby prove its applicability as a drug diffusion agent. Methods: In the in vivo efficacy test, Trypan blue was mixed with each original and HLB3-002 and administered subcutaneously to confirm diffusion and reconstruction equivalence in the nude mouse. The PK test was conducted using Rituximab, prepared in the same formulation as Rituximab SC by adding HLB3-002. A single dose was administered subcutaneously to the nape of the rat, and 12 points were collected for 28 days. The PK samples were measured by ELISA. When the Cmax and AUClast ratios of Rituximab between 2 groups were within 80.00 to 125.00%, they were evaluated as biologically equivalent. Results: As a result of efficacy test, the diffusion area of HLB3-002 was 104.7% compared to the original, which was confirmed to have an equivalent diffusion efficacy. In the skin reconstruction test, it was confirmed that both original and HLB3-002 rebuilt the skin layer to a similar to the negative control after 48 hours. As a result of the PK, Compared to Rituximab SC, the Cmax of Rituximab+HLB3-002 was similar at 98.53% and AUClast at 95.50%. Conclusions: Through an in vivo efficacy and PK test, we confirmed an equivalent drug diffusion effect, confirming that HLB3-002 applicability as an anticancer drug diffusion agent.[Table: see text]

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10

Jespersen, Sune Nørhøj. "Equivalence of double and single wave vector diffusion contrast at low diffusion weighting." NMR in Biomedicine 25, no. 6 (December 2, 2011): 813–18. http://dx.doi.org/10.1002/nbm.1808.

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11

Torrisi, Mariano, and Rita Tracinà. "An Application of Equivalence Transformations to Reaction Diffusion Equations." Symmetry 7, no. 4 (October 23, 2015): 1929–44. http://dx.doi.org/10.3390/sym7041929.

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12

Fetthauer, F., S. Weissbach, and O. Bryngdahl. "Equivalence of error diffusion and minimal average error algorithms." Optics Communications 113, no. 4-6 (January 1995): 365–70. http://dx.doi.org/10.1016/0030-4018(94)00574-e.

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13

Genon-Catalot, Valentine, and Catherine Larédo. "Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments." Annals of Statistics 42, no. 3 (June 2014): 1145–65. http://dx.doi.org/10.1214/14-aos1216.

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14

Manea, Mihai. "Bottleneck links, essential intermediaries, and competing paths of diffusion in networks." Theoretical Economics 16, no. 3 (2021): 1017–53. http://dx.doi.org/10.3982/te4385.

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We investigate how information goods are priced and diffused over links in a network. A new equivalence relation between nodes captures the effects of network architecture and locations of sellers on the division of profits, and characterizes the topology of competing (and potentially overlapping) diffusion paths. Sellers indirectly appropriate profits over intermediation chains from buyers in their equivalence classes. Links within the same class constitute bottlenecks for information diffusion and confer monopoly power. Links that bridge distinct classes are redundant for diffusion and generate competition among sellers. In dense networks, competition limits the scope of indirect appropriability and intellectual property rights foster innovation.

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15

Ethier, S. N. "Equivalence of two descriptions of the ages of alleles." Journal of Applied Probability 29, no. 1 (March 1992): 185–89. http://dx.doi.org/10.2307/3214802.

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It is shown that the two descriptions of the ages of alleles corresponding to the two formulations of the stationary infinitely-many-neutral-alleles diffusion model discussed by Ethier (1990a) are equivalent.

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16

Ethier, S. N. "Equivalence of two descriptions of the ages of alleles." Journal of Applied Probability 29, no. 01 (March 1992): 185–89. http://dx.doi.org/10.1017/s0021900200106734.

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It is shown that the two descriptions of the ages of alleles corresponding to the two formulations of the stationary infinitely-many-neutral-alleles diffusion model discussed by Ethier (1990a) are equivalent.

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17

Mariucci, Ester. "Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise." ESAIM: Probability and Statistics 19 (2015): 560–77. http://dx.doi.org/10.1051/ps/2015005.

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18

Iagar, Razvan Gabriel, Ariel Sánchez, and Juan Luis Vázquez. "Radial equivalence for the two basic nonlinear degenerate diffusion equations." Journal de Mathématiques Pures et Appliquées 89, no. 1 (January 2008): 1–24. http://dx.doi.org/10.1016/j.matpur.2007.09.002.

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19

Harutyunyan, Ani, and Ömer Özak. "Culture, diffusion, and economic development: The problem of observational equivalence." Economics Letters 158 (September 2017): 94–100. http://dx.doi.org/10.1016/j.econlet.2017.06.040.

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20

Freire, Igor Leite, and Mariano Torrisi. "Weak Equivalence Transformations for a Class of Models in Biomathematics." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/546083.

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A class of reaction-diffusion systems unifying severalAedes aegyptipopulation dynamics models is considered. Equivalence transformations are found. Extensions of the principal Lie algebra are derived for some particular cases.

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21

Liu, Zhi Bin, Jin Ma, Bing Shu Wang, and Xin Hui Duan. "The Study on Homogeneous Parameters of Light Water Reactor by the Nodal Diffusion Method." Applied Mechanics and Materials 666 (October 2014): 144–48. http://dx.doi.org/10.4028/www.scientific.net/amm.666.144.

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Recent progress in the development of coarse-mesh nodal methods for the numerical solution of the neutron diffusion and transport equations is reviewed. Compared with earlier nodal simulators, more recent nodal diffusion methods are characterized by the systematic derivation of spatial coupling relationships which are entirely consistent with the multi-group diffusion equation. These relationships most often are derived by developing approximations to the one-dimensional equations obtained by integrating the multidimensional diffusion equation over directions transverse to each coordinate axis. The objective of this research is to develop accurate and efficient spatial homogenization method for coarse mesh analysis of light water reactors. More sophisticated methods for computing approximate equivalence parameters are also introduced and make use of nonlinear iterations between homogenized reactor calculations and local fixed-source calculations to compute equivalence parameters. This special feature induces the need for the study on homogeneous parameters of light water reactor which takes phenomena of different scale and their interaction into account by means of the nodal diffusion method.

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22

Goldberg, Maxim J., and Seonja Kim. "A Natural Diffusion Distance and Equivalence of Local Convergence and Local Equicontinuity for a General Symmetric Diffusion Semigroup." Abstract and Applied Analysis 2018 (October 2, 2018): 1–9. http://dx.doi.org/10.1155/2018/6281504.

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In this paper, we consider a general symmetric diffusion semigroup Ttft≥0 on a topological space X with a positive σ-finite measure, given, for t>0, by an integral kernel operator: Ttf(x)≜∫X‍ρt(x,y)f(y)dy. As one of the contributions of our paper, we define a diffusion distance whose specification follows naturally from imposing a reasonable Lipschitz condition on diffused versions of arbitrary bounded functions. We next show that the mild assumption we make, that balls of positive radius have positive measure, is equivalent to a similar, and an even milder looking, geometric demand. In the main part of the paper, we establish that local convergence of Ttf to f is equivalent to local equicontinuity (in t) of the family Ttft≥0. As a corollary of our main result, we show that, for t0>0, Tt+t0f converges locally to Tt0f, as t converges to 0+. In the Appendix, we show that for very general metrics D on X, not necessarily arising from diffusion, ∫X‍ρt(x,y)D(x,y)dy→0 a.e., as t→0+. R. Coifman and W. Leeb have assumed a quantitative version of this convergence, uniformly in x, in their recent work introducing a family of multiscale diffusion distances and establishing quantitative results about the equivalence of a bounded function f being Lipschitz, and the rate of convergence of Ttf to f, as t→0+. We do not make such an assumption in the present work.

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23

Gyimóthy, Szabolcs. "Modeling stationary moving medium by static magneto-electric material." European Physical Journal Applied Physics 85, no. 1 (January 2019): 10901. http://dx.doi.org/10.1051/epjap/2018180161.

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The electromagnetic equivalence of a stationary moving medium to magneto-electric materials is studied. The equivalent material characteristics of the medium at rest is obtained in terms of the diffusion tensor coefficient of the governing partial differential equation. Special attention is paid to the transition condition of field quantities on the boundary of the moving medium; it is found that the nonmoving magneto-electric equivalent model must be supplied with surface sources. The method is demonstrated through examples and verified by finite element simulation.

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24

Zheng, Yang, Wei Liu, Xiaoqiang Li, Ming Yang, Peng Li, Yunhui Wu, and Xiaolei Chen. "Prediction and Analysis of Nuclear Explosion Radioactive Pollutant Diffusion Model." Pollutants 3, no. 1 (January 3, 2023): 43–56. http://dx.doi.org/10.3390/pollutants3010004.

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This study presents a model for the dispersion of radioactive smoke clouds from a nuclear weapon explosion. A model based on a modified Settlement model is chosen to simulate the dispersion of radioactive contaminants from a nuclear explosion in the atmosphere. The arrival time and dose rate of radioactive fallout at various distances in the downwind direction are given for different equivalents of the surface explosion and typical meteorological conditions. Thus, the prediction of the dispersion of radioactive contaminants from a nuclear explosion can be achieved under the conditions of known nuclear explosion equivalence and local meteorological parameters. This provides a theoretical basis for the estimation of the affected environment and the input of rescue forces after the explosion.

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25

Özer, Saadet. "On the equivalence groups for (2+1) dimensional nonlinear diffusion equation." Nonlinear Analysis: Real World Applications 43 (October 2018): 155–66. http://dx.doi.org/10.1016/j.nonrwa.2018.02.010.

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26

Pérez-Pinacho, Claudia A., and Cristina Verde. "A Note on an Integral Transformation for the Equivalence between a Fractional and Integer Order Diffusion Model." Mathematics 10, no. 5 (February 26, 2022): 753. http://dx.doi.org/10.3390/math10050753.

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This note tackles the equivalence problem between the fractional and integer order diffusion models. Unlike existing approaches, the existence of a unique integral transformation mapping the solution of the integer order model to a solution of the fractional order model of α=1/2 is proven. Moreover, the corresponding inverse integral transformation is formally established to guarantee the equivalence and well-posedness of the solutions of these models. Finally, as an example, the solution of a fractional order diffusion model α=1/2, obtained through the solution of its integer order counterpart and the proposed transformation, is compared with the solution derived by using the Fourier transform.

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27

Fresneda Portillo, Carlos, and Zenebe W. Woldemicheal. "Boundary-domain integral equations for Dirichlet diffusion problems with non-smooth coefficient." Electronic Journal of Differential Equations 2022, no. 01-87 (March 4, 2022): 26. http://dx.doi.org/10.58997/ejde.2022.26.

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We obtain a system of boundary-domain integral equations (BDIE) equivalent to the Dirichlet problem for the diffusion equation in non-homogeneous media. We use an extended version of the boundary integral method for PDEs with variable coefficients for which a parametrix is required. We generalize existing results for this family of parametrices considering a non-smooth variable coefficient in the PDE and source term in \(H^{s-2}(\Omega)\), \(1/2< s <3/2\) defined on a Lipschitz domain. The main results concern the equivalence between the original BVP and the corresponding BDIE system, as well as the well-posedness of the BDIE system

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28

Khushtova, F. G. "On the equivalence of two representations of Green's function of first boundary value problem for fractional-order diffusion equation." REPORTS ADYGE (CIRCASSIAN) INTERNATIONAL ACADEMY OF SCIENCES 20, no. 2 (2020): 12–15. http://dx.doi.org/10.47928/1726-9946-2020-20-2-12-15.

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29

Vaneeva, Olena, and Alexander Zhalij. "Group classification of variable coefficient quasilinear reaction-diffusion equations." Publications de l'Institut Math?matique (Belgrade) 94, no. 108 (2013): 81–90. http://dx.doi.org/10.2298/pim1308081v.

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The group classification of variable coefficient quasilinear reaction diffusion equations ut = uxx + h(x)B(u) is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the study of admissible point transformations within the class.

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30

Lavenda, B. H. "Derivation of the Prior Distribution in Bayesian Analysis from the Principle of Statistical Equivalence." Open Systems & Information Dynamics 08, no. 02 (June 2001): 103–14. http://dx.doi.org/10.1023/a:1011910512406.

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The distinction between uniform and logarithmic uniform prior distributions is made in terms of the principle of statistical equivalence, consisting of two statistically equivalent experiments, where the variable and parameter of the distribution exchange their roles. The two choices of the prior correspond to two terms in the drift of a diffusion process, and the condition for a stationary solution eliminates the choice of the uniform prior. Parameter randomization gives rise to a new distribution where the parameter of the original distribution is replaced by a ‘hitting point’ value of the variate.

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31

Wang, Yu, and M. Douglas LeVan. "Mixture Diffusion in Nanoporous Adsorbents: Equivalence of Fickian and Maxwell−Stefan Approaches." Journal of Physical Chemistry B 112, no. 29 (July 2008): 8600–8604. http://dx.doi.org/10.1021/jp710570k.

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32

Genon-Catalot, Valentine, Catherine Laredo, and Michael Nussbaum. "Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift." Annals of Statistics 30, no. 3 (June 2002): 731–53. http://dx.doi.org/10.1214/aos/1028674840.

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33

Parviainen, Mikko, and Juan Luis Vázquez. "Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications." ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE 21, no. 1 (December 2020): 303–59. http://dx.doi.org/10.2422/2036-2145.201808_006.

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34

KASSNER, K. "SIDEBRANCHING IN NOISELESS DIFFUSION-LIMITED AGGREGATION." Fractals 01, no. 02 (June 1993): 205–28. http://dx.doi.org/10.1142/s0218348x93000228.

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The equivalence between diffusion-limited aggregation (DLA) and growth in a Laplacian field is exploited to construct an algorithm for the simulation of DLA at large finite noise reduction. This algorithm allows performing of the limit towards infinite noise reduction, yielding a feasible prescription for the simulation of the noiseless, i.e., deterministic limit. Contrary to previous expectations as well as explicit predictions from an analytic theory, clusters grown without noise develop sidebranches. An explanation of this result in terms of the outer radius used in DLA simulations is suggested. Various implications, including the question whether or when noise reduction may accelerate the approach to asymptotic behavior, are discussed.

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35

Chen, Jingrun, Jason D. A. Lin, and Thuc-Quyen Nguyen. "Towards a Unified Macroscopic Description of Exciton Diffusion in Organic Semiconductors." Communications in Computational Physics 20, no. 3 (August 31, 2016): 754–72. http://dx.doi.org/10.4208/cicp.050615.010216a.

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AbstractWe study the exciton diffusion in organic semiconductors from a macroscopic viewpoint. In a unified way, we conduct the equivalence analysis between Monte-Carlo method and diffusion equation model for photoluminescence quenching and photocurrent spectrum measurements, in both the presence and the absence of Förster energy transfer effect. Connections of these two models to Stern-Volmer method and exciton-exciton annihilation method are also specified for the photoluminescence quenching measurement.

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36

Chaumont-Frelet, Théophile, Alexandre Ern, Simon Lemaire, and Frédéric Valentin. "Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods." ESAIM: Mathematical Modelling and Numerical Analysis 56, no. 1 (January 2022): 261–85. http://dx.doi.org/10.1051/m2an/2021082.

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We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source term. Under the idealized assumption that the local problems defining the multiscale basis functions are exactly solved, we prove that the equivalence holds for general polytopal (coarse) meshes and arbitrary approximation orders. We also leverage the interchange of properties to perform a unified convergence analysis, as well as to improve on both methods.

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37

Whipham, James W., Gamal A. I. Moustafa, Mohamed Sabba, Weidong Gong, Christian Bengs, and Malcolm H. Levitt. "Cross-correlation effects in the solution NMR spectra of near-equivalent spin-1/2 pairs." Journal of Chemical Physics 157, no. 10 (September 14, 2022): 104112. http://dx.doi.org/10.1063/5.0107221.

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The nuclear magnetic resonance (NMR) spectra of spin-1/2 pairs contain four peaks, with two inner peaks much stronger than the outer peaks in the near-equivalence regime. We have observed that the strong inner peaks have significantly different linewidths when measurements were performed on a 13C2-labelled triyne derivative. This linewidth difference may be attributed to strong cross-correlation effects. We develop the theory of cross-correlated relaxation in the case of near-equivalent homonuclear spin-1/2 pairs, in the case of a molecule exhibiting strongly anisotropic rotational diffusion. Good agreement is found with the experimental NMR lineshapes.

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38

Butterfield, David, Nicholas A. Martin, Georgie Coppin, and David E. Fryer. "Equivalence of UK nitrogen dioxide diffusion tube data to the EU reference method." Atmospheric Environment 262 (October 2021): 118614. http://dx.doi.org/10.1016/j.atmosenv.2021.118614.

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39

Mantegna, Michele, and Luigi Pietro Maria Colombo. "Diffusion through a half space: equivalence between different formulations of the unique solution." Applied Mathematical Sciences 8 (2014): 7727–48. http://dx.doi.org/10.12988/ams.2014.49723.

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40

Iagar, Razvan Gabriel, and Ariel Sánchez. "Radial equivalence and study of self-similarity for two very fast diffusion equations." Journal of Mathematical Analysis and Applications 351, no. 2 (March 2009): 635–52. http://dx.doi.org/10.1016/j.jmaa.2008.11.006.

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41

Tonarely, Michael E., Tommy Genova, Anthony J. Morales, Daniel Micka, Darin Knaus, and Kareem A. Ahmed. "Four-Line C2*/CH* Optical Sensor for Chemiluminescence Based Imaging of Flame Stoichiometry." Sensors 22, no. 15 (July 28, 2022): 5665. http://dx.doi.org/10.3390/s22155665.

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In the present work, an optical sensor was developed and calibrated for the purpose of non-intrusive equivalence ratio measurements in combustion systems. The sensor incorporates a unique four-line, single-sensor chemiluminescence imaging-based approach, which relies on the ratio of C2* and CH* radical-species intensities to obtain measurements of equivalence ratios. The advantage of the four-line sensor is the use of additional filtering to mitigate broadband luminescence signals, and its improvements over conventional two-line chemiluminescence diagnostics are discussed. The sensor was calibrated using a premixed bluff-body jet burner with a propane–air flame operating over a wide range of equivalence ratios. The results showed that the four-line processing technique improved the signal-to-noise ratio of the chemiluminescence images for all test cases. Calibrations of C2*/CH* intensity ratio to equivalence ratio were developed for both the four-line and two-line techniques. The calibrations were then used to create maps of local equivalence ratios in the flame-holding region. The maps revealed a non-uniform field of equivalence ratios due to the nature of the radical-species intensity profiles within the flame. Therefore, special consideration is required for calibration in order to accurately quantify equivalence ratios and apply these to diffusion flames.

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42

Freire, Igor Leite, and Mariano Torrisi. "A review on symmetries for certain Aedes aegypti models." International Journal of Modern Physics: Conference Series 38 (January 2015): 1560073. http://dx.doi.org/10.1142/s2010194515600733.

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We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.

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43

Merkle, Ana. "Equivalence to uniqueness in the concept of predictability between filtrations." Filomat 37, no. 30 (2023): 10153–60. http://dx.doi.org/10.2298/fil2330153m.

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In this paper we develop the concept of dependence between filtrations given in [11], named causal predictability, which is based on the Granger?s definition of causality. Then, we provide some new properties of this concept and prove a result that consider equivalence to uniqueness of the given concept. Also, a few examples that illustrate applications of the given concept are given with the main focus on stochastic differential equations (SDE) and financial mathematics. The study of Granger?s causality has been defined in the context of time series. Since continuous time models become more and more frequent in econometric practice, epidemiology, climatology, demographic, etc, we develop a concept connected to the continuous time processes. At the same time, the modern finance theory extensively uses diffusion processes.

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44

Liu, Jun, Qing Zhu, and Lihong Zhou. "New Stability Results of the Modified Craig-Sneyd Scheme in a Multidimensional Diffusion Equation with Mixed Derivative Terms." Journal of Physics: Conference Series 2650, no. 1 (November 1, 2023): 012002. http://dx.doi.org/10.1088/1742-6596/2650/1/012002.

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Abstract The time-dependent multidimensional diffusion equations with mixed derivative terms have been widely used in mathematics. Due to the mixed derivative terms, it is difficult to solve this pattern of multidimensional diffusion equations. The Modified Craig-Sneyd scheme (MCS), which has been applied to value the power derivatives, is one of the most promising methods for solving such equations. Therefore, it is of great importance to study its stability. The unconditional stability problem of MCS for a multidimensional diffusion equation with mixed derivative terms is investigated by taking into account the sizes. A new sufficient condition, necessary condition, and equivalence condition on the parameter of the MCS scheme for unconditional stability are proposed in case of the two and three-dimensional diffusion equations.

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45

Wassmer, Dominik, Bruno Schuermans, Christian Oliver Paschereit, and Jonas P. Moeck. "Measurement and modeling of the generation and the transport of entropy waves in a model gas turbine combustor." International Journal of Spray and Combustion Dynamics 9, no. 4 (April 24, 2017): 299–309. http://dx.doi.org/10.1177/1756827717696326.

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Indirect combustion noise is caused by entropy spots that are accelerated at the first turbine stage. These so-called entropy waves originate from the equivalence ratio fluctuations in the air–fuel mixture upstream of the flame. As entropy waves propagate convectively through the combustion chamber, they are subject to diffusion and dispersion. Because of the inherent difficulty of accurately measuring the burned gas temperature with sufficient temporal resolution, experimental data of entropy waves are scarce. In this work, the transfer function between equivalence ratio fluctuations and entropy fluctuations is modeled by a linearized reactor model, and the transport of entropy waves is investigated based on a convection-diffusion model. Temperature fluctuations are measured by means of a novel measurement technique at different axial positions downstream of the premixed flame, which is forced by periodic fuel injection. Experiments with various flow velocities and excitation frequencies enable model validation over a wide range of parameters.

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Riahi, Zouhair, Ali Mergheni, Jean-Charles Sautet, and Ben Nasrallah. "Numerical study of turbulent normal diffusion flame CH4-air stabilized by coaxial burner." Thermal Science 17, no. 4 (2013): 1207–19. http://dx.doi.org/10.2298/tsci110609042r.

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The practical combustion systems such as combustion furnaces, gas turbine, engines, etc. employ non-premixed combustion due to its better flame stability, safety, and wide operating range as compared to premixed combustion. The present numerical study characterizes the turbulent flame of methane-air in a coaxial burner in order to determine the effect of airflow on the distribution of temperature, on gas consumption and on the emission of NOx. The results in this study are obtained by simulation on FLUENT code. The results demonstrate the influence of different parameters on the flame structure, temperature distribution and gas emissions, such as turbulence, fuel jet velocity, air jet velocity, equivalence ratio and mixture fraction. The lift-off height for a fixed fuel jet velocity is observed to increase monotonically with air jet velocity. Temperature and NOx emission decrease of important values with the equivalence ratio, it is maximum about the unity.

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ARAYA, RODOLFO, ABNER H. POZA, and ERNST P. STEPHAN. "A HIERARCHICAL A POSTERIORI ERROR ESTIMATE FOR AN ADVECTION-DIFFUSION-REACTION PROBLEM." Mathematical Models and Methods in Applied Sciences 15, no. 07 (July 2005): 1119–39. http://dx.doi.org/10.1142/s0218202505000674.

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In this work we introduce a new a posteriori error estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the error and our error estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.

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Wiegel, F. W., and J. R. Heringa. "Diffusion coefficient of a protein in a fluid membrane: numerical calculation." Canadian Journal of Physics 63, no. 1 (January 1, 1985): 44–45. http://dx.doi.org/10.1139/p85-006.

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The drag force on an integral membrane protein is usually calculated with an asymptotic formula by Saffman. We have calculated this force by numerically solving the linearized Navier–Stokes equation. The results show that Saffman's formula is accurate within a few percent relative error for the usual range of parameter values. The mathematical equivalence of diffusion in an inhomogeneous membrane with the effective conduction of an inhomogeneous conductor is used to find a relation for the effective diffusion coefficient of a protein in an inhomogeneous membrane.

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Mukundakumar, Nithin, and Rob Bastiaans. "DNS Study of Spherically Expanding Premixed Turbulent Ammonia-Hydrogen Flame Kernels, Effect of Equivalence Ratio and Hydrogen Content." Energies 15, no. 13 (June 28, 2022): 4749. http://dx.doi.org/10.3390/en15134749.

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In this study, 3D premixed turbulent ammonia-hydrogen flames in air were studied using DNS. Mixtures with 75%, 50% and 25% ammonia (by mole fraction in the fuel mixture) and equivalence ratios of 0.8, 1.0 and 1.2 were studied. The studies were conducted in a decaying turbulence field with an initial Karlowitz number of 10. The flame structure and the influence of ammonia and the equivalence ratio were first studied. It was observed that the increase in equivalence ratio smoothened out the small scale wrinkles while leading to strongly curved leading edges. Increasing the amount of hydrogen in the fuel mixtures also led to increasingly distorted flames. These effects are attributed to local increases in the equivalence ratio due to the preferential diffusion effects of hydrogen. The effects of curvature on the flame chemistry were studied by looking at fuel consumption rates and key reactions. It was observed that the highly mobile H2 and H species were responsible for differential rates of fuel consumption in the positively curved and negatively curved regions of the flame. The indication of a critical amount of hydrogen in the fuel mixture was observed, after which the trends of reactions involving H radical reactions were flipped with respect to the sign of the curvature. This also has implications on NO formation. Finally, the spatial profiles of heat release and temperature for 50% hydrogen were studied, which showed that the flame brush of the lean case increases in width and that the flame propagation is slow for stoichiometric and rich cases attributed to suppression of flame chemistry due to preferential diffusion effects.

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Romano, Vittorio, and Mariano Torrisi. "Application of weak equivalence transformations to a group analysis of a drift-diffusion model." Journal of Physics A: Mathematical and General 32, no. 45 (October 28, 1999): 7953–63. http://dx.doi.org/10.1088/0305-4470/32/45/310.

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