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Journal articles on the topic 'Dissipative analysis'

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Author: Grafiati

Published: 17 July 2024

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1

DESMARAIS, MATHIEU, and RACHID AISSAOUI. "MODELING OF KNEE ARTICULAR CARTILAGE DISSIPATION DURING GAIT ANALYSIS." Journal of Mechanics in Medicine and Biology 08, no. 03 (September 2008): 377–94. http://dx.doi.org/10.1142/s021951940800267x.

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Articular cartilage dissipates contact loads according to three dissipative mechanisms: frictional drag, intrinsic viscoelasticity, and surface friction. Estimation of dissipation due to these three mechanisms during gait is required to understand the dissipative properties of articular cartilage. Fourteen healthy subjects performed a gait analysis on treadmill. Tibiofemoral contact forces were estimated from inverse dynamic analysis and from a reductionist knee contact model. These contact forces and the results obtained from a preloading creep simulation were introduced into a biphasic poroviscoelastic articular cartilage model, and a one-dimensional confined compression was performed. Articular dissipation from each dissipative mechanism was estimated. Sensitivity analysis was performed to determine the effects of material parameters and length of the preloading simulation on the patterns of the dissipative mechanisms. Dissipative force patterns for all dissipative mechanisms were found to be similar to those of tibiofemoral contact forces. Frictional drag was found to be the dominant dissipative mechanism. The initial permeability and the viscoelastic spectrum parameters were found to have an important impact on the magnitude of the peaks of dissipative patterns. If appropriate material parameters are introduced, this model could be used to compare the difference between healthy and osteoarthritic human articular cartilage.

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2

Taniue, Shogo, and Shuichi Kawashima. "Dissipative structure and asymptotic profiles for symmetric hyperbolic systems with memory." Journal of Hyperbolic Differential Equations 18, no. 02 (June 2021): 453–92. http://dx.doi.org/10.1142/s0219891621500144.

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We study symmetric hyperbolic systems with memory-type dissipation and investigate their dissipative structures under Craftsmanship condition. We treat two cases: memory-type diffusion and memory-type relaxation, and observe that the dissipative structures of these two cases are essentially different. Namely, we show that the dissipative structure of the system with memory-type diffusion is of the standard type, while that of the system with memory-type relaxation is of the regularity-loss type. Moreover, we investigate the asymptotic profiles of the solutions for [Formula: see text]. In the diffusion case, it is proved that the systems with memory and without memory have the same asymptotic profile for [Formula: see text], which is given by the superposition of linear diffusion waves. We have the same result also in the relaxation case under enough regularity assumption on the initial data.

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3

Fusco, G., and M. Oliva. "Dissipative systems with constraints." Journal of Differential Equations 63, no. 3 (July 1986): 362–88. http://dx.doi.org/10.1016/0022-0396(86)90061-6.

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4

LIANG, JIANFENG. "HYPERBOLIC SMOOTHING EFFECT FOR SEMILINEAR WAVE EQUATIONS AT A FOCAL POINT." Journal of Hyperbolic Differential Equations 06, no. 01 (March 2009): 1–23. http://dx.doi.org/10.1142/s0219891609001745.

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For semi-linear dissipative wave equation □u + |ut|p - 1ut = 0, we consider finite energy solutions with singularities propagating along a focusing light cone. At the tip of cone, the singularities are focused and partially smoothed out under strong nonlinear dissipation, i.e. the solution gets up to 1/2 more L2 derivative after the focus. The smoothing phenomenon is in fact the result of simultaneous action of focusing and nonlinear dissipation.

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5

Wang, Tao, Ji-jun Ao, and Mei-chun Yang. "A Classification of Fourth-Order Dissipative Differential Operators." Journal of Function Spaces 2020 (January 21, 2020): 1–9. http://dx.doi.org/10.1155/2020/7510313.

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This paper is devoted to the classification of the fourth-order dissipative differential operators by the boundary conditions. Subject to certain conditions, we determine some nonself-adjoint boundary conditions that generate the fourth-order differential operators to be dissipative. And under certain conditions, we prove that these dissipative operators have no real eigenvalues.

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6

Bratteli, Ola, and Palle E. T. Jørgensen. "Conservative derivations and dissipative Laplacians." Journal of Functional Analysis 82, no. 2 (February 1989): 404–11. http://dx.doi.org/10.1016/0022-1236(89)90077-3.

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7

Mustafayev, Heybetkulu. "Dissipative operators on Banach spaces." Journal of Functional Analysis 248, no. 2 (July 2007): 428–47. http://dx.doi.org/10.1016/j.jfa.2007.02.004.

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8

Sun, Jinyi, and Lingjuan Zou. "Global Well-Posedness of the Dissipative Quasi-Geostrophic Equation with Dispersive Forcing." Axioms 11, no. 12 (December 12, 2022): 720. http://dx.doi.org/10.3390/axioms11120720.

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The dissipative quasi-geostrophic equation with dispersive forcing is considered. By striking new balances between the dispersive effects of the dispersive forcing and the smoothing effects of the viscous dissipation, we obtain the global well-posedness for Cauchy problem of the dissipative quasi-geostrophic equation with dispersive forcing for arbitrary initial data, provided that the dispersive parameter is large enough.

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9

QU, Tonghuan, Shijie ZHU, Zhenqiang SONG, and Kazuhiro OHYAMA. "Analysis on the Electrical Dissipation of a Dissipative Dielectric Elastomer Generator." Proceedings of Mechanical Engineering Congress, Japan 2021 (2021): J031–21. http://dx.doi.org/10.1299/jsmemecj.2021.j031-21.

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10

Allahverdiev, B. P. "Dissipative Schrödinger Operators with Matrix Potentials." Potential Analysis 20, no. 4 (June 2004): 303–15. http://dx.doi.org/10.1023/b:pota.0000009815.97987.26.

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11

Scheel, Arnd, and J. Douglas Wright. "Colliding dissipative pulses—The shooting manifold." Journal of Differential Equations 245, no. 1 (July 2008): 59–79. http://dx.doi.org/10.1016/j.jde.2008.03.019.

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12

Faupin, Jérémy, and François Nicoleau. "Scattering matrices for dissipative quantum systems." Journal of Functional Analysis 277, no. 9 (November 2019): 3062–97. http://dx.doi.org/10.1016/j.jfa.2019.06.010.

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13

Wright, J. Douglas. "Separating Dissipative Pulses: The Exit Manifold." Journal of Dynamics and Differential Equations 21, no. 2 (March 10, 2009): 315–28. http://dx.doi.org/10.1007/s10884-009-9130-0.

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14

Zhang, Yi, Yile Zhang, Jinghao Li, and Baoyan Zhu. "Dissipative Output Tracking Control of Linear Systems with Time Delay." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/324741.

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The problem of dissipative output tracking control of linear systems with time delay is investigated. Firstly, an augmented system is constructed to describe dissipative output tracking control error, and the concept of dissipative output tracking is defined. Based on this, some sufficient conditions are derived in terms of linear matrix inequalities (LMIs) technique, which ensure that the augmented system is dissipative and stable; then design methods of dissipative output tracking state-feedback controller are provided, and the desired controller gain can be expressed through the solutions of LMIs. Finally, a numerical simulation example is given to illustrate the validity of the proposed results.

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15

Hintermüller, M., C. N. Rautenberg, and N. Strogies. "Dissipative and Non-Dissipative Evolutionary Quasi-Variational Inequalities with Gradient Constraints." Set-Valued and Variational Analysis 27, no. 2 (July 14, 2018): 433–68. http://dx.doi.org/10.1007/s11228-018-0489-0.

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16

Tian, Bo, and Yi-Tian Gao. "Painlevé Analysis and Symbolic Computation for a Nonlinear Schrödinger Equation with Dissipative Perturbations." Zeitschrift für Naturforschung A 51, no. 3 (March 1, 1996): 167–70. http://dx.doi.org/10.1515/zna-1996-0305.

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The nonlinear Schrödinger equations with small dissipative perturbations are of current importance in modeling weakly nonlinear dispersive media with dissipation. In this paper, the Painlevé formulation with symbolic computation is presented for one of those equations. An auto-Bäcklund transformation and some exact solutions are explicitly constructed

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17

Li, Kun, Maozhu Zhang, Jinming Cai, and Zhaowen Zheng. "Completeness Theorem for Eigenparameter Dependent Dissipative Dirac Operator with General Transfer Conditions." Journal of Function Spaces 2020 (February 13, 2020): 1–8. http://dx.doi.org/10.1155/2020/8718930.

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This paper deals with a singular (Weyl’s limit circle case) non-self-adjoint (dissipative) Dirac operator with eigenparameter dependent boundary condition and finite general transfer conditions. Using the equivalence between Lax-Phillips scattering matrix and Sz.-Nagy-Foiaş characteristic function, the completeness of the eigenfunctions and associated functions of this dissipative operator is discussed.

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18

CARTER, BRANDON, and NICOLAS CHAMEL. "COVARIANT ANALYSIS OF NEWTONIAN MULTI-FLUID MODELS FOR NEUTRON STARS III: TRANSVECTIVE, VISCOUS, AND SUPERFLUID DRAG DISSIPATION." International Journal of Modern Physics D 14, no. 05 (May 2005): 749–74. http://dx.doi.org/10.1142/s0218271805006845.

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As a follow up to papers dealing firstly with a convective variational formulation in a Milne–Cartan framework for non-dissipative multi-fluid models, and secondly with various ensuing stress energy conservation laws and generalized virial theorems, this work continues a series showing how analytical procedures developed in the context of General Relativity can be usefully adapted for implementation in a purely Newtonian framework where they provide physical insights that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. The present paper describes the 4-dimensionally covariant treatment of various dissipative mechanisms, including viscosity in non-superfluid constituents, superfluid vortex drag, ordinary resistivity (mutual friction) between relatively moving non-superfluid constituents, and the transvective dissipation that occurs when matter is transformed from one constituent to another due to chemical disequilibrium such as may be produced by meridional circulation in neutron stars. The corresponding non-dissipative limit cases of vortex pinning, convection and chemical equilibrium are also considered.

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19

D’Abbicco, Marcello, and Enrico Jannelli. "Dissipative higher order hyperbolic equations." Communications in Partial Differential Equations 42, no. 11 (October 11, 2017): 1682–706. http://dx.doi.org/10.1080/03605302.2017.1390674.

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20

Seubert, Steven M. "Unbounded dissipative compressed Toeplitz operators." Journal of Mathematical Analysis and Applications 290, no. 1 (February 2004): 132–46. http://dx.doi.org/10.1016/j.jmaa.2003.09.016.

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21

Maccamy, R. C. "Approximation of Dissipative Hereditary Systems." Journal of Mathematical Analysis and Applications 179, no. 1 (October 1993): 120–34. http://dx.doi.org/10.1006/jmaa.1993.1339.

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22

Ván, Peter, Róbert Kovács, and Federico Vázquez. "Spectral Properties of Dissipation." Journal of Non-Equilibrium Thermodynamics 47, no. 1 (December 21, 2021): 95–102. http://dx.doi.org/10.1515/jnet-2021-0050.

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Abstract The novel concept of spectral diffusivity is introduced to analyze the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is similar to mode analysis in wave propagation. The new modal quantities characterize dissipation and are best interpreted as effective diffusivities, or, in case of the heat conduction, as effective heat conductivities of the material.

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23

Chen, Wenhui. "Dissipative structure and diffusion phenomena for doubly dissipative elastic waves in two space dimensions." Journal of Mathematical Analysis and Applications 486, no. 2 (June 2020): 123922. http://dx.doi.org/10.1016/j.jmaa.2020.123922.

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24

Kmit, I., and L. Recke. "Hopf bifurcation for semilinear dissipative hyperbolic systems." Journal of Differential Equations 257, no. 1 (July 2014): 264–309. http://dx.doi.org/10.1016/j.jde.2014.04.003.

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25

Tan, Zhong, and Yanjin Wang. "On hyperbolic-dissipative systems of composite type." Journal of Differential Equations 260, no. 2 (January 2016): 1091–125. http://dx.doi.org/10.1016/j.jde.2015.09.025.

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26

Zhou, Shengfan, and Wei Shi. "Attractors and dimension of dissipative lattice systems." Journal of Differential Equations 224, no. 1 (May 2006): 172–204. http://dx.doi.org/10.1016/j.jde.2005.06.024.

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27

Kreiss, Heinz-Otto, Omar E. Ortiz, and Oscar A. Reula. "Stability of Quasi-linear Hyperbolic Dissipative Systems." Journal of Differential Equations 142, no. 1 (January 1998): 78–96. http://dx.doi.org/10.1006/jdeq.1997.3341.

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28

Kirchev, Kiril P., and Galina S. Borisova. "Regular Couplings of Dissipative and Anti-Dissipative Unbounded Operators, Asymptotics of the Corresponding Non-Dissipative Processes and the Scattering Theory." Integral Equations and Operator Theory 57, no. 3 (December 26, 2006): 339–79. http://dx.doi.org/10.1007/s00020-006-1458-9.

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29

Kasza, Gábor, László P. Csernai, and Tamás Csörgő. "New, Spherical Solutions of Non-Relativistic, Dissipative Hydrodynamics." Entropy 24, no. 4 (April 6, 2022): 514. http://dx.doi.org/10.3390/e24040514.

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We present a new family of exact solutions of dissipative fireball hydrodynamics for arbitrary bulk and shear viscosities. The main property of these solutions is a spherically symmetric, Hubble flow field. The motivation of this paper is mostly academic: we apply non-relativistic kinematics for simplicity and clarity. In this limiting case, the theory is particularly clear: the non-relativistic Navier–Stokes equations describe the dissipation in a well-understood manner. From the asymptotic analysis of our new exact solutions of dissipative fireball hydrodynamics, we can draw a surprising conclusion: this new class of exact solutions of non-relativistic dissipative hydrodynamics is asymptotically perfect.

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30

Obaya, Rafael, and Ana M. Sanz. "Non-autonomous scalar linear-dissipative and purely dissipative parabolic PDEs over a compact base flow." Journal of Differential Equations 285 (June 2021): 714–50. http://dx.doi.org/10.1016/j.jde.2021.03.027.

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31

Jamróz, Grzegorz. "On measures of accretion and dissipation for solutions of the Camassa–Holm equation." Journal of Hyperbolic Differential Equations 14, no. 04 (December 2017): 721–54. http://dx.doi.org/10.1142/s0219891617500242.

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We investigate the measures of dissipation and accretion related to the weak solutions of the Camassa–Holm equation. Demonstrating certain novel properties of nonunique characteristics, we prove a new representation formula for these measures and conclude about their structural features, such as the fact that they are singular with respect to the Lebesgue measure. We apply these results to gain new insights into the structure of weak solutions, proving in particular that measures of accretion vanish for dissipative solutions of the Camassa–Holm equation.

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32

Tan, K. B., L. Li, and C. H. Liang. "Canonical Analysis for Dissipative Electromagnetic Medium." Journal of Electromagnetic Waves and Applications 21, no. 11 (January 1, 2007): 1499–505. http://dx.doi.org/10.1163/156939307782000398.

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33

NAGARAJAN, RADHAKRISHNAN. "LOCAL ANALYSIS OF DISSIPATIVE DYNAMICAL SYSTEMS." International Journal of Bifurcation and Chaos 15, no. 05 (May 2005): 1515–47. http://dx.doi.org/10.1142/s0218127405012971.

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Linear transformation techniques such as singular value decomposition (SVD) have been used widely to gain insight into the qualitative dynamics of data generated by dynamical systems. There have been several reports in the past that had pointed out the susceptibility of linear transformation approaches in the presence of nonlinear correlations. In this tutorial review, the local dispersion along with the surrogate testing is suggested to discriminate nonlinear correlations arising in deterministic and non-deterministic settings.

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34

Allahverdiev, B. P., and Ahmet Canoǧlu. "Spectral analysis of dissipative Schrödinger operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 127, no. 6 (1997): 1113–21. http://dx.doi.org/10.1017/s0308210500026962.

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Dissipative Schrodinger operators are studied in L2(0, ∞) which are extensions of symmetric operators with defect index (2, 2). We construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix according to the scheme of Lax and Phillips. With the help of the incoming spectral representation, we construct a functional model of the dissipative operator and construct its characteristic function in terms of solutions of the corresponding differential equation. On the basis of the results obtained regarding the theory of the characteristic function, we prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operator.

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35

Zhang, Jun A. "Estimation of Dissipative Heating Using Low-Level In Situ Aircraft Observations in the Hurricane Boundary Layer." Journal of the Atmospheric Sciences 67, no. 6 (June 1, 2010): 1853–62. http://dx.doi.org/10.1175/2010jas3397.1.

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Abstract Data collected in the low-level atmospheric boundary layer in five hurricanes by NOAA research aircraft are analyzed to measure turbulence with scales small enough to retrieve the rate of dissipation. A total of 49 flux runs suitable for analysis are identified in the atmospheric boundary layer within 200 m above the sea surface. Momentum fluxes are directly determined using the eddy correlation method, and drag coefficients are also calculated. The dissipative heating is estimated using two different methods: 1) integrating the rate of dissipation in the surface layer and 2) multiplying the drag coefficient by the cube of surface wind speed. While the latter method has been widely used in theoretical models as well as several numerical models simulating hurricanes, these analyses show that using this method would significantly overestimate the magnitude of dissipative heating. Although the dataset used in this study is limited by the surface wind speed range <30 m s−1, this work highlights that it is crucial to understand the physical processes related to dissipative heating in the hurricane boundary layer for implementing it into hurricane models.

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36

Civelek, Cem. "Analysis of a coupled physical discrete time system by means of extended Euler-Lagrange difference equation and discrete dissipative canonical equation." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 6 (October 24, 2019): 1810–27. http://dx.doi.org/10.1108/compel-04-2019-0163.

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Purpose The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete. Design/methodology/approach The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well. Findings Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented. Originality/value The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.

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37

Sharif, M., and Iqra Nawazish. "Warm logamediate inflation in Starobinsky inflationary model." International Journal of Modern Physics D 27, no. 02 (January 2018): 1750191. http://dx.doi.org/10.1142/s0218271817501917.

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This paper investigates the dynamics of warm logamediate inflation for flat isotropic and homogeneous universe in Einstein frame representation of [Formula: see text] gravity. In this scenario, we study dissipative effects for weak and strong interactions of inflaton field via constant and generalized dissipative coefficient. In both interacting regimes, we find inflaton solution corresponding to scalar potential and radiation density of dissipating inflaton. Under slow-roll approximation, we formulate scalar and tensor power spectra, their spectral indices and tensor–scalar ratio for Starobinsky inflationary model and construct graphical analysis of these observational parameters. It is concluded that this model remains compatible with Planck 2015 constraints in weak and strong regimes for constant dissipative coefficient. For generalized dissipative coefficient, the inflationary model yields consistent results for [Formula: see text] and [Formula: see text] in strong regime while condition of warm inflation is violated for [Formula: see text] in weak regime.

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38

Phung, Kim Dang. "Polynomial decay rate for the dissipative wave equation." Journal of Differential Equations 240, no. 1 (September 2007): 92–124. http://dx.doi.org/10.1016/j.jde.2007.05.016.

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39

Waurick, Marcus, and Sven-Ake Wegner. "Dissipative extensions and port-Hamiltonian operators on networks." Journal of Differential Equations 269, no. 9 (October 2020): 6830–74. http://dx.doi.org/10.1016/j.jde.2020.05.014.

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40

Jones, Don A., and Edriss S. Titi. "C1Approximations of Inertial Manifolds for Dissipative Nonlinear Equations." Journal of Differential Equations 127, no. 1 (May 1996): 54–86. http://dx.doi.org/10.1006/jdeq.1996.0061.

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41

Boling, Guo, and Li Yongsheng. "Attractor for Dissipative Klein–Gordon–Schrödinger Equations inR3." Journal of Differential Equations 136, no. 2 (May 1997): 356–77. http://dx.doi.org/10.1006/jdeq.1996.3242.

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42

Zhang, Yu, Xue Yang, and Yong Li. "Affine-Periodic Solutions for Dissipative Systems." Abstract and Applied Analysis 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/157140.

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As generalizations of Yoshizawa’s theorem, it is proved that a dissipative affine-periodic system admits affine-periodic solutions. This result reveals some oscillation mechanism in nonlinear systems.

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43

Ramm, A. G. "Slow manifolds for dissipative dynamical systems." Journal of Mathematical Analysis and Applications 363, no. 2 (March 2010): 729–32. http://dx.doi.org/10.1016/j.jmaa.2009.09.049.

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44

Alabau Boussouira, Fatiha, Jaime E. Muñoz Rivera, and Dilberto da S. Almeida Júnior. "Stability to weak dissipative Bresse system." Journal of Mathematical Analysis and Applications 374, no. 2 (February 2011): 481–98. http://dx.doi.org/10.1016/j.jmaa.2010.07.046.

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45

Gomilko, A. M. "Invariant subspaces of J-dissipative operators." Functional Analysis and Its Applications 19, no. 3 (1986): 213–14. http://dx.doi.org/10.1007/bf01076623.

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46

Wang, Zenggui. "A dissipative hyperbolic affine curve flow." Journal of Mathematical Analysis and Applications 465, no. 2 (September 2018): 1094–111. http://dx.doi.org/10.1016/j.jmaa.2018.05.053.

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47

Chen, Xiaowei, Mingzhan Song, and Songhe Song. "A Fourth Order Energy Dissipative Scheme for a Traffic Flow Model." Mathematics 8, no. 8 (July 28, 2020): 1238. http://dx.doi.org/10.3390/math8081238.

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We propose, analyze and numerically validate a new energy dissipative scheme for the Ginzburg–Landau equation by using the invariant energy quadratization approach. First, the Ginzburg–Landau equation is transformed into an equivalent formulation which possesses the quadratic energy dissipation law. After the space-discretization of the Fourier pseudo-spectral method, the semi-discrete system is proved to be energy dissipative. Using diagonally implicit Runge–Kutta scheme, the semi-discrete system is integrated in the time direction. Then the presented full-discrete scheme preserves the energy dissipation, which is beneficial to the numerical stability in long-time simulations. Several numerical experiments are provided to illustrate the effectiveness of the proposed scheme and verify the theoretical analysis.

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48

MORI, NAOFUMI, and SHUICHI KAWASHIMA. "DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH FOURIER'S TYPE HEAT CONDUCTION." Journal of Hyperbolic Differential Equations 11, no. 01 (March 2014): 135–57. http://dx.doi.org/10.1142/s0219891614500039.

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We study the Timoshenko system with Fourier's type heat conduction in the one-dimensional (whole) space. We observe that the dissipative structure of the system is of the regularity-loss type, which is somewhat different from that of the dissipative Timoshenko system studied earlier by Ide–Haramoto–Kawashima. Moreover, we establish optimal L2decay estimates for general solutions. The proof is based on detailed pointwise estimates of solutions in the Fourier space. Also, we introuce here a refinement of the energy method employed by Ide–Haramoto–Kawashima for the dissipative Timoshenko system, which leads us to an improvement on their energy method.

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49

Michaelian, Karo, and Aleksandar Simeonov. "Reply to Lars Olof Björn's comment on “Fundamental molecules of life are pigments which arose and co-evolved as a response to the thermodynamic imperative of dissipating the prevailing solar spectrum” by Michaelian and Simeonov (2015)." Biogeosciences 19, no. 17 (September 1, 2022): 4029–34. http://dx.doi.org/10.5194/bg-19-4029-2022.

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Abstract. Lars Björn doubts our assertion that the driving force behind the origin and evolution of life has been the thermodynamic imperative of increasing the entropy production of the biosphere through increasing global solar photon dissipation. Björn bases his critique on the fact that the albedo of non-biological material can sometimes be lower than that of biological material and concludes that such examples counter our assertion. Our reply to Björn, however, is that albedo (reflection) is only one factor involved in the entropy production through photon dissipation occurring in the interaction of light with material. The other contributions to entropy production, which were listed in our article, are (1) the shift towards the infrared of the emitted spectrum (including a wavelength-dependent emissivity), (2) the diffuse reflection and emission of light into a greater outgoing solid angle, and (3) the heat of photon dissipation inducing evapotranspiration in the pigmented leaf, thereby coupling to the abiotic dissipative processes of the water cycle, which, besides shifting the emitted spectrum even further towards the infrared, promotes pigment production over the entire Earth surface. His analysis, therefore, does not provide a legitimate reason for doubting our assertion that life and evolution are driven by photon dissipation. We remain emphatic in our assertion that the fundamental molecules of life were originally dissipatively structured UV-C pigments arising in response to the thermodynamic imperative of dissipating the prevailing Archean solar spectrum. In the following, we respond to Björn's comment using the same section headings.

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Tuna, Hüseyin, and Aytekin Eryılmaz. "Dissipative Sturm-Liouville Operators with Transmission Conditions." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/248740.

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Abstract:

In this paper we study dissipative Sturm-Liouville operators with transmission conditions. By using Pavlov’s method (Pavlov 1947, Pavlov 1981, Pavlov 1975, and Pavlov 1977), we proved a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative Sturm-Liouville operators with transmission conditions.

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