Relevant bibliographies by topics / Equipartition

Academic literature on the topic 'Equipartition'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Equipartition"

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Komar, Arthur. "Relativistic equipartition." General Relativity and Gravitation 28, no. 4 (April 1996): 379–85. http://dx.doi.org/10.1007/bf02105082.

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Berdichevsky, V. "Generalized equipartition law." International Journal of Engineering Science 31, no. 4 (April 1993): 673–77. http://dx.doi.org/10.1016/0020-7225(93)90057-2.

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Seta, Amit, and Rainer Beck. "Revisiting the Equipartition Assumption in Star-Forming Galaxies." Galaxies 7, no. 2 (April 8, 2019): 45. http://dx.doi.org/10.3390/galaxies7020045.

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Energy equipartition between cosmic rays and magnetic fields is often assumed to infer magnetic field properties from the synchrotron observations of star-forming galaxies. However, there is no compelling physical reason to expect the same. We aim to explore the validity of the energy equipartition assumption. After describing popular arguments in favour of the assumption, we first discuss observational results that support it at large scales and how certain observations show significant deviations from equipartition at scales smaller than ≈ 1 kpc , probably related to the propagation length of the cosmic rays. Then, we test the energy equipartition assumption using test-particle and magnetohydrodynamic (MHD) simulations. From the results of the simulations, we find that the energy equipartition assumption is not valid at scales smaller than the driving scale of the ISM turbulence (≈ 100 pc in spiral galaxies), which can be regarded as the lower limit for the scale beyond which equipartition is valid. We suggest that one must be aware of the dynamical scales in the system before assuming energy equipartition to extract magnetic field information from synchrotron observations. Finally, we present ideas for future observations and simulations to investigate in more detail under which conditions the equipartition assumption is valid or not.
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Bormashenko, Edward, and Oleg Gendelman. "On the applicability of the equipartition theorem." Thermal Science 14, no. 3 (2010): 855–58. http://dx.doi.org/10.2298/tsci1003855b.

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Generalization of the equipartition theorem is presented for a broad range of potentials U(x) with quadratic minimum. It is shown, that the equipartition of energy in its standard form appears at the low temperatures limit. For potentials demonstrating the quadratic behavior for large displacements from the equilibrium the equipartition holds also in the high temperature limit. The temperature range of applicability of the equipartition theorem for the potential U = ax2 + bx4 was established.
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Scott, Paul R. "Equipartition of convex bodies." Bulletin of the Australian Mathematical Society 42, no. 1 (August 1990): 141–44. http://dx.doi.org/10.1017/s0004972700028240.

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Duric, Nebojsa. "Equipartition: Fact or Fiction?" Symposium - International Astronomical Union 140 (1990): 235–36. http://dx.doi.org/10.1017/s0074180900190084.

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The use of equipartition calculations in estimating magnetic field strengths and energetics of extragalactic radio sources is widespread and well known. Since it is one of the few ways in which to calculate radio source parameters, it is important to determine how reasonable the approach generally is. Since this assumption is approximately a minimum energy criterion one expects that deviations from equipartition are limited at some level by independently determined constraints on the total energy. In this regard we have analyzed radio images of nearby spiral galaxies in order to determine equipartition magnetic fields and relativistic gas energies and to explore their possible nonequipartition configurations.
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Bogoyavlenskij, Oleg I. "Unsteady equipartition MHD solutions." Journal of Mathematical Physics 45, no. 1 (2004): 381. http://dx.doi.org/10.1063/1.1629137.

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Mello, Pier A., and Rosalío F. Rodríguez. "The equipartition theorem revisited." American Journal of Physics 78, no. 8 (August 2010): 820–27. http://dx.doi.org/10.1119/1.3386255.

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Panagiotakis, Costas, Konstantin Athanassopoulos, and Georgios Tziritas. "The equipartition of curves." Computational Geometry 42, no. 6-7 (August 2009): 677–89. http://dx.doi.org/10.1016/j.comgeo.2009.01.003.

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Lewis, J. T., C. E. Pfister, R. P. Russell, and W. G. Sullivan. "Reconstruction sequences and equipartition measures: an examination of the asymptotic equipartition property." IEEE Transactions on Information Theory 43, no. 6 (1997): 1935–47. http://dx.doi.org/10.1109/18.641557.

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Dissertations / Theses on the topic "Equipartition"

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Carberry, David Michael, and dave_carberry@yahoo com au. "Optical Tweezers: Experimental Demonstrations of the Fluctuation Theorem." The Australian National University. Research School of Chemistry, 2006. http://thesis.anu.edu.au./public/adt-ANU20060410.122727.

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In the late 19th and early 20th centuries famous scientists like Boltzmann, Loschmidt, Maxwell and Einstein tried, unsuccessfully, to find the link between the time-reversible equations of motion of individual molecules and irreversible thermodynamics. The solution to this puzzle was found in 1993, and the link is now known as the Fluctuation Theorem (FT). In the decade that followed theory and computer simulation tested the FT and, in 2002, an experiment indirectly demonstrated the FT.¶ This thesis describes original experiments that demonstrate the FT directly using Optical Tweezers. A related expression, known as the Kawasaki Identity, is also experimentally demonstrated. These experimental results provide a rigorous demonstration that irreversible dynamics can be obtained from a system with time-reversible dynamics.
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Baschetti, Serafina. "Physical characterization and numerical modeling of a WEST-like tokamak divertor plasma." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016.

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Il presente elaborato è incentrato sulla modellizzazione del plasma di bordo nei dispositivi per la produzione di energia da fusione nucleare noti come tokamak. La tecnologia che nel corso di tutta la seconda metà del XX secolo fino ad oggi è stata sviluppata a questo fine deve necessariamente scontrarsi con alcuni limiti. Nei tokamak il confinamento del plasma è di tipo magnetico e vincola le particelle a muoversi di moto elicoidale all'interno del vessel, tuttavia il confinamento non risulta perfetto e parte dell'energia si scarica sulle pareti della camera, rischiando pertanto di fondere i materiali. Alcune strategie possono essere messe in atto per limitare questo problema, per esempio agendo sulla geometria del tokamak, oppure sulla fisica, inducendo nel plasma una data concentrazione di impurezze che ionizzino irraggiando parte dell'energia di plasma. Proprio tale meccanismo di perdita è stato simulato in un modello monodimensionale di plasma monofluido di bordo. I risultati del codice numerico relativo al modello dimostrano che per concentrazioni di impurezze crescenti è possibile diminuire in modo significativo flusso di calore e temperatura al divertore. Per di più risulta possibile controllare la posizione del fronte di irraggiamento per mezzo di parametri di controllo del plasma quali la pressione. Si osserva inoltre l'insorgere del cosiddetto fenomeno di biforcazione alle basse temperature di divertore, fenomeno in cui il plasma si comporta in modo instabile a causa di fenomeni fisici tipici delle basse energie ("detachment") e a seguito del quale può improvvisamente spegnersi (disruzione). Infine lo stesso modello è stato migliorato inserendo l'ipotesi di plasma bifluido. Anche per gli ioni viene osservato il fenomeno di biforcazione. I risultati numerici evidenziano le dinamiche dello scambio energetico fra le specie gettando le basi di una progettazione efficiente della chimica del plasma finalizzata al raffreddamento del divertore.
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Ulusoy, Suleyman. "The Mathematical Theory of Thin Film Evolution." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16213.

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We try to explain the mathematical theory of thin liquid film evolution. We start with introducing physical processes in which thin film evolution plays an important role. Derivation of the classical thin film equation and existing mathematical theory in the literature are also introduced. To explain the thin film evolution we derive a new family of degenerate parabolic equations. We prove results on existence, uniqueness, long time behavior, regularity and support properties of solutions for this equation. At the end of the thesis we consider the classical thin film Cauchy problem on the whole real line for which we use asymptotic equipartition to show H^1(R) convergence of solutions to the unique self-similar solution.
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Margerin, Ludovic. "Diffusion multiple des ondes élastiques dans la lithosphère." Phd thesis, Université Joseph Fourier (Grenoble), 1998. http://tel.archives-ouvertes.fr/tel-00749704.

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Nous étudions la dépendance spatio-temporelle de l'énergie de la coda courte-période (> 1Hz) des seismes. Pour celà, nous développons des solutions de l'équation de Transfert Radiatif (TR) pour les ondes élastiques dans des milieux réalistes. Deux approches sont adoptées, l'une numérique basée sur les méthodes de Monte-Carlo, l'autre analytique basée sur l'équation de diffusion. Dans l'approximation acoustique, nous résolvons l'équation de TR pour la croûte terrestre représentée par un guide d'ondes hétérogène. Pour ce modèle, l'énergie de la coda décroît exponentiellement en raison des fuites d'énergie à la base de la croûte. Nous confrontons cette théorie de façon critique à des données du Mexique. Nous concluons que notre modèle avec fuite rend parfaitement compte des observations et nous montrons que l'anélasticité des roches est faible. Enfin nous introduisons le temps de résidence des ondes diffuses pour décrire la décroissance énergétique de la coda. Nous abordons ensuite le problème de diffusion multiple en élasticité complète. Nous tenons compte des conversions entre ondes P et S, ainsi que de leur polarisation, décrite par 5 paramètres de Stokes. Nous montrons que l'énergie de la coda est rapidement dominée par les ondes S. Un équilibre d'énergie universel s'établit rapidement entre les modes P et S, en accord avec le principe d'équipartition . Le phénomène d'équilibrage de l'énergie est également observé pour les ondes de coda du Mexique, démontrant leur caractère diffusif. Enfin, nous calculons le cône de rétro-diffusion cohérente dynamique en champ proche. Nous montrons qu'après un régime transitoire, le cône se stabilise et s'étend sur une longueur d'onde autour de la source. L'ensemble des modèles et observations nous permettent de confirmer la nature diffusive de la coda.
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Khalisi, Emil [Verfasser]. "Equipartition and mass segregation : simulations of star clusters with two mass components / presented by Emil Khalisi." 2003. http://d-nb.info/966426266/34.

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Li, Tongcang. "Fundamental tests of physics with optically trapped microspheres." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-05-2930.

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This dissertation details our experiments on studying the Brownian motion of an optically trapped microsphere with ultrahigh resolution, and cooling of its motion towards the quantum ground state. We have trapped glass microspheres in water, air and vacuum with optical tweezers. We developed a detection system that can monitor the position of a trapped microsphere with Angstrom spatial resolution and microsecond temporal resolution. We studied the Brownian motion of a trapped microsphere in air over a wide range of pressures. We measured the instantaneous velocity of a Brownian particle. Our results provide direct verification of the Maxwell-Boltzmann velocity distribution and the energy equipartition theorem for a Brownian particle. For short time scales, the ballistic regime of Brownian motion is observed, in contrast to the usual diffusive regime. We are currently developing a new detection system to measure the instantaneous velocity of a Brownian particle in water. In vacuum, we have used active feedback to cool the three center-of-mass vibration modes of a trapped microsphere from room temperature to millikelvin temperatures with a minimum mode temperature of 1.5 mK, which corresponds to the reduction of the root mean square (rms) amplitude of the microsphere from 6.7 nm to 15 pm for that mode. The mean thermal occupation number of that mode is reduced from about 6.8$\times 10^8$ at 297 K to about 3400 at 1.5 mK.
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Meng, Jin. "Coding Theorems via Jar Decoding." Thesis, 2013. http://hdl.handle.net/10012/7359.

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In the development of digital communication and information theory, every channel decoding rule has resulted in a revolution at the time when it was invented. In the area of information theory, early channel coding theorems were established mainly by maximum likelihood decoding, while the arrival of typical sequence decoding signaled the era of multi-user information theory, in which achievability proof became simple and intuitive. Practical channel code design, on the other hand, was based on minimum distance decoding at the early stage. The invention of belief propagation decoding with soft input and soft output, leading to the birth of turbo codes and low-density-parity check (LDPC) codes which are indispensable coding techniques in current communication systems, changed the whole research area so dramatically that people started to use the term "modern coding theory'' to refer to the research based on this decoding rule. In this thesis, we propose a new decoding rule, dubbed jar decoding, which would be expected to bring some new thoughts to both the code performance analysis and the code design. Given any channel with input alphabet X and output alphabet Y, jar decoding rule can be simply expressed as follows: upon receiving the channel output y^n ∈ Y^n, the decoder first forms a set (called a jar) of sequences x^n ∈ X^n considered to be close to y^n and pick any codeword (if any) inside this jar as the decoding output. The way how the decoder forms the jar is defined independently with the actual channel code and even the channel statistics in certain cases. Under this jar decoding, various coding theorems are proved in this thesis. First of all, focusing on the word error probability, jar decoding is shown to be near optimal by the achievabilities proved via jar decoding and the converses proved via a proof technique, dubbed the outer mirror image of jar, which is also quite related to jar decoding. Then a Taylor-type expansion of optimal channel coding rate with finite block length is discovered by combining those achievability and converse theorems, and it is demonstrated that jar decoding is optimal up to the second order in this Taylor-type expansion. Flexibility of jar decoding is then illustrated by proving LDPC coding theorems via jar decoding, where the bit error probability is concerned. And finally, we consider a coding scenario, called interactive encoding and decoding, and show that jar decoding can be also used to prove coding theorems and guide the code design in the scenario of two-way communication.
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Χριστοδουλίδη, Ελένη. "Δυναμική χαμηλοδιάστατων τόρων και χάος σε χαμιλτώνια συστήματα πολλών βαθμών ελευθερίας." Thesis, 2009. http://nemertes.lis.upatras.gr/jspui/handle/10889/3147.

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Η παρούσα εργασία αφορά στη μελέτη Χαμιλτώνιων συστημάτων Ν μη γραμμικών ταλαντωτών, όπως είναι αυτό των Fermi Pasta και Ulam (FPU), με στόχο την βαθύτερη κατανόηση της δυναμικής των σχεδόν-περιοδικών τροχιών και του ρόλου των αντίστοιχων τόρων στο χώρο φάσεων, καθώς αυξάνουμε την ενέργεια Ε και τον αριθμό βαθμών ελευθερίας Ν του συστήματος. Το βασικό μας αποτέλεσμα είναι ότι υπάρχουν τόροι χαμηλής διάστασης, που προκύπτουν από τη συνέχεια των αντίστοιχων του γραμμικού συστήματος, οι οποίοι ευθύνονται για τις FPU επαναλήψεις και εμποδίζουν την ισοκατανομή της ενέργειας μεταξύ όλων των κανονικών τρόπων ταλάντωσης. Αναλύοντας ευστάθεια αυτών των τόρων, μπορέσαμε να δώσουμε μια πληρέστερη ερμηνεία στο Παράδοξο των FPU, συνδέοντας και συμπληρώνοντας έτσι δύο από τις επικρατέστερες ερμηνείες του εν λόγω φαινομένου.
The present work concerns the study of Hamiltonian systems of N nonlinear coupled oscillators, as it is the one by Fermi Pasta and Ulam (FPU), in order to understand the dynamics of quasi-periodic orbits and the role of their corresponding tori in phase space, as we increase the energy E and the number N of the degrees of freedom. Our fundamental result is that there exist tori of low dimension, that come from the continuation of the corresponding tori of the linear system, which are responsible for the FPU recurrences and prevent the system from equipartition of the energy among all normal modes. By investigating the stability of these tori, we achieved to provide a more complete explanation for the FPU paradox, connecting and supplementing in this way two of the most dominant approaches for this paradox.
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Blaschke, Johannes Paul. "Entropic Motors." Doctoral thesis, 2014. http://hdl.handle.net/11858/00-1735-0000-0022-5E50-C.

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Books on the topic "Equipartition"

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Darrigol, Olivier. The Analogical Turn (1884–1887). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0006.

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This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.
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Darrigol, Olivier. The Critical Turn (1895–1899). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0008.

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In the writings of this period, we see Boltzmann responding to criticism by British kinetic theorists and by the German mathematician Ernst Zermelo regarding the equipartition of energy and the H theorem. Boltzmann also acted as a critic of other authors. He ridiculed Joseph Bertrand’s attack on Maxwell’s kinetic-molecular reasoning and, after much pounding on Max Planck’s early radiation theory, he managed to convince Planck to alter his approach to irreversibility. Boltzmann also gave a last critical review of the problem of specific heats. During the same period, he was working on his Gastheorie and this prompted him to discuss Johannes Diderik van der Waals’s theory in the light of the Maxwell–Boltzmann theory, with similar reasoning adapted to the problem of chemical dissociation.
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Darrigol, Olivier. Consolidation (1887–1895). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0007.

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This chapter covers a period in which Boltzmann returned to the collision-based approach and consolidated it in answer to criticism and suggestions by William Thomson, Hendrik Lorentz, George Bryan, Gustav Kirchhoff, and Max Planck. He corrected errors in alleged counterexamples of equipartition by William Burnside and William Thomson; and in 1887, when the Dutch theorist Hendrik Lorentz detected an error in his earlier derivation of the H theorem for polyatomic gases, he devised a highly ingenious alternative. In 1894, he offered a new, simplified derivation of the Maxwell–Boltzmann distribution based on an idea by the British mathematician George Bryan. Together with Bryan, he also provided a kinetic-molecular model for the equalization of the temperatures of two contiguous gases. He denounced what he believed to be an error in Gustav Kirchhoff’s derivation of Maxwell’s distribution, and he strengthened Max Planck’s alternative derivation based on time reversal.
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Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.
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Book chapters on the topic "Equipartition"

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deLaubenfels, Ralph. "Equipartition of energy." In Existence Families, Functional Calculi and Evolution Equations, 175–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073427.

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Edmonds, Jeff. "Scheduling with Equipartition." In Encyclopedia of Algorithms, 806–9. Boston, MA: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-30162-4_357.

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Gallavotti, Giovanni. "Equipartition and Critique." In Statistical Mechanics, 89–110. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03952-6_3.

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Duric, Nebojsa. "Equipartition: Fact or Fiction?" In Galactic and Intergalactic Magnetic Fields, 235–36. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0569-6_72.

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Pramanick, Achintya Kumar. "Equipartition of Joulean Heat in Thermoelectric Generators." In Understanding Complex Systems, 219–30. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5049-8_13.

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Chakraborty, Sumanta. "Spacetime Evolution and Equipartition in Lanczos-Lovelock Gravity." In Springer Theses, 67–84. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63733-4_5.

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Olafsen, Jeffrey. "Continuous Energy Levels, the Density of States, and Equipartition." In Sturge’s Statistical and Thermal Physics, 115–39. Second edition. | Boca Raton, FL : CRC Press, Taylor & Francis Group, [2019]: CRC Press, 2019. http://dx.doi.org/10.1201/9781315156958-7.

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Nicoloso, S., and P. Nobili. "A Set Covering Formulation of the Matrix Equipartition Problem." In Combinatorial Optimization, 317–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-77489-8_35.

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Tondeur, Daniel, and Lingai Luo. "Flow Equipartition and Shape Optimization of Fluidic Channel Networks." In Heat and Mass Transfer Intensification and Shape Optimization, 45–79. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4742-8_3.

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Giorgilli, Antonio. "Energy Equipartition and Nekhoroshev-Type Estimates for Large Systems." In Hamiltonian Dynamical Systems, 147–61. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4613-8448-9_10.

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Conference papers on the topic "Equipartition"

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Dermer, Charles D. "Equipartition plasmas near accreting black holes." In The second Compton symposium. AIP, 1994. http://dx.doi.org/10.1063/1.45650.

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Panagiotakis, Costas, and Georgios Tziritas. "Signal segmentation and modelling based on EquiPartition principle." In 2009 16th International Conference on Digital Signal Processing (DSP). IEEE, 2009. http://dx.doi.org/10.1109/icdsp.2009.5201105.

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Chacón-Acosta, Guillermo, Leonardo Dagdug, Hugo A. Morales-Técotl, H. A. Morales-Tecotl, L. A. Urena-Lopez, R. Linares-Romero, and H. H. Garcia-Compean. "Relativistic Momentum and Manifestly Covariant Equipartition Theorem Revisited." In GRAVITATIONAL PHYSICS: TESTING GRAVITY FROM SUBMILLIMETER TO COSMIC: Proceedings of the VIII Mexican School on Gravitation and Mathematical Physics. AIP, 2010. http://dx.doi.org/10.1063/1.3473859.

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Bobkov, Sergey, and Mokshay Madiman. "An equipartition property for high-dimensional log-concave distributions." In 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2012. http://dx.doi.org/10.1109/allerton.2012.6483257.

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Campillo, M. "Field Correlation, Emergence of the Green Function and Equipartition." In 68th EAGE Conference and Exhibition - Workshop Package. European Association of Geoscientists & Engineers, 2006. http://dx.doi.org/10.3997/2214-4609.201405161.

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Bhat, S. P., and D. S. Bernstein. "Average-preserving symmetries and equipartition in linear Hamiltonian systems." In 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). IEEE, 2004. http://dx.doi.org/10.1109/cdc.2004.1430367.

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Zeng, Xianlin, and Qing Hui. "Energy Equipartition Control for Geospatial Cyber-Physical Network Systems." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-5944.

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This paper develops three novel hybrid control techniques addressing fast energy equipartition for cyber-physical network systems, and discusses the future application of the proposed approaches to power network systems. The proposed hybrid distributed controller architectures are designed to mimick the dynamic behavior of thermodynamic systems to achieve the robust performance of cyber-physical network systems. The proposed controller architectures are constructed in such a way that each controller has a one-directional energy transfer from a plant to itself, and exchanges energy with its neighboring controllers. Energy-based resetting laws and power-based resetting laws are utilized in the hybrid controllers. Then, the hybrid control techniques are applied to power network systems, and simulation studies are carried out to show the efficacy of the proposed approaches.
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Yang, En-Hui, and Jin Meng. "Non-asymptotic equipartition properties for independent and identically distributed sources." In 2012 Information Theory and Applications Workshop (ITA). IEEE, 2012. http://dx.doi.org/10.1109/ita.2012.6181822.

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Mori, Takayoshi, Taiji Sakamoto, Masaki Wada, Takashi Yamamoto, Nobutomo Hanzawa, and Fumihiko Yamamoto. "Equipartition multiplexing technique for equalizing channel dependent degradation in MDM transmission." In Optical Fiber Communication Conference. Washington, D.C.: OSA, 2015. http://dx.doi.org/10.1364/ofc.2015.tu2d.2.

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Peng, Weicai. "The Asymptotic Equipartition Property for Homogeneous Markov Chains Indexed by Trees." In 2011 International Conference on Business Computing and Global Informatization (BCGIn). IEEE, 2011. http://dx.doi.org/10.1109/bcgin.2011.96.

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Reports on the topic "Equipartition"

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Hahm, T. S., P. H. Diamond, O. D. Gurcan, and G. Rewoldt. Comment on Turbulent Equipartition Theory of Toroidal Momentum Pinch. Office of Scientific and Technical Information (OSTI), March 2009. http://dx.doi.org/10.2172/951303.

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Isichenko, M. B., and V. V. Yankov. Turbulent equipartitions in two dimensional drift convection. Office of Scientific and Technical Information (OSTI), July 1995. http://dx.doi.org/10.2172/468593.

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You might also be interested in the extended bibliographies on the topic 'Equipartition' for particular source types:
Journal articles
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