Minimizers with discontinuous velocities for the electromagnetic variational method

The electromagnetic two-body problem has \emph{neutral differential delay} equations of motion that, for generic boundary data, can have solutions with \emph{discontinuous} derivatives. If one wants to use these neutral differential delay equations with \emph{arbitrary} boundary data, solutions with discontinuous derivatives must be expected and allowed. Surprisingly, Wheeler-Feynman electrodynamics has a boundary value variational method for which minimizer trajectories with discontinuous derivatives are also expected, as we show here. The variational method defines continuous trajectories with piecewise defined velocities and accelerations, and electromagnetic fields defined \emph{by} the Euler-Lagrange equations \emph{% on} trajectory points. Here we use the piecewise defined minimizers with the Li{\'{e}}nard-Wierchert formulas to define generalized electromagnetic fields almost everywhere (but on sets of points of zero measure where the advanced/retarded velocities and/or accelerations are discontinuous). Along with this generalization we formulate the \emph{generalized absorber hypothesis} that the far fields vanish asymptotically \emph{almost everywhere%} and show that localized orbits with far fields vanishing almost everywhere \emph{must} have discontinuous velocities on sewing chains of breaking points. We give the general solution for localized orbits with vanishing far fields by solving a (linear) neutral differential delay equation for these far fields. We discuss the physics of orbits with discontinuous derivatives stressing the differences to the variational methods of classical mechanics and the existence of a spinorial four-current associated with the generalized variational electrodynamics.Comment: corrected minor typo: piecewise differentiable on closed instead of open interval

Variational principle for the Wheeler-Feynman electrodynamics

We adapt the formally-defined Fokker action into a variational principle for the electromagnetic two-body problem. We introduce properly defined boundary conditions to construct a Poincare-invariant-action-functional of a finite orbital segment into the reals. The boundary conditions for the variational principle are an endpoint along each trajectory plus the respective segment of trajectory for the other particle inside the lightcone of each endpoint. We show that the conditions for an extremum of our functional are the mixed-type-neutral-equations with implicit state-dependent-delay of the electromagnetic-two-body problem. We put the functional on a natural Banach space and show that the functional is Frechet-differentiable. We develop a method to calculate the second variation for C2 orbital perturbations in general and in particular about circular orbits of large enough radii. We prove that our functional has a local minimum at circular orbits of large enough radii, at variance with the limiting Kepler action that has a minimum at circular orbits of arbitrary radii. Our results suggest a bifurcation at some radius below which the circular orbits become saddle-point extrema. We give a precise definition for the distributional-like integrals of the Fokker action and discuss a generalization to a Sobolev space of trajectories where the equations of motion are satisfied almost everywhere. Last, we discuss the existence of solutions for the state-dependent delay equations with slightly perturbated arcs of circle as the boundary conditions and the possibility of nontrivial solenoidal orbits

The Complexity of Helly-B1B_{1} EPG Graph Recognition

Golumbic, Lipshteyn, and Stern defined in 2009 the class of EPG graphs, the intersection graph class of edge paths on a grid. An EPG graph $G$ is a graph that admits a representation where its vertices correspond to paths in a grid $Q$, such that two vertices of $G$ are adjacent if and only if their corresponding paths in $Q$ have a common edge. If the paths in the representation have at most $k$ bends, we say that it is a $B_k$-EPG representation. A collection $C$ of sets satisfies the Helly property when every sub-collection of $C$ that is pairwise intersecting has at least one common element. In this paper, we show that given a graph $G$ and an integer $k$, the problem of determining whether $G$ admits a $B_k$-EPG representation whose edge-intersections of paths satisfy the Helly property, so-called Helly-$B_k$-EPG representation, is in NP, for every $k$ bounded by a polynomial function of $|V(G)|$. Moreover, we show that the problem of recognizing Helly-$B_1$-EPG graphs is NP-complete, and it remains NP-complete even when restricted to 2-apex and 3-degenerate graphs

Composição química de vinte e cinco híbridos de sorgo com capim-sudão (Sorghum bicolor x Sorghum sudanense) utilizados para produção de forragem.

Utilizando-se um delineamento experimental de blocos ao acaso e a comparacao das medias pelo teste de agrupamentos de Scott-Knott, vinte e tres hibridos experimentais e dos hibridos comerciais (AG 2501C e BRS 800) de Sorghum bicolor x Sorghum sudanense, foram avaliados quanto ao teor de materia seca (MS), fibra em detergente neutro (FDN), fibra em detergente acido (FDA), lignina e proteina bruta (PB). Com a colheita realizada aos 57 dias apos o plantio, os teores de MS variaram de 13,78 a 17,67% com media de 15,30%. Nao foram observadas diferenaas significativas (P<0,05) para os teores FDN e FDA, que variaram de 65,07 a 70,47% e 37,38 a 41,90%, respectivamente. Os valores obtidos para a lignina, tambem sem diferencas significativas (P<0,05) entre os 25 hibridos, ficaram entre 3,84 a 6,45%. Ja os conteudos de PB foram de 10,81 a 14,52%. alguns dos 23 hibridos experimentais demonstraram ter potencial para serem lancados comercialmente e apresentaram teores de MS e PB mais elevados (P<0,05) que os hibridos comerciais. Contudo, novos estudos que incluam avaliacoes com animais ainda sao necessarias

Tunneling in Fractional Quantum Mechanics

We study the tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schr\"odinger equation for these potentials, we calculate the corresponding reflection and transmission coefficients. These coefficients have a very interesting behaviour. In particular, we can have zero energy tunneling when the order of the Riesz fractional derivative is different from 2. For both potentials, the zero energy limit of the transmission coefficient is given by $\mathcal{T}_0 = \cos^2{\pi/\alpha}$, where $\alpha$ is the order of the derivative ($1 < \alpha \leq 2$).Comment: 21 pages, 3 figures. Revised version; accepted for publication in Journal of Physics A: Mathematical and Theoretica

Degradabilidade in situ da fibra em detergente neutro de silagens de milheto em ovinos.

O objetivo do trabalho foi avaliar a degradabilidade in situ da fibra em detergente neutro (FDN) das silagens de três genótipos de milheto, BRS-1501, NPM-I e CMS-3. Utilizou-se um delineamento experimental em blocos inteiramente ao acaso, em arranjo de parcelas subdivididas, empregando-se três ovinos como blocos. As médias foram comparadas pelo teste SNK a 5 % de probabilidade. Os potenciais de degradação variaram de 57,6 % para a silagem do genótipo NPM-I a 46,6 % para a silagem do CMS-3 e as taxas de degradação foram de 2,39 o/oIh (CMS-3), 2,32 %/h (BRS-1501) e 1,38 %/h (NPM-I). As silagens dos genõtipos BRS-1501 e CMS-3 se destacaram por apresentarem maiores degradabilidades efetivas e taxas de degradação. As silagens avaliadas apresentaram 'baixos valores de degradabilidade efetiva da FDN, sendo necessária a realização de mais estudos relacionando o momento de colheita da cultura ao seu valor nutritivo

Hydrocarbon seepage in the deep seabed links subsurface and seafloor biospheres

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Chakraborty, A., Ruff, S. E., Dong, X., Ellefson, E. D., Li, C., Brooks, J. M., McBee, J., Bernard, B. B., & Hubert, C. R. J. Hydrocarbon seepage in the deep seabed links subsurface and seafloor biospheres. Proceedings of the National Academy of Sciences of the United States of America, 117(20), (2020): 11029-11037, doi: 10.1073/pnas.2002289117.Marine cold seeps transmit fluids between the subseafloor and seafloor biospheres through upward migration of hydrocarbons that originate in deep sediment layers. It remains unclear how geofluids influence the composition of the seabed microbiome and if they transport deep subsurface life up to the surface. Here we analyzed 172 marine surficial sediments from the deep-water Eastern Gulf of Mexico to assess whether hydrocarbon fluid migration is a mechanism for upward microbial dispersal. While 132 of these sediments contained migrated liquid hydrocarbons, evidence of continuous advective transport of thermogenic alkane gases was observed in 11 sediments. Gas seeps harbored distinct microbial communities featuring bacteria and archaea that are well-known inhabitants of deep biosphere sediments. Specifically, 25 distinct sequence variants within the uncultivated bacterial phyla Atribacteria and Aminicenantes and the archaeal order Thermoprofundales occurred in significantly greater relative sequence abundance along with well-known seep-colonizing members of the bacterial genus Sulfurovum, in the gas-positive sediments. Metabolic predictions guided by metagenome-assembled genomes suggested these organisms are anaerobic heterotrophs capable of nonrespiratory breakdown of organic matter, likely enabling them to inhabit energy-limited deep subseafloor ecosystems. These results point to petroleum geofluids as a vector for the advection-assisted upward dispersal of deep biosphere microbes from subsurface to surface environments, shaping the microbiome of cold seep sediments and providing a general mechanism for the maintenance of microbial diversity in the deep sea.We wish to thank Jody Sandel as well as the crew of R/V GeoExplorer for collection of piston cores, onboard core processing, sample preservation, and shipment. Cynthia Kwan and Oliver Horanszky are thanked for assistance with amplicon library preparation. We also wish to thank Jayne Rattray, Daniel Gittins, and Marc Strous for valuable discussions and suggestions, and Rhonda Clark for research support. Collaborations with Andy Mort from the Geological Survey of Canada, and Richard Hatton from Geoscience Wales are also gratefully acknowledged. This work was financially supported by a Mitacs Elevate Postdoctoral Fellowship awarded to A.C.; an Alberta Innovates-Technology Futures/Eyes High Postdoctoral Fellowship to S.E.R.; and a Natural Sciences and Engineering Research Council Strategic Project Grant, a Genome Canada Genomics Applications Partnership Program grant, a Canada Foundation for Innovation grant (CFI-JELF 33752) for instrumentation, and Campus Alberta Innovates Program Chair funding to C.R.J.H

Qualidade e valor nutritivo das silagens de três híbridos de sorgo (Sorghum bicolor L.) colhidos em diferentes estádios de maturação.

Dois híbridos de sorgo de porte médio e colmo seco e um híbrido de porte alto e colmo suculento foram ensilados em oito estádios de maturação, a partir do florescimento. Foram 24 tratamentos com três repetições cada, sendo os três híbridos (AG 2006 e BR 700 - colmo seco, e BR 601 - colmo suculento) colhidos em oito estádios de maturação. Foram determinados os teores de MS, PB, perdas de MS, densidade, pH, nitrogênio amoniacal (N-NH3), fibra em detergente neutro (FDN), hemicelulose, celulose e lignina, DIVMS e porcentagem de fenóis totais. Utilizou-se o teste SNK para comparação das médias, com um delineamento inteiramente casualizado, em esquema fatorial 3x8. Com o avanço do estádio de maturação, ocorreu aumento na produção de MS até o quinto estádio. Houve, ainda, aumento nos teores de MS, que atingiram o nível ideal entre 21 e 28 dias após o florescimento. Os teores de PB e das frações fibrosas reduziram-se com a maturidade. Obtiveram-se baixos níveis de pH e N-NH3 em todas as silagens, além de baixas perdas de MS. Os híbridos tiveram comportamentos diferentes nos parâmetros lignina e DIVMS. Avaliaram-se os fenóis totais pelo método de azul da Prússia e todas as silagens apresentaram-se com tanino. Não foi encontrada correlação negativa entre os fenóis e a DIVMS. O híbrido AG2006 foi superior aos outros dois híbridos em algumas características e o híbrido BR 601 apesar de ser de porte alto, foi superior ao híbrido BR 700, de duplo propósito, nas variáveis DIVMS e frações fibrosas. Palavras-chave: ensilagem, forragem, nutrição animal, ruminante

Fluctuation theorem for constrained equilibrium systems

We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as iso-kinetic and Nos\'e-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless finite-time averages of the phase-space contraction rate have non-trivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for non-equilibrium stationary states, and appropriate to constrained equilibrium states. Moreover we show these fluctuations are distributed according to a Gaussian curve for long-enough times. Three different systems are considered here, namely (i) a fluid composed of particles interacting with Lennard-Jones potentials; (ii) a harmonic oscillator with Nos\'e-Hoover thermostatting; (iii) a simple hyperbolic two-dimensional map.Comment: To appear in Phys. Rev.

Avaliação pela técnica semiautomática de produção de gases das silagens de quatro genótipos de girassol (Helianthus annus) (Rumbosol 91, Victoria 627, Victoria 807 e Mycogen 9338)

Foram avaliadas as silagens de quatro genótipos de girassol (Helianthus annus) (Rumbosol 91, Victoria 627, Victoria 807 e Mycogen 93338), pela técnica semiautomática de produção de gases. O delineamento experimental utilizado foi o de blocos ao acaso, em esquema de parcelas subdivididas, sendo as médias comparadas pelo teste SNK (p<0,05). O genótipo Rumbosol 91 apresentou a maior produção acumulativa de gases para o tempo de 96 horas de incubação com valor de 128,47mL/g de MS, e o menor valor foi observado para o genótipo Victoria 807 com 92,88. Não foram observadas diferenças entre os valores de degradabilidade da matéria seca (DMS) para as silagens avaliadas nos diferentes tempos. O potencial máximo de produção de gases variou de 91,67 para o genótipo Victoria 807 a 125,46mL/g de MS para a silagem do genótipo Rumbosol 46,39 e 43,26%. O maior valor para taxa de passagem (8%) foi observado para o genótipo Victoria 627. As silagens dos genótipos Rumbosol 91 e Victoria 627 mostraram destacado potencial para produção de gases e taxa de produção de gases