Topological resonance energy,bond resonance energy,and circuit resonance energy

Circuit resonance energy (CRE) is a key quantity that links energetic and magnetic criteria of aromaticity for a polycyclic π‐system. Topological resonance energy (TRE) correlates well with the sum of CREs for an entire π‐system. We found that bond resonance energy (BRE), so far defined to estimate the degree of kinetic stability for a polycyclic π‐system, also correlates very well with the corresponding quantity defined with CREs. These findings justify the view that graph‐theoretical quantities, such as TRE and BRE, can be used safely even though they rely on unrealistic reference structures. Copyright © 2007 John Wiley & Sons, Ltd.     

Statistical energy analysis, energy distribution models and system modes

Expressions for the energy influence coefficients of a built-up structure are found in terms of the modes of the whole structure. These coefficients relate the time and frequency average energies of the subsystems to the subsystem input powers. Rain-on-the-roof excitation over a frequency band Ω is assumed. It is then seen that the system can be described by an SEA model only if a particular condition involving the mode shapes of the system is satisfied. Broadly, the condition holds if the mode shapes of the modes in the frequency band of excitation are, on average, typical enough of all the modes of the system in terms of the distribution of energy throughout the system. If this condition is satisfied then the system can be modelled using an “quasi-SEA” approach, irrespective of the level of damping or of the strength of coupling. However, the resulting model need not be of a proper SEA form, and in particular the indirect coupling loss factors may not be negligible.     

Mass, energy, and the electron

The two-component solutions of the Dirac equation currently in use are not separately a particle equation or an antiparticle equation. We present a unitary transformation that uncouples the four-component, force-free Dirac equation to yield a two-component spinor equation for the force-free motion of a relativistic particle and a corresponding two-component, time-reversed equation for an antiparticle. The particle-antiparticle nature of the two equations is established by applying to the solutions of these two-component equations criteria analogous to those applied for establishing the four-component particle and antiparticle solutions of the four-component Dirac equation. Wave function solutions of our two-component particle equation describe both a right and a left circularly polarized particle. Interesting characteristics of our solutions include spatial distributions that are confined in extent along directions perpendicular to the motion, without the artifice of wave packets, and an intrinsic chirality (handedness) that replaces the usual definition of chirality for particles without mass. Our solutions demonstrate that both the rest mass and the relativistic increase in mass with velocity of the force-free electron are due to an increase in the rate of Zitterbewegung with velocity. We extend this result to a bound electron, in which case the loss of energy due to binding is shown to decrease the rate of Zitterbewegung.     

Equipartition energy, Noether energy and boundary term in gravitational action

In the study of horizon thermodynamics and emergent gravity two natural expressions for energy, E = 2T S (equipartition energy) and E = T S (Noether energy) arise which differ by a factor 2. I clarify the role of these two expressions in different contexts and show how E = T S is also closely related to the Noether charge arising from the boundary term of the Einstein–Hilbert action.     

Dark energy,curvature, and cosmic coincidence

The fact that the energy densities of dark energy and matter are similar currently, known as the coincidence problem, is one of the main unsolved problems of cosmology. We present here a model in which a spatial curvature of the universe can lead to a transition in the present epoch from a matter dominated universe to a scaling dark energy dominance in a very natural way. In particular, we show that if the exponential potential of the dark energy field depends linearly on the spatial curvature density of a closed universe, the observed values of some cosmological parameters can be obtained assuming acceptable values for the present spatial curvature of the universe, and without fine tuning in the only parameter of the model. We also comment on possible variations of this model, and realistic scenarios in which it could arise.     

Rotational energy,pulsars, and active nebulae

A number of different expressions for the rotational energy of a slowly rotating star have appeared in the literature. Here it is shown that these expressions are equivalent. Application to pulsars and the Crab Nebulae are discussed.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.     

Cointegration of output, capital, labor, and energy

Cointegration analysis is applied to the linear combinations of the time series of (the logarithms of) output, capital, labor, and energy for Germany, Japan, and the USA since 1960. The computed cointegration vectors represent the output elasticities of the aggregate energy-dependent Cobb-Douglas function. The output elasticities give the economic weights of the production factors capital, labor, and energy. We find that they are for labor much smaller and for energy much larger than the cost shares of these factors. In standard economic theory output elasticities equal cost shares. Our heterodox findings support results obtained with LINEX production functions.     

Ultra high energy cosmic rays: Identification of possible sources, energy spectra, and propagation

This review is devoted to the problem of the origin of cosmic rays (CR) with energy E >4 × 10¹⁹ eV. The review mainly deals with the hypothesis of CR acceleration in active galactic nuclei (AGN). The review consists of the following five sections: Introduction, three chapters, and Conclusions. The following points are considered in Introduction: shower arrays for detecting ultra high energy cosmic rays (UHECR), the Greisen-Zatsepin-Kuzmin (GZK) cutoff, and the hypotheses of the UHECR origin. Since CRs are of extraterrestrial origin, some astrophysical data used in CR physics are presented in a special section. The identification of UHECR sources with energies E > 4 × 10¹⁹ eV is analyzed in Chapter 2. Chapter 3 deals with CR acceleration in sources and CR escape from sources. Chapter 4 is devoted to particle propagation in intergalactic space with allowance for CR interaction with the microwave background radiation and energy losses (blackbody or GZK cutoff). The propagation of UHECR protons is analyzed and their spectra at the Earth are calculated numerically. In Conclusions, we formulate the results and list the nuclear data needed to develop the model in more detail, namely, to study the propagation of CR nuclei in intergalactic space and to analyze the UHECR composition at the Earth.     

n-p pairing, Wigner energy, and shell gaps

The diagonal correlation energy due to n-n, p-p, and n-p pairing is shown to resolve the discrepancies between shell gaps determined from binding energy differences and the gaps calculated with Woods-Saxon potentials or with other mean-field models. The difference in diagonal correlation energy between an N=Z nucleus with filled shells and the nucleus with one less nucleon resolves this problem in lowest order. A previously derived result, that the diagonal correlation energy in the last occupied orbital for the latter nuclei is 1/2 of the equivalent correlation energy for closed shell nuclei, is tested against observed binding energies and found to be fairly accurate.     

Stationary solutions,energy, and the Bel-Robinson tensor

The absence of stationary source-free solutions and the positive energy problem in general relativity are discussed, at the linearized level, in terms of the Bel-Robinson tensor. The possibility is raised that there may exist stationary solutions to the full Einstein equations in five dimensions.Dedicated to Achille Papapetrou on the occasion of his retirement.Supported in part by NSF grant No. PHY-76-07299.     

Isotope effect,energy gap law and temperature effect in resonance energy transfer

The purpose of this paper is to derive an expression for the energy transfer probability that differs from that of Förster and Dexter in that it can be used explicitly for discussing the effects of deuteration and temperature on the rate of energy transfer, and the relation between the energy gap of the donor and acceptor molecules and the rate of energy transfer. It is found that, as in radiationless transitions, the temperature dependence of the rate of energy transfer can be expressed as

and effects of isotope substitution, and the energy gap between the excited donor and unexcited acceptor molecules on the energy transfer probability, are determined mainly by the Franck-Condon factor.     

Collision cascade evolution in media with energy independent scattering: spatial,energy, and angular distribution

The evolution of an ion induced collision cascade in a solid medium is studied by means of a DPl-approximation to the linear transport equation. Infinite medium and half space geometries are considered. Special attention is given to the effect of the anisotropy of the energy independent scattering cross section. We present results on the spatial distribution of particles moving at different energies, and the energy and angle distribution at the target surface. The spatial distributions are found to obey simple scaling laws; the energy and angular distributions are independent of the form of the scattering cross section, unless it is very strongly forward peaked.     

金属的高能二次电子发射系数与入射能量和能量幂次的关系

 根据原电子射程表达式和金属的有效真二次电子发射系数表达式,推导出金属的高能有效真二次电子发射系数与入射能量、能量幂次的关系式;并根据金属的高能有效真二次电子发射系数与金属的高能二次电子发射系数的关系,推导出金属的高能二次电子发射系数与入射能量、能量幂次的关系式。用实验数据计算出高能原电子轰击在金或银上时原电子入射能量幂次n,采用实验数据证实高能二次电子发射系数与原电子入射能量和能量幂次三者的关系,对结果进行讨论并得出结论：当高能原电子轰击在同一块金属上时,高能二次电子发射系数与原电子入射能量的n-1次幂之积近似为一常数。     

Hydration,entropy, and energy relationships for periodate oxidations

Periodate oxidations of ethanediol and pinacol each occur in two phases; these are (1) formation and (2) decomposition of the intermediate complex. In phase (1), an increase in acidity gives . The rate of oxidation of ethanediol decreases with increasing acidity, whereas the rate of oxidation of pinacol maximizes with H₅IO₆. For both glycols, the activation energy increases and ΔS_act decreases with increasing acidity. In phase (2), the energy of activation is essentially constant with pH, whereas the rate decreases, and the entropy of activation decreases modestly as pH decreases. The latter correlates with the nonhomogeniuty of product formation. Rates for 3‐chloro‐1,2‐propanediol are also listed. Pentaerythritol forms an inactive complex with or H₅IO₆ indicating the importance of chelation in the formation of the intermediate complex. Copyright © 2007 John Wiley & Sons, Ltd.     

Mass,matter, and energy. A relativistic approach

The debate concerning the relations between matter and motion has the same age as philosophy itself. In modern times this problem was transformed into the one concerning the relations between mass and energy. Newton identified mass with matter. Classical thermodynamics brought this conception to its logical conclusion, establishing an ontic dichotomy between mass-matter and energy. On the basis of this pre-relativistic conception, Einstein's famous equation has been interpreted as a relation of equivalence between mass-matter and energy. Nevertheless, if we reject this epistemologically illegitimate identification, it is possible to elaborate a unitary conception of matter, which at the same time is an argument for the unity between matter and motion. In particular, the classical antithesis between matter and field becomes obsolete in the frame of the proposed interpretation.