Symmetry of the Schr\"odinger equation with variable potential

We study symmetry properties of the Schr\"odinger equation with the potential as a new dependent variable, i.e., the transformations which do not change the form of the class of equations. We also consider systems of the Schr\"odinger equations with certain conditions on the potential. In addition we investigate symmetry properties of the equation with convection term. The contact transformations of the Schr\"odinger equation with potential are obtained

Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect

The formulae for Planck length, Hawking temperature and Unruh-Davies temperature are derived by using only laws of classical physics together with the Heisenberg principle. Besides, it is shown how the Hawking relation can be deduced from the Unruh relation by means of the principle of equivalence; the deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure

Scaling Symmetries of Scatterers of Classical Zero-Point Radiation

Classical radiation equilibrium (the blackbody problem) is investigated by the use of an analogy. Scaling symmetries are noted for systems of classical charged particles moving in circular orbits in central potentials V(r)=-k/r^n when the particles are held in uniform circular motion against radiative collapse by a circularly polarized incident plane wave. Only in the case of a Coulomb potential n=1 with fixed charge e is there a unique scale-invariant spectrum of radiation versus frequency (analogous to zero-point radiation) obtained from the stable scattering arrangement. These results suggest that non-electromagnetic potentials are not appropriate for discussions of classical radiation equilibrium.Comment: 13 page

Self-organization, scaling and collapse in a coupled automaton model of foragers and vegetation resources with seed dispersal

We introduce a model of traveling agents ({\it e.g.} frugivorous animals) who feed on randomly located vegetation patches and disperse their seeds, thus modifying the spatial distribution of resources in the long term. It is assumed that the survival probability of a seed increases with the distance to the parent patch and decreases with the size of the colonized patch. In turn, the foraging agents use a deterministic strategy with memory, that makes them visit the largest possible patches accessible within minimal travelling distances. The combination of these interactions produce complex spatio-temporal patterns. If the patches have a small initial size, the vegetation total mass (biomass) increases with time and reaches a maximum corresponding to a self-organized critical state with power-law distributed patch sizes and L\'evy-like movement patterns for the foragers. However, this state collapses as the biomass sharply decreases to reach a noisy stationary regime characterized by corrections to scaling. In systems with low plant competition, the efficiency of the foraging rules leads to the formation of heterogeneous vegetation patterns with $1/f^{\alpha}$ frequency spectra, and contributes, rather counter-intuitively, to lower the biomass levels.Comment: 11 pages, 5 figure

On the new approach to variable separation in the time-dependent Schr\"odinger equation with two space dimensions

We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schr\" odinger equation with the anisotropic harmonic oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schr\" odinger equation ($V=0$).Comment: 21 pages, latex, to appear in the "Journal of Mathematical Physics" (1995

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243 [physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011

Evaluation of Amino Acid Composition as a Geochronometer in Buried Soils on Mount Kenya, East Africa

A sequence of surface and buried paleosols from the slopes of Mount Kenya, East Africa, has been identified and dated by radiocarbon and amino acid dating techniques in order to elucidate the Quaternary history of the area. Buried paleosols vary in radiocarbon age from 900 to > 40,000 yrs BP. They have developed in glacial and periglacial deposits of variable texture, consisting of a high percentage of clasts of phonolite, basalt and syenite. All but two paleosols are located in the Afroalpine zone (above 3200 m). D/L ratios of amino acids in Ab horizons were determined in order to establish their reliability for relative age dating. Alanine, aspartic acid, glutamic acid, leucine, valine, and phenylalanine were routinely analyzed. Aspartic acid, as in other cases, proved reliable yielding remarkably consistent results, with higher ratios corresponding to increasing age. Other acids analyzed showed distinct trends, although not as convincing as aspartic acid. In most cases, the aspartic acid ratio/ age relationships were supported by radiocarbon dates. D/L ratios of aspartic acid varied from approximately 0.07 for modern samples, to approximately 0.45 in samples > 40,000 years old.On a identifié et daté, au radiocarbone et à l'aide de techniques de datations à l'acide aminé, des paléosols enfouis et de surface afin de comprendre l'évolution quaternaire de la région. Les datations au radiocarbone des paléosols enfouis varient de 900 à plus de 40 000 BP. Les sols se sont développés dans des dépôts glaciaires et périglaciaires de différentes textures, constitués de fragments de roches détritiques, de phonolite, de basalte et de syénite. Tous les paléosols, sauf deux, sont situés dans la zone afroalpine (au-dessus de 3200 m). On a déterminé par racémisation les rapports D/L des acides aminés dans les horizons Ab en vue d'évaluer leur fiabilité pour la datation des âges relatifs. On a fait l'analyse de l'alaline, de l'acide aspartique, de l'acide glutamique, de la leucine, de la valine et du phénylalaline. L'acide aspartique, comme dans d'autres cas, a donné des résultats particulièrement satisfaisants, les quotients plus élevés correspondant aux âges les plus anciens. D'autres acides montraient des tendances bien distinctes, mais moins convaincantes que dans le cas de l'acide aspartique. Ainsi, dans la plupart des cas, les relations quotients/âges de l'acide aspartique étaient corroborées par les datations au radiocarbone. Les rapports D/L de l'acide aspartique variaient d'environ 0,07 pour les échantillons modernes à environ 0,45 pour les échantillons de plus de 40 000 ans.Eine Série von an der Oberflâche Negenden und begrabenen Palàobôden von den Hàngen des Mount Kenya, Ost-Afrika, wurde mittels Radiokarbon- und Aminosâuredatierungs-techniken identifiziert und datiert, um die Geschichte dieses Gebiets im Quaternàr zu erhellen. Das durch Radiokarbon bestimmte Alter der begrabenen Palàobôden variiert von 900 bis > 40,000 Jahren v.u.Z. Dièse Bôden haben sich in glazialen und periglazialen Ablagerungen verschiedener Beschaffenheit entwickelt, welche zu einem hohen Prozentsatz aus Trùmmern von Phonolith, Basait und Syenit bestehen. AuBer zweien befinden sich aile Palàobôden in der afroalpinen Zone (oberhalb 3200 m). Die D/L Anteile der Aminosâuren in den Ab-Horizonten wurden bestimmt, um ihre Verlâpiichkeit bei der relativen Altersbestimmung festzustellen. Alamin, aspartische Sàure, Glutamin-Sàure, Leuzin, Valin und Phenylalanin wurden laufend analysiert. Wie in anderen Fallen erwies sich die aspartische Sàure als verlàpiich, indem sie bemerkenswert bestàndige Ergebnisse ergab, bei denen die hôheren Quotienten dem hôheren Alter entsprachen. Andere analysierte Sàuren zeigten ausgepràgte Trends, wenn auch nicht so ùberzeugend wie die aspartische Sàure. In den meisten Fallen wurden die Beziehungen Quotient/Alter der aspartischen Sàure durch Radiokarbondatierungen gestùtzt. Die D/L Anteile der aspartischen Sàure variierten von ungefâhr 0.07 fur moderne Proben bis ungefâhr 0.45 in Proben, die > 40,000 Jahre ait sind

An auxiliary capacitor based ultra-fast drive circuit for shear piezoelectric motors

Shear piezoelectric motors frequently require large voltage changes on very short time scales. Since piezos behave electrically as capacitors, this requires a drive circuit capable of quickly sourcing or sinking a large amount of current at high voltages. Here we describe a novel circuit design using a high voltage amplifier, transistor switching stage, and auxiliary capacitor. This circuit can drive piezoelectric motors at higher speeds and lower costs than conventional methods and with greater flexibility for computer automation. We illustrate its application in a controller for a scanning tunneling microscope coarse approach mechanism and discuss other possible applications and modifications of this circuit.National Science Foundation CAREER programNational Science Foundation MRSEC ProgramResearch Corporation Cottrell Scholarshi

Quasi-local contribution to the scalar self-force: Non-geodesic Motion

We extend our previous calculation of the quasi-local contribution to the self-force on a scalar particle to general (not necessarily geodesic) motion in a general spacetime. In addition to the general case and the case of a particle at rest in a stationary spacetime, we consider as examples a particle held at rest in Reissner-Nordstrom and Kerr-Newman space-times. This allows us to most easily analyse the effect of non-geodesic motion on our previous results and also allows for comparison to existing results for Schwarzschild spacetime.Comment: 11 pages, 1 figure, corrected typo in Eq. 2.

Bohm and Einstein-Sasaki Metrics, Black Holes and Cosmological Event Horizons

We study physical applications of the Bohm metrics, which are infinite sequences of inhomogeneous Einstein metrics on spheres and products of spheres of dimension 5 <= d <= 9. We prove that all the Bohm metrics on S^3 x S^2 and S^3 x S^3 have negative eigenvalue modes of the Lichnerowicz operator and by numerical methods we establish that Bohm metrics on S^5 have negative eigenvalues too. We argue that all the Bohm metrics will have negative modes. These results imply that higher-dimensional black-hole spacetimes where the Bohm metric replaces the usual round sphere metric are classically unstable. We also show that the stability criterion for Freund-Rubin solutions is the same as for black-hole stability, and hence such solutions using Bohm metrics will also be unstable. We consider possible endpoints of the instabilities, and show that all Einstein-Sasaki manifolds give stable solutions. We show how Wick rotation of Bohm metrics gives spacetimes that provide counterexamples to a strict form of the Cosmic Baldness conjecture, but they are still consistent with the intuition behind the cosmic No-Hair conjectures. We show how the Lorentzian metrics may be created ``from nothing'' in a no-boundary setting. We argue that Lorentzian Bohm metrics are unstable to decay to de Sitter spacetime. We also argue that noncompact versions of the Bohm metrics have infinitely many negative Lichernowicz modes, and we conjecture a general relation between Lichnerowicz eigenvalues and non-uniqueness of the Dirichlet problem for Einstein's equations.Comment: 53 pages, 11 figure