1,721,064 research outputs found
Complete Hamiltonian Description of Wave-Like Features in Classical and Quantum Physics
No full textThe analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system describing in terms of ray trajectories, for a stationary refractive medium, a very wide family of wave-like phenomena (including diffraction and interference) going much beyond the limits of the geometrical optics (“eikonal”) approximation, which is contained as a simple limiting case. Due to the fact, moreover, that the time independent Schrödinger equation is itself a Helmholtz-like equation, the same mathematics holding for a classical optical beam turns out to apply to a quantum particle beam moving in a stationary force field, and leads to a system of Hamiltonian equations providing exact and deterministic particle trajectories and dynamical laws, and containing the laws of Classical Mechanics in the eikonal limit
Is wave mechanics consistent with classical logic?
No full textContrary to a wide-spread commonplace, an exact, ray-based treatment holding for any kind of monochromatic wavelike features (such as diffraction and interference) is provided by the structure itself of the Helmholtz equation. This observation allows to dispel-in apparent violation of the uncertainty principle-another commonplace, forbidding an exact, trajectory-based approach to wave mechanics
From Classical to Wave-Mechanical Dynamics
No full textThe time-independent Schroedinger and Klein-Gordon equations - as well as any other Helmholtz-like equation - turn out to be associated with exact sets of Hamiltonian ray-trajectories (coupled by a "Wave Potential" function, encoded in their structure itself) describing any kind of wave-like features, such as diffraction and interference. This property suggests to view Wave Mechanics as a direct, causal and realistic, extension of Classical Mechanics, based on exact trajectories and motion laws of point-like particles "piloted" by de Broglie’s mono-energetic matter waves and avoiding the probabilistic content and the wave-packets both of the standard Copenhagen interpretation and of Bohm’s theory
A non-probabilistic insight into wave mechanics
No full textThe behavior of classical monochromatic waves in stationary media is shown to be ruled by a novel, frequency-dependent function which we call Wave Potential, and which we show to be encoded in the structure of the Helmholtz equation. An exact, Hamiltonian, ray-based kinematical treatment, reducing to the usual eikonal approximation in the absence of Wave Potential, shows that its presence induces a mutual, perpendicular ray-coupling, which is the one and only cause of wave-like phenomena such as diffraction and interference. The "piloting" role of the Wave Potential, whose discovery does already constitute a striking novelty in the case of classical waves, turns out to play an even more important role in the quantum case. Recalling, indeed, that the time-independent Schrödinger equation (associating the motion of mono-energetic particles with stationary monochromatic matter waves) is itself a Helmholtz-like equation, the exact, ray-based treatment developed in the classical case is extended - without resorting to statistical concepts - to the exact, trajectory-based Hamiltonian dynamics of mono-energetic point-like particles. Exact, classical-looking particle trajectories may be defined, contrary to common belief, and turn out to be perpendicularly coupled and piloted by an exact, energydependent Wave Potential, similar in the form, but not in the physical meaning, to the statistical, energy-independent "Quantum Potential" of Bohm's theory, which is affected, as is well known, by the practical necessity of representing particles by means of statistical wave packets, moving along probability flux lines. This result, together with the connection shown to exist betweenWave Potential and Uncertainty Principle, allows a novel, non-probabilistic interpretation of Wave Mechanics, in the original spirit both of de Broglie and Schrödinger
Morphological and karyotypical characterization of four biotypes of red rice (Oryza sativa subsp. Japonica var. sylvatica)
No full textThe present work relates to a morphological and karyotypical analysis of four phenotypically different weedy red rice biotypes in comparison with the cultivar Loto, used as control. A preliminary analysis, by means of a computerized chromosome image method (CHIA – EA), showed that in the red rice various traslocations occur which always involve a chromosome of the first pair together with other elements of the set (Sparacino et al., 2004). The results presented here clearly indicate that each red rice biotype is characterized by a specific traslocation, showing a relationship between different phenotypes and karyotypes
Step by step development of HIRM-KW: a field-scale runoff model
Full text linkOne of the major causes of land degradation and loss of fertility is the soil erosion due to water runoff. In Italy, the 77% of the territory is estimated to be threatened by accelerated erosion, because of both its natural structure and anthropic action. This leads to the need of developing modelling tools able to provide useful information for runoff risk assessment. This paper presents a detailed description of HIRM-KW (Hydrological Infiltration Runoff Model), a physics-based hydrological model for simulating the dynamics of water runoff and infiltration in lowland soils. The model was developed by coupling a Kinematic Wave model with the Smith-Parlange infiltration theory and by making use of the basic laws of motion. Moreover, it was built up step by step in order to obtain a system of equations, lending itself to numerical treatment. HIRM-KW performances were evaluated, for demonstration purposes, by comparing the results of three simulations with corresponding outputs provided by the EUROSEM (European Soil Erosion Model), resulting in a good degree of agreement. HIRM-KW is implemented by a freeware software and the executable program can be requested to the Authors
Identification and characterization of somatic chromosomes of red rice (Oryza sativa subsp. japonica var. sylvatica) by means of a computerized chromosome image method (CHIA-EA)
No full textThe infesting habit of the red rice (Oryza sativa subsp. japonica var. sylvatica, 2n=24) and its diffusion have become a serious problem in rice cultivation because of seed shattering, which reduces rice yield and grain quality. The purpose of this work is to characterize red rice chromosomes and to reveal any differences from the karyotype of cultivated rice Loto (Oryza sativa subsp. japonica) used as reference. The first results, obtained by using a detailed chromosome analysis by means of a chromosome image method (CHIA-EA), showed that in the red rice various translocations occur which always involve a chromosome of the first pair together with other elements of the set. Occasional aneuploid cells with 23 (2n-1) and 25 (2n+1) chromosomes were also observed
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