Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Assessing the potential of the rust fungus Puccinia spegazzinii as a classical biological control agent for the invasive weed Mikania micrantha in Papua New Guinea

The rust fungus Puccinia spegazzinii was introduced into Papua New Guinea (PNG) in 2008 as a classical biological control agent of the invasive weed Mikania micrantha (Asteraceae), following its earlier release in India, mainland China and Taiwan. Prior to implementing field releases in PNG, assessments were conducted to determine the most suitable rust pathotype for the country, potential for damage to non-target species, most efficient culturing method and potential impact to M. micrantha. The pathotype from eastern Ecuador was selected from the seven pathotypes tested, since all the plant populations evaluated from PNG were highly susceptible to it. None of the 11 plant species (representing eight families) tested to confirm host specificity showed symptoms of infection, supporting previous host range determination. A method of mass-producing inoculum of the rust fungus, using a simple technology which can be readily replicated in other countries, was developed. Comparative growth trials over one rust generation showed that M. micrantha plants infected with the rust generally had both lower growth rates and lower final dry weights, and produced fewer nodes than uninfected plants. There were significant correlations between the number of pustules and (a) the growth rate, (b) number of new nodes and (c) final total dry weight of single-stemmed plants placed in open sunlight and between the number of pustules and number of new nodes of multi-stemmed plants placed under cocoa trees. The trials suggest that field densities of M. micrantha could be reduced if the rust populations are sufficiently high. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.

Prospects for the classical biological control of Calotropis procera (Apocynaceae) using co-evolved insects

Calotropis procera (Apocynaceae), a native of tropical Africa, the Middle East and the Indian subcontinent, is a serious environmental and rangeland weed of Australia and Brazil. It is also a weed in Hawaii in USA, the Caribbean Islands, the Seychelles, Mexico, Thailand, Vietnam and many Pacific Islands. In the native range C. procera has many natural enemies, thus classical biological control could be the most cost-effective option for its long-term management. Based on field surveys in India and a literature search, some 65 species of insects and five species of mites have been documented on C. procera and another congeneric-invador C. gigantea in the native range. All the leaf-feeding and stem-boring agents recorded on Calotropis spp. have wide host range. Three pre-dispersal seed predators,the Aak weevil Paramecops farinosus and the Aak fruit fly Dacuspersicus in the Indian subcontinent, and the Sodom apple fruit fly Dacus longistylus in the Middle East have been identified as prospective biological control agents based on their field host range. In Australia and Brazil, where C. procera has the potential to spread across vast areas, pre-dispersal seed predators would help to limit the spread of the weed. While the fruits of C. procera vary in size and shape across its range, those from India are similar to the ones in Australia and Brazil. Hence, seed-feeding insects from India are more likely to be suitable due to adaptation to fruit size and morphology. Future survey efforts for potential biological control agents should focus on North Africa.

Classical solitons with no quantum counterparts and their supersymmetric revival

We demonstrate the phenomenon stated in the title, using for illustration a two-dimensional scalar-field model with a triple-well potential {fx837-1}. At the classical level, this system supports static topological solitons with finite energy. Upon quantisation, however, these solitons develop infinite energy, which cannot be renormalised away. Thus this quantised model has no soliton sector, even though classical solitons exist. Finally when the model is extended supersymmetrically by adding a Majorana field, finiteness of the soliton energy is recovered.

Overcoming barriers to the successful implementation of a classical biological control strategy for the exotic invasive weed Mikania micrantha in the Asia-Pacific region

Mikania micrantha (Asteraceae) commonly known as mikania, is a major invasive alien plant (IAP) in the tropical humid agricultural and forest zones of the Asia-Pacific region. This fast-growing Neotropical vine is able to smother plants in agricultural ecosystems, agroforestry and natural habitats, reducing productivity and biodiversity. Fungal pathogens were first investigated for the classical biological control of this weed in 1996. This resulted in the selection and screening of the highly host-specific and damaging rust pathogen, Puccinia spegazzinii (Pucciniales). It was first released in India and China in 2005/6, although it is not believed to have established. Since then, it has been released successfully in Taiwan, Papua New Guinea (PNG), Fiji and most recently Vanuatu. The rust has established and is spreading rapidly after applying lessons learned from the first releases on the best rust pathotype and release strategy. In PNG, direct monitoring of vegetation change has demonstrated that the rust is having a significant impact on M. micrantha, with no unpredicted non-target impacts. Despite this, the authorities in many countries where mikania is a problem remain cautious about releasing the rust. In Western Samoa, introduction of the rust was not pursued because of a conflict of interest, and the perception that mikania suppresses even worse weeds. For some, ‘pathophobia’ is still a major obstacle. In Indonesia, where insects for weed CBC have been introduced, pathogens will currently not be considered. In other countries such as Bhutan and Myanmar, there are no baseline data on the presence and impact of IAPs and, with no history of CBC, no institutional framework for implementing this approach. Malaysia has a well-developed framework, but capacity needs to be built in the country. Overall, it remains critical to have champions at decision making levels. Hence, even with an effective ‘off-the-shelf’ agent available, implementation of mikania CBC still requires significant inputs tailored to the countries’ specific needs.

Non-diffusive classical transport in a medium with static randomness

The probability distribution for the displacement x of a particle moving in a one-dimensional continuum is derived exactly for the general case of combined static and dynamic gaussian randomness of the applied force. The dynamics of the particle is governed by the high-friction limit of Brownian motion discussed originally by Einstein and Smoluchowski. In particular, the mean square displacement of the particle varies as t2 for t to infinity . This ballistic motion induced by the disorder does not give rise to a 1/f power spectrum, contrary to recent suggestions based on the above dynamical model.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

The virial expansion of a classical interacting system

We consider N particles interacting pairwise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). For a system placed in a harmonic trap, its classical partition function for the repulsive regime is recognised in the literature. We start by presenting a concise re-derivation of this result. The equation of state is then calculated both for the trapped and the homogeneous gas. Finally, the classical limit of Wu's distribution function for fractional exclusion statistics is obtained and we re-derive the classical virial expansion of the homogeneous gas using this distribution function.

Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

A semi-classical model of the electron containing tachyonic matter

It is shown that the mass of the electron could be conceived as the energy associated with its spinning motion and the angular velocity is such that the linear velocities at the surface exceed the velocity of light; this in fact accounts for its stability against the centrifugal forces in the core region.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

A simple classical approach for the melting temperature of inert-gas nanoparticles

Like the metal and semiconductor nanoparticles, the melting temperature of free inert-gas nanoparticles decreases with decreasing size. The variation is linear with the inverse of the particle size for large nanoparticles and deviates from the linearity for small nanoparticles. The decrease in the melting temperature is slower for free nanoparticles with non-wetting surfaces, while the decrease is faster for nanoparticles with wetting surfaces. Though the depression of the melting temperature has been reported for inert-gas nanoparticles in porous glasses, superheating has also been observed when the nanoparticles are embedded in some matrices. By using a simple classical approach, the influence of size, geometry and the matrix on the melting temperature of nanoparticles is understood quantitatively and shown to be applicable for other materials. It is also shown that the classical approach can be applied to understand the size-dependent freezing temperature of nanoparticles.

Activation barriers for d.c. conductivity in ionic glasses: Classical calculations using the small-cluster approximation

A small-cluster approximation has been used to calculate the activation barriers for the d.c. conductivity in ionic glasses. The main emphasis of this approach is on the importance of the hitherto ignored polarization energy contribution to the total activation energy. For the first time it has been demonstrated that the d.c. conductivity activation energy can be calculated by considering ionic migration to a neighbouring vacancy in a smali cluster of ions consisting of face-sharing anion polyhedra. The activation energies from the model calculations have been compared with the experimental values in the case of highly modified lithium thioborate glasses.