Matrix exponential via Clifford algebras

We use isomorphism $\varphi$ between matrix algebras and simple orthogonal Clifford algebras \cl(Q) to compute matrix exponential ${e}^{A}$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in \cl(Q), where the quadratic form $Q$ has a suitable signature $(p,q),$ is exponentiated modulo a minimal polynomial of $p$ using Clifford exponential. Elements of \cl(Q) are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in \cl(Q) are performed with a Maple package `CLIFFORD'. Three examples of matrix exponentiation are given

Sediment Composition Influences Spatial Variation in the Abundance of Human Pathogen Indicator Bacteria within an Estuarine Environment

Faecal contamination of estuarine and coastal waters can pose a risk to human health, particularly in areas used for shellfish production or recreation. Routine microbiological water quality testing highlights areas of faecal indicator bacteria (FIB) contamination within the water column, but fails to consider the abundance of FIB in sediments, which under certain hydrodynamic conditions can become resuspended. Sediments can enhance the survival of FIB in estuarine environments, but the influence of sediment composition on the ecology and abundance of FIB is poorly understood. To determine the relationship between sediment composition (grain size and organic matter) and the abundance of pathogen indicator bacteria (PIB), sediments were collected from four transverse transects of the Conwy estuary, UK. The abundance of culturable Escherichia coli, total coliforms, enterococci, Campylobacter, Salmonella and Vibrio spp. in sediments was determined in relation to sediment grain size, organic matter content, salinity, depth and temperature. Sediments that contained higher proportions of silt and/or clay and associated organic matter content showed significant positive correlations with the abundance of PIB. Furthermore, the abundance of each bacterial group was positively correlated with the presence of all other groups enumerated. Campylobacter spp. were not isolated from estuarine sediments. Comparisons of the number of culturable E. coli, total coliforms and Vibrio spp. in sediments and the water column revealed that their abundance was 281, 433 and 58-fold greater in sediments (colony forming units (CFU)/100 g) when compared with the water column (CFU/100 ml), respectively. These data provide important insights into sediment compositions that promote the abundance of PIB in estuarine environments, with important implications for the modelling and prediction of public health risk based on sediment resuspension and transport

A plasticity model for powder compaction processes incorporating particle deformation and rearrangement

This article is available open access through the publisher’s website at the link below. Copyright @ 2008 Elsevier Ltd.This paper develops a mechanistic model of granular materials that can be used with a commercial finite element package (ABAQUS). The model draws on the ideas of critical state soil mechanics and combines them with the theory of envelopes to develop an elasto-plastic model with a non-associated flow rule. The model incorporates both local deformation at the granule contacts, and rearrangement of the granules so that jointly they account for any bulk deformation. The mechanics of the model closely reflect the physicality of the material behaviour and the model parameters are closely linked (although not simplistically identical) to the characteristics of the granules. This not only gives an insight into the material behaviour, but also enables the model to be used to facilitate design of the material, its processing properties and, hence, component development. The model is used to simulate drained triaxial tests, settlement of a powder in a bin, and some examples of die pressing. Simulations are compared with experimental data and with predictions obtained using other models

Surface tension of the isotropic-nematic interface

We present the first calculations of the pressure tensor profile in the vicinity of the planar interface between isotropic liquid and nematic liquid crystal, using Onsager's density functional theory and computer simulation. When the liquid crystal director is aligned parallel to the interface, the situation of lowest free energy, there is a large tension on the nematic side of the interface and a small compressive region on the isotropic side. By contrast, for perpendicular alignment, the tension is on the isotropic side. There is excellent agreement between theory and simulation both in the forms of the pressure tensor profiles, and the values of the surface tension.Comment: Minor changes; to appear in Phys. Rev.

Bose Einstein condensation at reheating

We discuss the possibility that a perturbative reheating stage after inflation produces a scalar particle gas in a Bose condensate state, emphasizing the possible cosmological role of this phenomenon for symmetry restoration.Comment: 4 pages, 4 figures. Revised version, with an improved analysis of the condensate formatio

Personalized connectome fingerprints: Their importance in cognition from childhood to adult years

Structural neural network architecture patterns in the human brain could be related to individual differences in phenotype, behavior, genetic determinants, and clinical outcomes from neuropsychiatric disorders. Recent studies have indicated that a personalized neural (brain) fingerprint can be identified from structural brain connectomes. However, the accuracy, reproducibility and translational potential of personalized fingerprints in terms of cognition is not yet fully determined. In this study, we introduce a dynamic connectome modeling approach to identify a critical set of white matter subnetworks that can be used as a personalized fingerprint. Several individual variable assessments were performed that demonstrate the accuracy and practicality of personalized fingerprint, specifically predicting the identity and IQ of middle age adults, and the developmental quotient in toddlers. Our findings suggest the fingerprint found by our dynamic modeling approach is sufficient for differentiation between individuals, and is also capable of predicting general intellectual ability across human development. © 2020 The AuthorsSignificance Statement We demonstrate that white matter connections obtained from high resolution medical imaging data form a personalized fingerprint is capable of estimating individual identity and neurodevelopmental variables across human life-span. This important finding provides strong evidence to support the concept of neurological identity and function through human brain connectome mapping

Growth of Inflaton Perturbations and the Post-Inflation Era in Supersymmetric Hybrid Inflation Models

It has been shown that hybrid inflation may end with the formation of non-topological solitons of inflaton field. As a first step towards a fully realistic picture of the post-inflation era and reheating in supersymmetric hybrid inflation models, we study the classical scalar field equations of a supersymmetric hybrid inflation model using a semi-analytical ansatz for the spatial dependence of the fields. Using the minimal D-term inflation model as an example, the inflaton field is evolved using the full 1-loop effective potential from the slow-rolling era to the U(1)_{FI} symmetry-breaking phase transition. Spatial perturbations of the inflaton corresponding to quantum fluctuations are introduced for the case where there is spatially coherent U(1)_{FI} symmetry breaking. The maximal growth of the dominant perturbation is found to depend only on the ratio of superpotential coupling \lambda to the gauge coupling g. The inflaton condensate fragments to non-topological solitons for \lambda/g > 0.09. Possible consequences of non-topological soliton formation in fully realistic SUSY hybrid inflation models are discussed.Comment: 27 pages LaTeX, 8 figures. Additional references and discussio

Approach to ergodicity in quantum wave functions

According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that relates the rate of approach to the decay of certain classical fluctuations. For uniformly hyperbolic systems we find that the variance of the quantum matrix elements is proportional to the variance of the integral of the associated classical operator over trajectory segments of length $T_H$, and inversely proportional to $T_H^2$, where $T_H=h\bar\rho$ is the Heisenberg time, $\bar\rho$ being the mean density of states. Since for these systems the classical variance increases linearly with $T_H$, the variance of the matrix elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians with a mixed phase space and the stadium billiard, our results predict a slower decay due to sticking in marginally unstable regions. Numerical computations supporting these conclusions are presented for the bakers map and the hydrogen atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and uuencoded using uufiles, to appear in Phys Rev E. For related papers, see http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm

The role of self-gentrification in sustainable tourism: Indigenous entrepreneurship at Honghe Hani Rice Terraces World Heritage Site, China

This article examines three forms of tourism gentrification occurring within the newly inscribed (2013) Honghe Hani Rice Terraces UNESCO World Heritage Site in Yunnan, China. The indigenous Hani and Yi communities who populate this remote mountainous area, possess distinct cultural practices that have supported the rice terrace ecosystem for centuries. This article draws on interviews and non-participant observation conducted with inhabitants and newcomers to analyse the types of gentrification occurring within the site. We argue that indigenous cultural practices, and consequently rice cultivation in the area, are threatened by gentrifier-led and state-led gentrification combined with high levels of outward migration of indigenous persons. This could pose a significant threat to the sustainability of tourism at this site and may ultimately compromise the site’s World Heritage Status. In the midst of these dangers, some indigenous people are shown to be improving their socioeconomic standing – and becoming “middle class” or “gentry” – particularly through adopting entrepreneurial strategies gleaned from their encounters with outside-gentrifiers and tourists. This article proposes the concept of “self-gentrification” as a way to describe individuals who seek to improve themselves and their own community, while under threat of gentrification

Leptogenesis and rescattering in supersymmetric models

The observed baryon asymmetry of the Universe can be due to the $B-L$ violating decay of heavy right handed (s)neutrinos. The amount of the asymmetry depends crucially on their number density. If the (s)neutrinos are generated thermally, in supersymmetric models there is limited parameter space leading to enough baryons. For this reason, several alternative mechanisms have been proposed. We discuss the nonperturbative production of sneutrino quanta by a direct coupling to the inflaton. This production dominates over the corresponding creation of neutrinos, and it can easily (i.e. even for a rather small inflaton-sneutrino coupling) lead to a sufficient baryon asymmetry. We then study the amplification of MSSM degrees of freedom, via their coupling to the sneutrinos, during the rescattering phase which follows the nonperturbative production. This process, which mainly influences the (MSSM) $D-$flat directions, is very efficient as long as the sneutrinos quanta are in the relativistic regime. The rapid amplification of the light degrees of freedom may potentially lead to a gravitino problem. We estimate the gravitino production by means of a perturbative calculation, discussing the regime in which we expect it to be reliable.Comment: (20 pages, 6 figures), references added, typos corrected. Final version in revte