Covariant Hamiltonian Field Theory

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.Comment: 93 pages, no figure

A model-based assessment of the effects of projected climate change on the water resources of Jordan

This paper is concerned with the quantification of the likely effect of anthropogenic climate change on the water resources of Jordan by the end of the twenty-first century. Specifically, a suite of hydrological models are used in conjunction with modelled outcomes from a regional climate model, HadRM3, and a weather generator to determine how future flows in the upper River Jordan and in the Wadi Faynan may change. The results indicate that groundwater will play an important role in the water security of the country as irrigation demands increase. Given future projections of reduced winter rainfall and increased near-surface air temperatures, the already low groundwater recharge will decrease further. Interestingly, the modelled discharge at the Wadi Faynan indicates that extreme flood flows will increase in magnitude, despite a decrease in the mean annual rainfall. Simulations projected no increase in flood magnitude in the upper River Jordan. Discussion focuses on the utility of the modelling framework, the problems of making quantitative forecasts and the implications of reduced water availability in Jordan

Families of Canonical Transformations by Hamilton-Jacobi-Poincar\'e equation. Application to Rotational and Orbital Motion

The Hamilton-Jacobi equation in the sense of Poincar\'e, i.e. formulated in the extended phase space and including regularization, is revisited building canonical transformations with the purpose of Hamiltonian reduction. We illustrate our approach dealing with orbital and attitude dynamics. Based on the use of Whittaker and Andoyer symplectic charts, for which all but one coordinates are cyclic in the Hamilton-Jacobi equation, we provide whole families of canonical transformations, among which one recognizes the familiar ones used in orbital and attitude dynamics. In addition, new canonical transformations are demonstrated.Comment: 21 page

A Translation of the T. Levi-Civita paper: Interpretazione Gruppale degli Integrali di un Sistema Canonico Rend. Acc. Lincei, s. 3^a, vol. VII, 2^o sem. 1899, pp. 235--238

In this paper we provide a translation of a paper by T. Levi-Civita, published in 1899, about the correspondence between symmetries and conservation laws for Hamilton's equations. We discuss the results of this paper and their relationship with the more general classical results by E. Noether.Comment: 12 page

Efficient unfolding pattern recognition in single molecule force spectroscopy data

BackgroundSingle-molecule force spectroscopy (SMFS) is a technique that measures the force necessary to unfold a protein. SMFS experiments generate Force-Distance (F-D) curves. A statistical analysis of a set of F-D curves reveals different unfolding pathways. Information on protein structure, conformation, functional states, and inter- and intra-molecular interactions can be derived.ResultsIn the present work, we propose a pattern recognition algorithm and apply our algorithm to datasets from SMFS experiments on the membrane protein bacterioRhodopsin (bR). We discuss the unfolding pathways found in bR, which are characterised by main peaks and side peaks. A main peak is the result of the pairwise unfolding of the transmembrane helices. In contrast, a side peak is an unfolding event in the alpha-helix or other secondary structural element. The algorithm is capable of detecting side peaks along with main peaks.Therefore, we can detect the individual unfolding pathway as the sequence of events labeled with their occurrences and co-occurrences special to bR\u27s unfolding pathway. We find that side peaks do not co-occur with one another in curves as frequently as main peaks do, which may imply a synergistic effect occurring between helices. While main peaks co-occur as pairs in at least 50% of curves, the side peaks co-occur with one another in less than 10% of curves. Moreover, the algorithm runtime scales well as the dataset size increases.ConclusionsOur algorithm satisfies the requirements of an automated methodology that combines high accuracy with efficiency in analyzing SMFS datasets. The algorithm tackles the force spectroscopy analysis bottleneck leading to more consistent and reproducible results

From Global to Local and Vice Versa: On the Importance of the 'Globalization' Agenda in Continental Groundwater Research and Policy-Making.

Groundwater is one of the most important environmental resources and its use continuously rises globally for industrial, agricultural, and drinking water supply purposes. Because of its importance, more knowledge about the volume of usable groundwater is necessary to satisfy the global demand. Due to the challenges in quantifying the volume of available global groundwater, studies which aim to assess its magnitude are limited in number. They are further restricted in scope and depth of analysis as, in most cases, they do not explain how the estimates of global groundwater resources have been obtained, what methods have been used to generate the figures and what levels of uncertainty exist. This article reviews the estimates of global groundwater resources. It finds that the level of uncertainty attached to existing numbers often exceeds 100 % and strives to establish the reasons for discrepancy. The outcome of this study outlines the need for a new agenda in water research with a more pronounced focus on groundwater. This new research agenda should aim at enhancing the quality and quantity of data provision on local and regional groundwater stocks and flows. This knowledge enhancement can serve as a basis to improve policy-making on groundwater resources globally. Research-informed policies will facilitate more effective groundwater management practices to ensure a more rapid progress of the global water sector towards the goal of sustainability

Polymers and biopolymers at interfaces

This review updates recent progress in the understanding of the behaviour of polymers at surfaces and interfaces, highlighting examples in the areas of wetting, dewetting, crystallization, and 'smart' materials. Recent developments in analysis tools have yielded a large increase in the study of biological systems, and some of these will also be discussed, focussing on areas where surfaces are important. These areas include molecular binding events and protein adsorption as well as the mapping of the surfaces of cells. Important techniques commonly used for the analysis of surfaces and interfaces are discussed separately to aid the understanding of their application

Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation

According to Yang \& Mills (1954), a {\it conserved} current and a related rigid (`global') symmetry lie at the foundations of gauge theory. When the rigid symmetry is extended to a {\it local} one, a so-called gauge symmetry, a new interaction emerges as gauge potential $A$; its field strength is $F\sim {\rm curl} A$. In gravity, the conservation of the energy-momentum current of matter and the rigid translation symmetry in the Minkowski space of special relativity lie at the foundations of a gravitational gauge theory. If the translation invariance is made local, a gravitational potential $\vartheta$ arises together with its field strength $T\sim {\rm curl}\,\vartheta$. Thereby the Minkowski space deforms into a Weitzenb\"ock space with nonvanishing torsion $T$ but vanishing curvature. The corresponding theory is reviewed and its equivalence to general relativity pointed out. Since translations form a subgroup of the Poincar\'e group, the group of motion of special relativity, one ought to straightforwardly extend the gauging of the translations to the gauging of full Poincar\'e group thereby also including the conservation law of the {\it angular momentum} current. The emerging Poincar\'e gauge (theory of) gravity, starting from the viable Einstein-Cartan theory of 1961, will be shortly reviewed and its prospects for further developments assessed.Comment: 46 pages, 4 figures, minor corrections, references added, contribution to "One Hundred Years of Gauge Theory" edited by S. De Bianchi and C. Kiefe