Molecular dynamics simulations of the interactions of potential foulant molecules and a reverse osmosis membrane

Reverse osmosis (RO) is increasingly one of the most common technologies for desalination worldwide. However, fouling of the membranes used in the RO process remains one of the main challenges. In order to better understand the molecular basis of fouling the interactions of a fully atomistic model of a polyamide membrane with three different foulant molecules, oxygen gas, glucose and phenol, are investigated using molecular dynamics simulations. In addition to unbiased simulations, umbrella sampling methods have been used to calculate the free energy profiles of the membrane-foulant interactions. The results show that each of the three foulants interacts with the membrane in a different manner.It is found that a build up of the two organic foulants, glucose and phenol, occurs at the membrane-saline solution, due to the favourable nature of the interaction in this region, and that the presence of these foulants reduces the rate of flow of water molecules over the membrane-solution interface. However, analysis of the hydrogen bonding shows that the origin of attraction of the foulant for the membrane differs. In the case of oxygen gas the simulations show that a build up of gas within the membrane is likely, although, no deterioration in the membrane performance was observed

Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution

We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with $2 \pi p/q$ flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl group and by the use of its irreducible representation on the space of theta functions, we find a nested set of Bethe equations, which determine the eigenstates and energy spectrum. The Bethe equations have simple form which allows to consider them further in the limit $p, q \to \infty$ by the technique of Thermodynamic Bethe Ansatz and analyze Hofstadter problem for the irrational flux.Comment: 7 pages, 2 figures, Revte

Performance evaluation of a six-axis generalized force-reflecting teleoperator

Work in real-time distributed computation and control has culminated in a prototype force-reflecting telemanipulation system having a dissimilar master (cable-driven, force-reflecting hand controller) and a slave (PUMA 560 robot with custom controller), an extremely high sampling rate (1000 Hz), and a low loop computation delay (5 msec). In a series of experiments with this system and five trained test operators covering over 100 hours of teleoperation, performance was measured in a series of generic and application-driven tasks with and without force feedback, and with control shared between teleoperation and local sensor referenced control. Measurements defining task performance included 100-Hz recording of six-axis force/torque information from the slave manipulator wrist, task completion time, and visual observation of predefined task errors. The task consisted of high precision peg-in-hole insertion, electrical connectors, velcro attach-de-attach, and a twist-lock multi-pin connector. Each task was repeated three times under several operating conditions: normal bilateral telemanipulation, forward position control without force feedback, and shared control. In shared control, orientation was locally servo controlled to comply with applied torques, while translation was under operator control. All performance measures improved as capability was added along a spectrum of capabilities ranging from pure position control through force-reflecting teleoperation and shared control. Performance was optimal for the bare-handed operator

Breathing in the other : enthusiasm and the sublime in eighteenth-century Britain

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on July 31, 2009)Thesis (Ph. D.) University of Missouri-Columbia 2008.This project assesses enthusiasm and the sublime as important eighteenth-century phenomena for establishing the limits and bases of reason and polite discourse. My research focuses eighteenth-century and current sources to try to recover what has been lost in the often heated rhetoric on enthusiasm and the sublime. In looking at eighteenth century philosophy, criticism, and literature, this project re-imagines possibilities of the sublime beyond ideological repression and ethical kindness. It also recasts enthusiasm as more than mere madness or a matter of emotion and takes the problem of inspiration seriously. The method applied here is largely psychoanalytic. Jacques Lacan's concepts of the subject and the Other inform this dissertation's return to enthusiasm and his idea of logical time informs its reassessment of the sublime. This approach sheds new light on non-canonical critics such as John Dennis, long-misunderstood poets such as William Collins, and newly canonized novelists such as Charlotte Lennox.Includes bibliographical reference

On quantum mechanics with a magnetic field on R^n and on a torus T^n, and their relation

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L. The latter theory provides a global description of the former: the quasiperiodic wavefunctions defined on R^n play the role of sections of the associated hermitean line bundle E on T^n, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B = dA generate a Lie algebra g_Q and together with the periodic functions the algebra of observables O_Q . The non-abelian part of g_Q is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G_Q acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g in G_Q . We identify the socalled magnetic translation group as a subgroup of the observables' group Y_Q . We determine the unitary irreducible representations of O_Q, Y_Q corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n = 2m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on R^n and on T^n in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists.Comment: Latex2e file, 22 pages. Final version appeared in IJT

Theory of a magnetic microscope with nanometer resolution

We propose a theory for a type of apertureless scanning near field microscopy that is intended to allow the measurement of magnetism on a nanometer length scale. A scanning probe, for example a scanning tunneling microscope (STM) tip, is used to scan a magnetic substrate while a laser is focused on it. The electric field between the tip and substrate is enhanced in such a way that the circular polarization due to the Kerr effect, which is normally of order 0.1% is increased by up to two orders of magnitude for the case of a Ag or W tip and an Fe sample. Apart from this there is a large background of circular polarization which is non-magnetic in origin. This circular polarization is produced by light scattered from the STM tip and substrate. A detailed retarded calculation for this light-in-light-out experiment is presented.Comment: 17 pages, 8 figure

Topological Graph Inverse Semigroups

To every directed graph $E$ one can associate a \emph{graph inverse semigroup} $G(E)$, where elements roughly correspond to possible paths in $E$. These semigroups generalize polycylic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, Cuntz-Krieger $C^*$-algebras, and Toeplitz $C^*$-algebras. We investigate topologies that turn $G(E)$ into a topological semigroup. For instance, we show that in any such topology that is Hausdorff, $G(E)\setminus \{0\}$ must be discrete for any directed graph $E$. On the other hand, $G(E)$ need not be discrete in a Hausdorff semigroup topology, and for certain graphs $E$, $G(E)$ admits a $T_1$ semigroup topology in which $G(E)\setminus \{0\}$ is not discrete. We also describe, in various situations, the algebraic structure and possible cardinality of the closure of $G(E)$ in larger topological semigroups.Peer reviewe

Diffractive energy spreading and its semiclassical limit

We consider driven systems where the driving induces jumps in energy space: (1) particles pulsed by a step potential; (2) particles in a box with a moving wall; (3) particles in a ring driven by an electro-motive-force. In all these cases the route towards quantum-classical correspondence is highly non-trivial. Some insight is gained by observing that the dynamics in energy space, where $n$ is the level index, is essentially the same as that of Bloch electrons in a tight binding model, where $n$ is the site index. The mean level spacing is like a constant electric field and the driving induces long range hopping 1/(n-m).Comment: 19 pages, 11 figs, published version with some improved figure

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M