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

Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of Berry-phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.Comment: 12 pages, RevTe

Orthogonal localized wave functions of an electron in a magnetic field

We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems.Comment: RevTex, 18 pages, 5 ps fi

Plant Diversity, Soil Microbial Communities, And Ecosystem Function: Are There Any Links?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/117152/1/ecy20038482042.pd

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

Piezoelectricity: Quantized Charge Transport Driven by Adiabatic Deformations

We study the (zero temperature) quantum piezoelectric response of Harper-like models with broken inversion symmetry. The charge transport in these models is related to topological invariants (Chern numbers). We show that there are arbitrarily small periodic modulations of the atomic positions that lead to nonzero charge transport for the electrons.Comment: Latex, letter. Replaced version with minor change in style. 1 fi

Algebraic Geometry Approach to the Bethe Equation for Hofstadter Type Models

We study the diagonalization problem of certain Hofstadter-type models through the algebraic Bethe ansatz equation by the algebraic geometry method. When the spectral variables lie on a rational curve, we obtain the complete and explicit solutions for models with the rational magnetic flux, and discuss the Bethe equation of their thermodynamic flux limit. The algebraic geometry properties of the Bethe equation on high genus algebraic curves are investigated in cooperationComment: 28 pages, Latex ; Some improvement of presentations, Revised version with minor changes for journal publicatio

Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands

We have derived a new set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is used to study general electron transport in a DC or AC electric field. We also find a close connection between the cyclotron orbits in magnetic Bloch bands and the energy subbands in the Hofstadter spectrum. Based on this formalism, the pattern of band splitting, the distribution of Hall conduct- ivities, and the positions of energy subbands in the Hofstadter spectrum can be understood in a simple and unified picture.Comment: 26 pages, Revtex, 6 figures included, submitted to Phys.Rev.

Area versus Length Distribution for Closed Random Walks

Using a connection between the $q$-oscillator algebra and the coefficients of the high temperature expansion of the frustrated Gaussian spin model, we derive an exact formula for the number of closed random walks of given length and area, on a hypercubic lattice, in the limit of infinite number of dimensions. The formula is investigated in detail, and asymptotic behaviours are evaluated. The area distribution in the limit of long loops is computed. As a byproduct, we obtain also an infinite set of new, nontrivial identities.Comment: 17 page

Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte