On the Phase-Space Distribution of Bloch Eigenmodes for Periodic Point Scatterers

Consider the 3-dimensional Laplacian with a potential described by point scatterers placed on the integer lattice. We prove that for Floquet-Bloch modes with fixed quasi-momentum satisfying a certain Diophantine condition, there is a subsequence of eigenvalues of positive density whose eigenfunctions exhibit equidistribution in position space and localisation in momentum space. This result complements the result of Uebersch\"{a}r and Kurlberg who show momentum localisation for zero quasi-momentum in 2-dimensions, and is the first result in this direction in 3-dimensions.Comment: 16 pages, 2 figure

The ammonolysis of esters in liquid ammonia

The rates of ammonolysis of alkyl benzoate and phenylacetate esters in liquid ammonia increase with the acidity of the leaving group alcohol and show relatively large Brønsted βlg values of −1.18 and −1.34, respectively, when plotted against the aqueous pKa of the alcohol. The Brønsted βlg obtained using the pKa of the leaving group alcohol in liquid ammonia is significantly reduced to ~ −0.7, which indicates that the rate-limiting step involves a reaction of the tetrahedral intermediate with little C–OR bond fission in the transition state. The solvolysis reaction is subject to significant catalysis by ammonium ion, which, surprisingly, generates a similar Brønsted βlg indicating little interaction between the ammonium ion and the leaving group. It is concluded that the rate-limiting step for the ammonium-ion-catalysed solvolysis of alkyl esters in liquid ammonia is the diffusion-controlled protonation of the zwitterionic tetrahedral intermediate T+- to give T+, which is rapidly deprotonated to give T0 which is compatible with the rate-limiting step for the uncatalysed reaction being the formation of the neutral T0 by a ‘proton switc

Recent trends in the incidence of anxiety diagnoses and symptoms in primary care.

Anxiety is common, with significant morbidity, but little is known about presentations and recording of anxiety diagnoses and symptoms in primary care. This study aimed to determine trends in incidence and socio-demographic variation in General Practitioner (GP) recorded diagnoses of anxiety, mixed anxiety/depression, panic and anxiety symptoms

Acoustic waves and heating due to molecular energy transfer in an electric discharge CO laser

This paper summarizes analytical studies and the interpretation of experimental results for the compression and rarefaction waves generated in the cavity of a pulsed CO electric discharge laser. A one-dimensional analysis of acoustic waves is applied to a transversely excited laser. The influences of heating in the cathode fall, heat transfer to the cathode, flow through both the anode and cathode, and bulk heating of the plasma are included. The analysis is used to relate the bulk heating rate to observable features of the pressure and density waves. Data obtained from interferograms and reported elsewhere are used to infer the bulk heating rates in a pulsed CO laser. Results are presented for CO/Ar, CO/N2, and N2 plasmas. Comparison of the data with recent theoretical results for the heating due to electron/ neutral collisions and the anharmonic defect associated with V-V energy transfer shows substantial differences at lower values of total energy deposition. The change of heating with E/N is in fairly good agreement with predicted values

The Role of ADA3 Overexpression in Proliferation Through Enhancing MYC Expression

Breast cancer is a heterogeneous disease that is the second leading cause of cancer related deaths in women. Cancer is defined as abnormally heightened proliferation. In order for gene transcription and eventual translation to occur to drive the cell cycle to generate more cells, DNA must be uncoiled from nucleosomes by histone acetylation complexes. One of the key evolutionarily conserved components of these HAT complexes is alteration/deficiency in activation 3 (ADA3). In addition to the role in histone acetylation, this protein also functions as a coactivator for nuclear hormone receptors. Recent findings indicated that nuclear Ada3 correlates with ER+ breast cancers and a favorable survival, while cytoplasmic (overexpression) Ada3 correlates with ErbB2+ and EGFR+ breast cancers and a poor survival. My thesis work focused on the role of Ada3 knockdown and overexpression on cellular proliferation in human derived cell lines. We showed knockdown of ADA3 in immortal hMECs led to inhibition of cell cycle progression, decrease in cyclin B, c-myc or H3K56 levels, and increase in p27 protein. In contrast, ADA3 overexpression in two immortal hMECs and two ER+ breast cancer cell lines enhanced proliferation. Cell cycle analyses showed increased cyclin B and decreased p27 upon ADA3 overexpression. Decreased p27 levels were due to increased turnover of p27 protein. Furthermore, ADA3 overexpression led to increased mRNA levels of early response genes c-fos, EGR1, and c-myc. Analysis of a large cohort of ER+ breast cancer tissue specimens showed a subset of ER+ tumors express higher levels of ADA3 and these tumors also express higher levels of c-myc (

Multiobjective analysis for the design and control of an electromagnetic valve actuator

The electromagnetic valve actuator can deliver much improved fuel efficiency and reduced emissions in spark ignition (SI) engines owing to the potential for variable valve timing when compared with cam-operated, or conventional, variable valve strategies. The possibility exists to reduce pumping losses by throttle-free operation, along with closed-valve engine braking. However, further development is required to make the technology suitable for accept- ance into the mass production market. This paper investigates the application of multiobjective optimization techniques to the conflicting objective functions inherent in the operation of such a device. The techniques are utilized to derive the optimal force–displacement characteristic for the solenoid actuator, along with its controllability and dynamic/steady state performance