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Publication A CHROMATIN FOLDING MODEL THAT INCORPORATES LINKER VARIABILITY GENERATES FIBERS RESEMBLING THE NATIVE STRUCTURES(1993) WOODCOCK, CL; GRIGORYEV, SA; HOROWITZ, RA; Whitaker, NPublication Exponents of class groups and elliptic curves(2001-01-01) Wong, SPublication SOME NUMERICAL-METHODS FOR THE HELE-SHAW EQUATIONS(1994) Whitaker, NPublication Densities of quartic fields with even Galois groups(2005-01-01) Wong, SMPublication On the genus of generalized Laguerre polynomials(2005-01-01) Wong, SPublication Effect of backleak in nephron dynamics(2003-01-01) Kevrekidis, PG; Whitaker, NPublication Radially symmetric nonlinear states of harmonically trapped Bose-Einstein condensates(2008-01-01) Herring, G; Carr, LD; Carretero-Gonzalez, R; Kevrekidis, PG; Frantzeskakis, DJStarting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with nr=0,1, and 2 radial nodes, respectively, are systematically continued as a function of the chemical potential and their linear stability is analyzed in detail, in the absence as well as in the presence of topological charge m, i.e., vorticity. It is found that for repulsive interatomic interactions only the ground state is linearly stable throughout the parameter range examined. Furthermore, this is true for topological charges m=0 or 1; solutions with higher topological charge can be unstable even in that case. All higher excited states are found to be unstable in a wide parametric regime. However, for the focusing (attractive) case the ground state with nr=0 and m=0 can only be stable for a sufficiently low number of atoms. Once again, excited states are found to be generically unstable. For unstable profiles, the dynamical evolution of the corresponding branches is also followed to monitor the temporal development of the instability.Publication Towards a reduced model for anglogenesis: A hybrid approach(2005-01-01) Kevrekidis, PG; Whitaker, N; Good, DJPublication Minimal model for tumor angiogenesis(2006-01-01) Kevrekidis, PG; Whitaker, N; Good, DJ; Herring, GJPublication Solitary waves in discrete media with four-wave mixing(2006-01-01) Horne, RL; Kevrekidis, PG; Whitaker, NIn this paper, we examine in detail the principal branches of solutions that arise in vector discrete models with nonlinear intercomponent coupling and four wave mixing. The relevant four branches of solutions consist of two single mode branches (transverse electric and transverse magnetic) and two mixed mode branches, involving both components (linearly polarized and elliptically polarized). These solutions are obtained explicitly and their stability is analyzed completely in the anticontinuum limit (where the nodes of the lattice are uncoupled), illustrating the supercritical pitchfork nature of the bifurcations that give rise to the latter two, respectively, from the former two. Then the branches are continued for finite coupling constructing a full two-parameter numerical bifurcation diagram of their existence. Relevant stability ranges and instability regimes are highlighted and, whenever unstable, the solutions are dynamically evolved through direct computations to monitor the development of the corresponding instabilities. Direct connections to the earlier experimental work of Meier et al. [Phys. Rev. Lett., 91, 143907 (2003)] that motivated the present work are given.Publication A hybrid model for tumor-induced angiogenesis in the cornea in the presence of inhibitors(2007-01-01) Harrington, HA; Maier, M; Naidoo, L; Whitaker, N; Kevrekidis, PGPublication Vortex structures formed by the interference of sliced condensates(2008-01-01) Carretero-Gonzalez, R; Whitaker, N; Kevrekidis, PG; Frantzeskakis, DJWe study the formation of vortices, vortex necklaces, and vortex ring structures as a result of the interference of higher-dimensional Bose-Einstein condensates (BECs). This study is motivated by earlier theoretical results pertaining to the formation of dark solitons by interfering quasi-one-dimensional BECs, as well as recent experiments demonstrating the formation of vortices by interfering higher-dimensional BECs. Here, we demonstrate the genericness of the relevant scenario, but also highlight a number of additional possibilities emerging in higher-dimensional settings. A relevant example is, e.g., the formation of a “cage” of vortex rings surrounding the three-dimensional bulk of the condensed atoms. The effects of the relative phases of the different BEC fragments and the role of damping due to coupling with the thermal cloud are also discussed. Our predictions should be immediately tractable in currently existing experimental BEC setups.Publication Iwasawa invariants of galois deformations(2005-01-01) Weston, TFix a residual ordinary representation :GF→GLn(k) of the absolute Galois group of a number field F. Generalizing work of Greenberg–Vatsal and Emerton–Pollack–Weston, we show that the Iwasawa invariants of Selmer groups of deformations of depends only on and the ramification of the deformation.Publication Explicit unobstructed primes for modular deformation problems of squarefree level(2005-01-01) Weston, TLet f be a newform of weight k3 with Fourier coefficients in a number field K. We give explicit bounds on the set of primes λ of K for which the deformation problem associated to the mod λ Galois representation of f is obstructed. We include some explicit examples.Publication Power residues of Fourier coefficients of modular forms(2005-01-01) Weston, TLet ρ:G\Q→\GLn(\Ql) be a motivic ℓ-adic Galois representation. For fixed m>1 we initiate an investigation of the density of the set of primes p such that the trace of the image of an arithmetic Frobenius at p under ρ is an m-th power residue modulo p. Based on numerical investigations with modular forms we conjecture (with Ramakrishna) that this density equals 1/m whenever the image of ρ is open. We further conjecture that for such ρ the set of these primes p is independent of any set defined by Cebatorev-style Galois-theoretic conditions (in an appropriate sense). We then compute these densities for certain m in the complementary case of modular forms of CM-type with rational Fourier coefficients; our proofs are a combination of the Cebatorev density theorem (which does apply in the CM case) and reciprocity laws applied to Hecke characters. We also discuss a potential application (suggested by Ramakrishna) to computing inertial degrees at p in abelian extensions of imaginary quadratic fields unramified away from p.Publication COROTATING STEADY VORTEX FLOWS WITH N-FOLD SYMMETRY(1985) Turkington, BPublication Local torsion on elliptic curves and the deformation theory of galois representations(2008-01-01) David, C; Weston, TPublication POWER RESIDUES OF FOURIER COEFFICIENTS OF ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION(2009-01-01) Weston, T; Zaurova, EFix m greater than one and let E be an elliptic curve over Q with complex multiplication. We formulate conjectures on the density of primes p (congruent to one modulo m) for which the pth Fourier coefficient of E is an mth power modulo p; often these densities differ from the naive expectation of 1/m. We also prove our conjectures for m dividing the number of roots of unity lying in the CM field of E; the most involved case is m = 4 and complex multiplication by Q(i).Publication Variation of Iwasawa invariants in Hida families(2006-01-01) Emerton, M; Pollack, R; Weston, TPublication A COMPUTATIONAL METHOD OF SOLVING FREE-BOUNDARY PROBLEMS IN VORTEX DYNAMICS(1988) EYDELAND, A; Turkington, B