5,070 research outputs found
Naive Noncommutative Blowing Up
Let B(X,L,s) be the twisted homogeneous coordinate ring of an irreducible
variety X over an algebraically closed field k with dim X > 1. Assume that c in
X and s in Aut(X) are in sufficiently general position. We show that if one
follows the commutative prescription for blowing up X at c, but in this
noncommutative setting, one obtains a noncommutative ring R=R(X,c,L,s) with
surprising properties. In particular:
(1) R is always noetherian but never strongly noetherian.
(2) If R is generated in degree one then the images of the R-point modules in
qgr(R) are naturally in (1-1) correspondence with the closed points of X.
However, both in qgr(R) and in gr(R), the R-point modules are not parametrized
by a projective scheme.
(3) qgr R has finite cohomological dimension yet H^1(R) is infinite
dimensional.
This gives a more geometric approach to results of the second author who
proved similar results for X=P^n by algebraic methods.Comment: Latex, 42 page
On the critical free-surface flow over localised topography
Flow over bottom topography at critical Froude number is examined with a focus on steady, forced solitary wave solutions with algebraic decay in the far-field, and their stability. Using the forced Korteweg-de Vries (fKdV) equation the weakly-nonlinear steady solution space is examined in detail for the particular case of a Gaussian dip using a combination of asymptotic analysis and numerical computations. Non-uniqueness is established and a seemingly infinite set of steady solutions is uncovered. Non-uniqueness is also demonstrated for the fully nonlinear problem via boundary-integral calculations. It is shown analytically that critical flow solutions have algebraic decay in the far-field both for the fKdV equation and for the fully nonlinear problem and, moreover, that the leading-order form of the decay is the same in both cases. The linear stability of the steady fKdV solutions is examined via eigenvalue computations and by a numerical study of the initial value fKdV problem. It is shown that there exists a linearly stable steady solution in which the deflection from the otherwise uniform surface level is everywhere negative
The effects of the coastal environment on the atmospheric mercury cycle
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95186/1/jgrd10304.pd
Existence and Stability of Steady Fronts in Bistable CML
We prove the existence and we study the stability of the kink-like fixed
points in a simple Coupled Map Lattice for which the local dynamics has two
stable fixed points. The condition for the existence allows us to define a
critical value of the coupling parameter where a (multi) generalized
saddle-node bifurcation occurs and destroys these solutions. An extension of
the results to other CML's in the same class is also displayed. Finally, we
emphasize the property of spatial chaos for small coupling.Comment: 18 pages, uuencoded PostScript file, J. Stat. Phys. (In press
Steady two dimensional free-surface flow over semi-infinite and finite-length corrugations in an open channel
Free-surface flow past a semi-infinite or a finite length corrugation in an otherwise flat and horizontal open channel is considered. Numerical solutions for the steady flow problem are computed using both a weakly nonlinear and fully nonlinear model. The new solutions are classified in terms of a depth-based Froude number and the four classical flow types (supercritical, subcritical, generalised hydraulic rise and hydraulic rise) for flow over a small bump. While there is no hydraulic fall solution for semi-infinite topography, we provide strong numerical evidence that such a solution does exist in the case of a finite length corrugation. Numerical solutions are also found for the other flow types for either semi-infinite or finite length corrugation. For subcritical flow over a semi-infinite corrugation, the free-surface profile is found to be quasiperiodic in nature. A discussion of the new results is made with reference to the classical problem of flow over a bump
Finding the point of no return : dynamical systems theory applied to the moving contact-line instability
The wetting and dewetting of solid surfaces is ubiquitous in physical systems across a range of length scales, and it is well known that there are maximum speeds at which these processes are stable. Past this maximum, flow transitions occur, with films deposited on solids (dewetting) and the outer fluid entrained into the advancing one (wetting). These new flow states may be desirable, or not, and significant research effort has focused on understanding when and how they occur. Up until recently, numerical simulations captured these transitions by focussing on steady calculations. This review concentrates on advances made in the computation of the time-dependent problem, utilising dynamical systems theory. Facilitated via a linear stability analysis, unstable solutions act as âedge statesâ, which form the âpoint of no returnâ for which perturbations from stable flow cease decaying and, significantly, show the system can become unstable before the maximum speed is achieved
Probabilistic Guarded P Systems, A New Formal Modelling Framework
Multienvironment P systems constitute a general, formal
framework for modelling the dynamics of population biology, which consists
of two main approaches: stochastic and probabilistic. The framework
has been successfully used to model biologic systems at both micro (e.g.
bacteria colony) and macro (e.g. real ecosystems) levels, respectively.
In this paper, we extend the general framework in order to include
a new case study related to P. Oleracea species. The extension is made
by a new variant within the probabilistic approach, called Probabilistic
Guarded P systems (in short, PGP systems). We provide a formal definition,
a simulation algorithm to capture the dynamics, and a survey of
the associated software.Ministerio de EconomĂa y Competitividad TIN2012- 37434Junta de AndalucĂa P08-TIC-0420
Predictors of Arterial Stiffness in Law Enforcement Officers
Background: Compare arterial stiffness among law enforcement officers (LEOs) versus general population normative values and identify predictors of arterial stiffness in LEOs. Methods: Seventy male LEOs (age: 24â54 years) completed body composition, blood pressures, physical activity level, and carotid-femoral pulse wave velocity (cfPWV) measurements. T-tests and regression analyses were utilized to compare LEO data to normative data and predict cfPWV, respectively. Results: Compared to similar age strata within the general population, cfPWV was lower among LEOâs under 30-years (mean difference = â0.6 m·sâ1), but higher among LEOs 50â55-years (mean difference = 1.1 m·sâ1). Utilizing regression, age, relative body fat, and diastolic blood pressure explained the greatest variance in LEOâs cfPWV (adj. R2 = 0.56, p \u3c 0.001). Conclusion: This investigation demonstrated that arterial stiffness may progress more rapidly in LEOs and LEOsâ relative body fat and blood pressure may primarily affect arterial stiffness and risk of CVD
Explicitly solvable cases of one-dimensional quantum chaos
We identify a set of quantum graphs with unique and precisely defined
spectral properties called {\it regular quantum graphs}. Although chaotic in
their classical limit with positive topological entropy, regular quantum graphs
are explicitly solvable. The proof is constructive: we present exact periodic
orbit expansions for individual energy levels, thus obtaining an analytical
solution for the spectrum of regular quantum graphs that is complete, explicit
and exact
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