Pressures on water resources due to changing climate, increasing demands, and enhanced recognition of environmental flow needs result in the need for hydrology information to support informed water allocation decision...
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Pressures on water resources due to changing climate, increasing demands, and enhanced recognition of environmental flow needs result in the need for hydrology information to support informed water allocation decisions. However, the absence of hydrometric measurements and limited access to hydrology information in many areas impairs water allocation decision-making. This paper describes a water balance-based modeling approach and an innovative web-based decision-support hydrology tool developed to address this need. Using high-resolution climate, vegetation, and watershed data, a simple gridded water balance model, adjusted to account for locational variability, was developed and calibrated against gauged watersheds, to model mean annual runoff. Mean monthly runoff was modeled empirically, using multivariate regression. The modeled annual runoff results are within 20% of the observed mean annual discharge for 78% of the calibration watersheds, with a mean absolute error of 16%. Modeled monthly runoff corresponds well to observed monthly runoff, with a median Nash-Sutcliffe statistic of 0.92 and a median Spearman rank correlation statistic of 0.98. Monthly and annual flow estimates produced from the model are incorporated into a map- and watershed-based decision-support system referred to as the Northeast Water Tool, to provide critical information to decision makers and others on natural water supply, existing allocations, and the needs of the environment.
A computational method, in which a system is mapped to the time-dependent Schrödinger equation driven by a periodic external force, is formulated for computing linear response functions of quantum systems. This m...
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A computational method, in which a system is mapped to the time-dependent Schrödinger equation driven by a periodic external force, is formulated for computing linear response functions of quantum systems. This method, which scales linearly with the system size N, includes computing the Kubo-Greenwood formula for the dynamic conductivities of systems described by large-scale Hamiltonian matrices. In addition, a scaling approach, derived from this algorithm, is presented to determine the exponent of the conductivity σ(ω)∝ωδ near the metal-insulator quantum transition with high speed and accuracy.
The incompressible two-dimensional Euler equations on a sphere constitute a fundamental model in hydrodynamics. The long-time behaviour of solutions is largely unknown;statistical mechanics predicts a steady vorticity...
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The incompressible two-dimensional Euler equations on a sphere constitute a fundamental model in hydrodynamics. The long-time behaviour of solutions is largely unknown;statistical mechanics predicts a steady vorticity configuration, but detailed numerical results in the literature contradict this theory, yielding instead persistent unsteadiness. Such numerical results were obtained using artificial hyperviscosity to account for the cascade of enstrophy into smaller scales. Hyperviscosity, however, destroys the underlying geometry of the phase flow (such as conservation of Casimir functions), and therefore might affect the qualitative long-time behaviour. Here, we develop an efficient numerical method for long-time simulations that preserve the geometric features of the exact flow, in particular conservation of Casimirs. Long-time simulations on a non-rotating sphere then reveal three possible outcomes for generic initial conditions: the formation of either 2, 3 or 4 coherent vortex structures. These numerical results contradict the statistical mechanics theory and show that previous numerical results, suggesting 4 coherent vortex structures as the generic behaviour, display only a special case. Through integrability theory for point vortex dynamics on the sphere we present a theoretical model which describes the mechanism by which the three observed regimes appear. We show that there is a correlation between a first integral gamma (the ratio of total angular momentum and the square root of enstrophy) and the long-time behaviour: gamma small, intermediate and large yields most likely 4, 3 or 2 coherent vortex formations. Our findings thus suggest that the likely long-time behaviour can be predicted from the first integral gamma.
Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fl...
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Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we present an efficient computational method for the dynamic simulation of Brownian suspensions with fluctuating hydrodynamics that handles both computations and provides a similar approximation as Stokesian Dynamics for dilute and semidilute suspensions. This advancement relies on combining the fluctuating force-coupling method (FCM) with a new midpoint time-integration scheme we refer to as the drifter-corrector (DC). The DC resolves the drift term for fluctuating hydrodynamics-based methods at a minimal computational cost when constraints are imposed on the fluid flow to obtain the stresslet corrections to the particle hydrodynamic interactions. With the DC, this constraint needs only to be imposed once per time step, reducing the simulation cost to nearly that of a completely deterministic simulation. By performing a series of simulations, we show that the DC with fluctuating FCM is an effective and versatile approach as it reproduces both the equilibrium distribution and the evolution of particulate suspensions in periodic as well as bounded domains. In addition, we demonstrate that fluctuating FCM coupled with the DC provides an efficient and accurate method for large-scale dynamic simulation of colloidal dispersions and the study of processes such as colloidal gelation. (C) 2015 AIP Publishing LLC.
The analytical and semi-analytical solutions to the quadratic-cubic fractional nonlinear Schrodinger equation are discussed in this research article. The model's fractional formula is transformed into an integer-o...
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The analytical and semi-analytical solutions to the quadratic-cubic fractional nonlinear Schrodinger equation are discussed in this research article. The model's fractional formula is transformed into an integer-order model by using a new fractional operator. The theoretical and computational approaches can now be applied to fractional models, thanks to this transition. The application of two separate computing schemes yields a large number of novel analytical strategies. The obtained solutions secure the original and boundary conditions, which are used to create semi-analytical solutions using the Adomian decomposition process, which is often used to verify the precision of the two computational methods. All the solutions obtained are used to describe the shifts in a physical structure over time in cases where the quantum effect is present, such as wave-particle duality. The precision of all analytical results is tested by re-entering them into the initial model using Mathematica software 12.
We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point type introduced by Gibbon et al. (Physica D, vol. 132, 1999, pp. 497-510)...
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We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point type introduced by Gibbon et al. (Physica D, vol. 132, 1999, pp. 497-510). By employing the method of mapping to regular systems, presented by Bustamante (Physica D, vol. 240 (13), 2011, pp. 1092-1099) and extended to the symmetry-plane case by Mulungye et al. (J. Fluid Mech., Vol. 771, 2015, pp. 468-502), we establish a curious property of this solution that was not observed in early studies: before but near singularity time, the blowup goes from a fast transient to a slower regime that is well resolved spectrally, even at mid-resolutions of 512(2). This late-time regime has an atypical spectrum: it is Gaussian rather than exponential in the wavenumbers. The analyticity-strip width decays to zero in a finite time, albeit so slowly that it remains well above the collocation-point scale for all simulation times t < T* - 10(-9000), where T* is the singularity time. Reaching such a proximity to singularity time is not possible in the original temporal Variable, because floating-point double precision (approximate to 10(-16)) creates a 'machine-epsilon' barrier. Due to this limitation on the original independent variable, the mapped variables now provide an improved assessment of the relevant blowup quantities, crucially with acceptable accuracy at an unprecedented closeness to the singularity time T* - t approximate to 10(-140).
A mathematical approach to the concept of shape of a submanifold M of a Euclidean space had previously been given by means of 'measuring functions' (e.g. diameter or volume) and of the derived 'size functi...
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A mathematical approach to the concept of shape of a submanifold M of a Euclidean space had previously been given by means of 'measuring functions' (e.g. diameter or volume) and of the derived 'size functions'. This paper relates the study and the computation of any such size function to the structure of critical points of the associated measuring function.
This paper introduces a new modification to the convective Cahn-Hilliard equation and a lattice Boltzmann framework to simulate liquid-solid phase transitions in multicomponent systems. The model takes into account ch...
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This paper introduces a new modification to the convective Cahn-Hilliard equation and a lattice Boltzmann framework to simulate liquid-solid phase transitions in multicomponent systems. The model takes into account changes in properties, such as density, caused by solidification, which leads to volume expansion or contraction. After validating the proposed model against classical problems and experimental data, the solidification of a sessile droplet was investigated in detail. Results of numerical simulations suggest that the environmental conditions are as important as the surface condition in deciding the freezing time and the final shape of the droplet. The environmental properties can also affect the freezing time indirectly through interaction with surface wettability. It has been demonstrated that hydrophobic surfaces may lose their advantages over hydrophilic surfaces in terms of anti-icing performance when primary solidification is initiated from the interface between the droplet and the environment fluid. The deformations of droplets, either with contraction or expansion, were confirmed and compared in different environments. This study offers a new perspective on droplet solidification by exposing the strong influence of environmental conditions and meanwhile provides a useful numerical method to predict the phase change process.
We develop a multiple shooting parameterization method for studying stable/unstable manifolds attached to periodic orbits of systems whose dynamics is determined by an implicit rule. We represent the local invariant m...
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We develop a multiple shooting parameterization method for studying stable/unstable manifolds attached to periodic orbits of systems whose dynamics is determined by an implicit rule. We represent the local invariant manifold using high order polynomials and show that the method leads to efficient numerical calculations. We implement the method for several example systems in dimension two and three. The resulting manifolds provide useful information about the orbit structure of the implicit system even in the case that the implicit relation is neither invertible nor single-valued.
The linear variational method is a standard computational method in quantum mechanics and quantum chemistry. As taught in most classes, the general guidance is to include as many basis functions as practical in the va...
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The linear variational method is a standard computational method in quantum mechanics and quantum chemistry. As taught in most classes, the general guidance is to include as many basis functions as practical in the variational wave function. However, if it is desired to study the patterns of energy change accompanying the change of system parameters such as the shape and strength of the potential energy, the problem becomes more complicated. We use one-dimensional systems with a particle in a rectangular or in a harmonic potential confined in an infinite rectangular box to illustrate situations where a variational calculation can give incorrect results. These situations result when the energy of the lowest eigenvalue is strongly dependent on the parameters that describe the shape and strength of the potential. The numerical examples described in this work are provided as cautionary notes for practitioners of numerical variational calculations.
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