Author

# Michele L. Joyner

Other affiliations: University of West Georgia, North Carolina State University

Bio: Michele L. Joyner is an academic researcher from East Tennessee State University. The author has contributed to research in topics: Anelosimus studiosus & Nearest neighbour distribution. The author has an hindex of 6, co-authored 19 publications receiving 145 citations. Previous affiliations of Michele L. Joyner include University of West Georgia & North Carolina State University.

##### Papers

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TL;DR: This paper uses eddy current based techniques and reduced order modeling to explore the feasibility of detecting a subsurface damage in structures such as air foils and pipelines and suggests it can reduce the computational time on average by a factor of 3000.

Abstract: This paper uses eddy current based techniques and reduced order modeling to explore the feasibility of detecting a subsurface damage in structures such as air foils and pipelines. To identify the geometry of a damage, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. Therefore, our computational methods are based on the reduced order Karhunen-Loeve or Proper Orthogonal Decomposition (POD) techniques. For proof-of-concept, we implement the methodology on a 2-D problem and find the methods to be efficient and robust even with data containing 10 Furthermore, the methods are fast; our findings suggest we can reduce the computational time on average by a factor of 3000.

69 citations

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TL;DR: Through mathematical models, the use of a new antibiotic that is distributed in various ways and how this could reduce total resistance in the hospital is examined and the benefits and limitations of each scenario are examined.

Abstract: The increase in antibiotic resistance continues to pose a public health risk as very few new antibiotics are being produced, and bacteria resistant to currently prescribed antibiotics is growing. Within a typical hospital setting, one may find patients colonized with bacteria resistant to a single antibiotic, or, of a more emergent threat, patients may be colonized with bacteria resistant to multiple antibiotics. Precautions have been implemented to try to prevent the growth and spread of antimicrobial resistance such as a reduction in the distribution of antibiotics and increased hand washing and barrier preventions; however, the rise of this resistance is still evident. As a result, there is a new movement to try to re-examine the need for the development of new antibiotics. In this paper, we use mathematical models to study the possible benefits of implementing a new antibiotic in this setting; through these models, we examine the use of a new antibiotic that is distributed in various ways and how this could reduce total resistance in the hospital. We compare several different models in which patients colonized with both single and dual-resistant bacteria are present, including a model with no additional treatment protocols for the population colonized with dual-resistant bacteria as well as models including isolation and/or treatment with a new antibiotic. We examine the benefits and limitations of each scenario in the simulations presented.

11 citations

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TL;DR: Which factors impact the effectiveness of the POD method in the NDE damage detection problem are explored and whether or not the answers are the same for different damage parameters or if the parameter the authors wish to approximate has an impact on the answers to these questions.

10 citations

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TL;DR: This paper points out some of the problems in the traditional implementation of the reduced-order POD/Galerkin method when used in conjunction with eddy current damage detection and argues that in certain circumstances, the P OD/interpolation method may be a better choice.

8 citations

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TL;DR: The numerical results suggest that the SSA is the best choice due to its simplicity and accuracy for the simpler VRE model, and with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred.

Abstract: In this paper, we investigate three particular algorithms: a stochastic simulation algorithm (SSA), and explicit and implicit tau-leaping algorithms. To compare these methods, we used them to analyze two infection models: a Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunodeficiency Virus (HIV) within host infection model. While the first has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative efficiency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational efficiency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred.

7 citations

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TL;DR: Error estimates for Galerkin proper orthogonal decomposition (POD) methods for nonlinear parabolic systems arising in fluid dynamics are proved and the backward Euler scheme is considered.

Abstract: Error estimates for Galerkin proper orthogonal decomposition (POD) methods for nonlinear parabolic systems arising in fluid dynamics are proved For the time integration the backward Euler scheme is considered The asymptotic estimates involve the singular values of the POD snapshot set and the grid-structure of the time discretization as well as the snapshot locations

752 citations

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01 Jan 2005TL;DR: In this article, the authors consider the problem of nonlinear evolution in real separable Hilbert spaces, where the inner product in V is given by a symmetric bounded, coercive, bilinear form.

Abstract: Nonlinear Dynamical System Let V and H be real separable Hilbert spaces and suppose that V is dense in H with compact embedding. By 〈· , ·〉H we denote the inner product in H. The inner product in V is given by a symmetric bounded, coercive, bilinear form a : V × V → IR: 〈φ,ψ〉V = a(φ,ψ) for all φ,ψ ∈ V (10.16) with associated norm given by ‖ · ‖V = √ a(· , ·). Since V is continuously injected into H, there exists a constant cV > 0 such that ‖φ‖H ≤ cV ‖φ‖V for all φ ∈ V. (10.17) We associate with a the linear operator A: 〈Aφ,ψ〉V ′,V = a(φ,ψ) for all φ,ψ ∈ V, where 〈· , ·〉V ′,V denotes the duality pairing between V and its dual. Then, by the Lax-Milgram lemma, A is an isomorphism from V onto V ′. Alternatively, A can be considered as a linear unbounded self-adjoint operator in H with domain D(A) = {φ ∈ V : Aφ ∈ H}. By identifying H and its dual H ′ it follows that 10 POD: Error Estimates and Suboptimal Control 269 D(A) ↪→ V ↪→ H = H ′ ↪→ V ′, each embedding being continuous and dense, when D(A) is endowed with the graph norm of A. Moreover, let F : V × V → V ′ be a bilinear continuous operator mapping D(A) × D(A) into H. To simplify the notation we set F (φ) = F (φ,φ) for φ ∈ V . For given f ∈ C([0, T ];H) and y0 ∈ V we consider the nonlinear evolution problem d dt 〈y(t), φ〉H + a(y(t), φ) + 〈F (y(t)), φ〉V ′,V = 〈f(t), φ〉H (10.18a) for all φ ∈ V and t ∈ (0, T ] a.e. and y(0) = y0 in H. (10.18b) Assumption (A1). For every f ∈ C([0, T ];H) and y0 ∈ V there exists a unique solution of (10.18) satisfying y ∈ C([0, T ];V ) ∩ L(0, T ;D(A)) ∩H(0, T ;H). (10.19) Computation of the POD Basis Throughout we assume that Assumption (A1) holds and we denote by y the unique solution to (10.18) satisfying (10.19). For given n ∈ IN let 0 = t0 < t1 < . . . < tn ≤ T (10.20) denote a grid in the interval [0, T ] and set δtj = tj − tj−1, j = 1, . . . , n. Define ∆t = max (δt1, . . . , δtn) and δt = min (δt1, . . . , δtn). (10.21) Suppose that the snapshots y(tj) of (10.18) at the given time instances tj , j = 0, . . . , n, are known. We set V = span {y0, . . . , y2n}, where yj = y(tj) for j = 0, . . . , n, yj = ∂ty(tj−n) for j = n + 1, . . . , 2n with ∂ty(tj) = (y(tj)−y(tj−1))/δtj , and refer to V as the ensemble consisting of the snapshots {yj} j=0, at least one of which is assumed to be nonzero. Furthermore, we call {tj}j=0 the snapshot grid. Notice that V ⊂ V by construction. Throughout the remainder of this section we let X denote either the space V or H. 270 Michael Hinze and Stefan Volkwein Remark 10.2.1 (compare [KV01, Remark 1]). It may come as a surprise at first that the finite difference quotients ∂ty(tj) are included into the set V of snapshots. To motivate this choice let us point out that while the finite difference quotients are contained in the span of {yj} j=0, the POD bases differ depending on whether {∂ty(tj)}j=1 are included or not. The linear dependence does not constitute a difficulty for the singular value decomposition which is required to compute the POD basis. In fact, the snapshots themselves can be linearly dependent. The resulting POD basis is, in any case, maximally linearly independent in the sense expressed in (P ) and Proposition 10.2.5. Secondly, in anticipation of the rate of convergence results that will be presented in Section 10.3.3 we note that the time derivative of y in (10.18) must be approximated by the Galerkin POD based scheme. In case the terms {∂ty(tj)}j=1 are included in the snapshot ensemble, we are able to utilize the estimate

294 citations

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TL;DR: A new multi-scale method for the homogenization analysis of hyperelastic solids undergoing finite strains, coined as reduced model multiscale method (R3M), allows reducing significantly the computation times, as no large matrix needs to be inverted and as the convergence of both macro and micro problems is enhanced.

251 citations

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TL;DR: In this article, a 4DVAR approach based on proper orthogonal decomposition (POD) is proposed to reduce the dimension of control space and reduce the size of dynamical model, both in dramatic ways.

Abstract: Four-dimensional variational data assimilation (4DVAR) is a powerful tool for data assimilation in meteorology and oceanography. However, a major hurdle in use of 4DVAR for realistic general circulation models is the dimension of the control space (generally equal to the size of the model state variable and typically of order 10 7 -10 8 ) and the high computational cost in computing the cost function and its gradient that require integration model and its adjoint model. In this paper, we propose a 4DVAR approach based on proper orthogonal decomposition (POD). POD is an efficient way to carry out reduced order modelling by identifying the few most energetic modes in a sequence of snapshots from a time-dependent system, and providing a means of obtaining a low-dimensional description of the system's dynamics. The POD-based 4DVAR not only reduces the dimension of control space, but also reduces the size of dynamical model, both in dramatic ways. The novelty of our approach also consists in the inclusion of adaptability, applied when in the process of iterative control the new control variables depart significantly from the ones on which the POD model was based upon. In addition, these approaches also allow to conveniently constructing the adjoint model. The proposed POD-based 4DVAR methods are tested and demonstrated using a reduced gravity wave ocean model in Pacific domain in the context of identical twin data assimilation experiments. A comparison with data assimilation experiments in the full model space shows that with an appropriate selection of the basis functions the optimization in the POD space is able to provide accurate results at a reduced computational cost. The POD-based 4DVAR methods have the potential to approximate the performance of full order 4DVAR with less than 1/100 computer time of the full order 4DVAR. The HFTN (Hessian-free truncated-Newton)algorithm benefits most from the order reduction (see (Int. J. Numer. Meth. Fluids, in press)) since computational savings are achieved both in the outer and inner iterations of this method.

215 citations

01 Jan 2016

TL;DR: The elements of mathematical ecology is universally compatible with any devices to read, allowing you to get the most less latency time to download any of the authors' books like this one.

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203 citations