1
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Ohtani T, Kanai Y, Kantartzis NV. Accurate Nonstandard Path Integral Models for Arbitrary Dielectric Boundaries in 2-D NS-FDTD Domains. Sensors (Basel) 2024; 24:2373. [PMID: 38610584 PMCID: PMC11014161 DOI: 10.3390/s24072373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Revised: 03/31/2024] [Accepted: 04/07/2024] [Indexed: 04/14/2024]
Abstract
An efficient path integral (PI) model for the accurate analysis of curved dielectric structures on coarse grids via the two-dimensional nonstandard finite-difference time-domain (NS-FDTD) technique is introduced in this paper. In contrast to previous PI implementations of the perfectly electric conductor case, which accommodates orthogonal cells in the vicinity of curved surfaces, the novel PI model employs the occupation ratio of dielectrics in the necessary cells, providing thus a straightforward and instructive means to treat an assortment of practical applications. For its verification, the reflection from a flat plate and the scattering from a cylinder using the PI model are investigated. Results indicate that the featured methodology can enable the reliable and precise modeling of arbitrarily shaped dielectrics in the NS-FDTD algorithm on coarse grids.
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Affiliation(s)
- Tadao Ohtani
- Independent Researcher, Asahikawa 070-0841, Japan;
| | - Yasushi Kanai
- Department of Engineering, Faculty of Engineering, Niigata Institute of Technology, Kashiwazaki 945-1195, Japan;
| | - Nikolaos V. Kantartzis
- School of Electrical and Computer Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece
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2
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Guryev GD, Milshteyn E, Giannakopoulos II, Lattanzi R, Wald LL, Adalsteinsson E, White JK. MARIE 2.0: A Perturbation Matrix Based Patient-Specific MRI Field Simulator. IEEE Trans Biomed Eng 2023; 70:1575-1586. [PMID: 36383593 PMCID: PMC10689076 DOI: 10.1109/tbme.2022.3222748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
High static field MR scanners can produce human tissue images of astounding clarity, but rely on high frequency electromagnetic radiation that generates complicated in-tissue field patterns that are patient-specific and potentially harmful. Many such scanners use parallel transmitters to better control field patterns, but then adjust the transmitters based on general guidelines rather than optimizing for the specific patient, mostly because computing patient-specific fields was presumed far too slow. It was recently demonstrated that the combination of fast low-resolution tissue mapping and fast voxel-based field simulation can be used to perform a patient-specific MR safety check in minutes. However, the field simulation required several of those minutes, making it too slow to perform the dozens of simulations that would be needed for patient-specific optimization. In this paper we describe a compressed-perturbation-matrix technique that nearly eliminates the computational cost of including complex coils (or coils and shields) in voxel-based field simulation of tissue, thereby reducing simulation time from minutes to seconds. The approach is demonstrated on a wide variety of head+coil and head+coil+shield configurations, using the implementation in MARIE 2.0, the latest version of the open-source MR field simulator MARIE.
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3
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Musolino P, Mishuris G. Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem. Philos Trans A Math Phys Eng Sci 2022; 380:20220159. [PMID: 36154481 PMCID: PMC9510036 DOI: 10.1098/rsta.2022.0159] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 07/08/2022] [Indexed: 06/16/2023]
Abstract
We study the asymptotic behaviour of solutions of a boundary value problem for the Laplace equation in a perforated domain in [Formula: see text], [Formula: see text], with a (nonlinear) Robin boundary condition on the boundary of the small hole. The problem we wish to consider degenerates in three respects: in the limit case, the Robin boundary condition may degenerate into a Neumann boundary condition, the Robin datum may tend to infinity, and the size ϵ of the small hole where we consider the Robin condition collapses to 0. We study how these three singularities interact and affect the asymptotic behaviour as ϵ tends to 0, and we represent the solution and its energy integral in terms of real analytic maps and known functions of the singular perturbation parameters. This article is part of the theme issue 'Non-smooth variational problems and applications'.
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Affiliation(s)
- Paolo Musolino
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, via Torino 155, 30172 Venezia Mestre, Italy
| | - Gennady Mishuris
- Department of Mathematics, Aberystwyth University, Ceredigion, Aberystwyth SY23 3BZ, UK
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4
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Daniele VG, Lombardi G. The generalized Wiener-Hopf equations for the elastic wave motion in angular regions. Proc Math Phys Eng Sci 2022; 478:20210624. [PMID: 35153614 PMCID: PMC8753162 DOI: 10.1098/rspa.2021.0624] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 11/29/2021] [Indexed: 11/28/2022] Open
Abstract
In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener-Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.
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5
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Alvarez L, Colom M, Morel JD, Morel JM. Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique. Proc Natl Acad Sci U S A 2021; 118:e2105112118. [PMID: 34876517 PMCID: PMC8685677 DOI: 10.1073/pnas.2105112118] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/11/2021] [Indexed: 12/20/2022] Open
Abstract
The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt But it estimates Rt with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it Our signal-processing approach to this problem yields both Rt and a restored it corrected for the "weekend effect" by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.
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Affiliation(s)
- Luis Alvarez
- Centro de Tecnologías de la Imagen, Departamento de Informática y Sistemas, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain;
| | - Miguel Colom
- Centre Borelli, Université Paris-Saclay, École Normale Supérieure Paris-Saclay, CNRS, F-91190 Gif-sur-Yvette, France
| | - Jean-David Morel
- Laboratoire de Physiologie Intégrative et Systémique, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Jean-Michel Morel
- Centre Borelli, Université Paris-Saclay, École Normale Supérieure Paris-Saclay, CNRS, F-91190 Gif-sur-Yvette, France
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6
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Alvarez L, Colom M, Morel JD, Morel JM. Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique. Proc Natl Acad Sci U S A 2021. [PMID: 34876517 DOI: 10.1073/pnas.210511211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/14/2023] Open
Abstract
The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt But it estimates Rt with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it Our signal-processing approach to this problem yields both Rt and a restored it corrected for the "weekend effect" by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.
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Affiliation(s)
- Luis Alvarez
- Centro de Tecnologías de la Imagen, Departamento de Informática y Sistemas, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain;
| | - Miguel Colom
- Centre Borelli, Université Paris-Saclay, École Normale Supérieure Paris-Saclay, CNRS, F-91190 Gif-sur-Yvette, France
| | - Jean-David Morel
- Laboratoire de Physiologie Intégrative et Systémique, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Jean-Michel Morel
- Centre Borelli, Université Paris-Saclay, École Normale Supérieure Paris-Saclay, CNRS, F-91190 Gif-sur-Yvette, France
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7
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Daniele VG, Lombardi G. The generalized Wiener-Hopf equations for wave motion in angular regions: electromagnetic application. Proc Math Phys Eng Sci 2021; 477:20210040. [PMID: 35153569 PMCID: PMC8385354 DOI: 10.1098/rspa.2021.0040] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2021] [Accepted: 07/28/2021] [Indexed: 11/12/2022] Open
Abstract
In this work, we introduce a general method to deduce spectral functional equations and, thus, the generalized Wiener-Hopf equations (GWHEs) for wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity with application to electromagnetics. The functional equations are obtained by solving vector differential equations of first order that model the problem. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper shows the general theory and the validity of GWHEs in the context of electromagnetic applications with respect to the current literature. Extension to scattering problems by wedges in arbitrarily linear media in different physics will be presented in future works.
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Affiliation(s)
- V G Daniele
- Department of Electronics and Communications, Politecnico di Torino, 10129 Torino, Italy
| | - G Lombardi
- Department of Electronics and Communications, Politecnico di Torino, 10129 Torino, Italy
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8
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Aguirre-Manzo LA, González-Mozuelos P. A self-consistent Ornstein-Zernike jellium for highly charged colloids (microgels) in suspensions with added salt. J Phys Condens Matter 2021; 33:275101. [PMID: 34047280 DOI: 10.1088/1361-648x/abfe95] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 05/06/2021] [Indexed: 06/12/2023]
Abstract
This work discusses a jellium scheme, built within the framework of the multicomponent Ornstein-Zernike (OZ) equation, which is capable of describing the collective structure of suspensions of highly charged colloids with added salt, even in the presence of finite-size multivalent microions. This approach uses a suitable approximation to decouple the microion-microion correlations from the macroion-microion profiles, which in combination with the methodology from the dressed ion theory (DIT) gives a full account of the electrostatic effective potential among the colloids. The main advantages of the present contribution reside in its ability to manage the short-range potentials and non-linear correlations among the microions, as well as its realistic characterization of the ionic clouds surrounding each macroion. The structure factors predicted by this jellium scheme are contrasted with previously reported experimental results for microgel suspensions with monovalent salts (2019Phys. Rev. E100032602), thus validating its high accuracy in these situations. The present theoretical analysis is then extended to microgel suspensions with multivalent salts, which reveals the prominent influence of the counterion valence on the makeup of the effective potentials. Although the induced differences may be difficult to identify through the mesoscopic structure, our results suggest that the microgel collapsing transition may be used to enhance these distinct effects, thus giving a feasible experimental probe for these phenomena.
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Affiliation(s)
- L A Aguirre-Manzo
- Departamento de Física, Cinvestav del I. P. N., Av. Instituto Politécnico Nacional 2508, Ciudad de México, C. P. 07360, Mexico
| | - P González-Mozuelos
- Departamento de Física, Cinvestav del I. P. N., Av. Instituto Politécnico Nacional 2508, Ciudad de México, C. P. 07360, Mexico
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9
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Munaò G, Saija F. Evidence of Structural Inhomogeneities in Hard-Soft Dimeric Particles without Attractive Interactions. Materials (Basel) 2019; 13:ma13010084. [PMID: 31877947 PMCID: PMC6981562 DOI: 10.3390/ma13010084] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Revised: 12/16/2019] [Accepted: 12/17/2019] [Indexed: 11/16/2022]
Abstract
We perform Monte Carlo simulations of a simple hard-soft dimeric model constituted by two tangent spheres experiencing different interactions. Specifically, two hard spheres belonging to different dimers interact via a bare hard-core repulsion, whereas two soft spheres experience a softly repulsive Hertzian interaction. The cross correlations are soft as well. By exploring a wide range of temperatures and densities we investigate the capability of this model to document the existence of structural inhomogeneities indicating the possible onset of aggregates, even if no attraction is set. The fluid phase behavior is studied by analyzing structural and thermodynamical properties of the observed structures, in particular by computing radial distribution functions, structure factors and cluster size distributions. The numerical results are supported by integral equation theories of molecular liquids which allow for a finer and faster spanning of the temperature-density diagram. Our results may serve as a framework for a more systematic investigation of self-assembled structures of functionalized hard-soft dimers able to aggregate in a variety of structures widely oberved in colloidal dispersion.
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Affiliation(s)
- Gianmarco Munaò
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy
- Correspondence: (G.M.); (F.S.)
| | - Franz Saija
- CNR-IPCF, Viale F. Stagno d’Alcontres 37, 98158 Messina, Italy
- Correspondence: (G.M.); (F.S.)
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10
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Yucel AC, Sheng W, Zhou C, Liu Y, Bagci H, Michielssen E. An FMM-FFT Accelerated SIE Simulator for Analyzing EM Wave Propagation in Mine Environments Loaded With Conductors. IEEE J Multiscale Multiphys Comput Tech 2018; 3:3-15. [PMID: 29726545 PMCID: PMC5928803 DOI: 10.1109/jmmct.2018.2802420] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
A fast and memory efficient three-dimensional full-wave simulator for analyzing electromagnetic (EM) wave propagation in electrically large and realistic mine tunnels/galleries loaded with conductors is proposed. The simulator relies on Muller and combined field surface integral equations (SIEs) to account for scattering from mine walls and conductors, respectively. During the iterative solution of the system of SIEs, the simulator uses a fast multipole method-fast Fourier transform (FMM-FFT) scheme to reduce CPU and memory requirements. The memory requirement is further reduced by compressing large data structures via singular value and Tucker decompositions. The efficiency, accuracy, and real-world applicability of the simulator are demonstrated through characterization of EM wave propagation in electrically large mine tunnels/galleries loaded with conducting cables and mine carts.
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Affiliation(s)
- Abdulkadir C Yucel
- Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA. He is now with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
| | - Weitian Sheng
- Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA
| | - Chenming Zhou
- Office of Mine Safety and Health Research, National Institute for Occupational Safety and Health, Pittsburgh, PA 15236 USA
| | - Yang Liu
- Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA
| | - Hakan Bagci
- Computer, Electrical, and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
| | - Eric Michielssen
- Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA
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11
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Nashine HK, Arab R, Agarwal RP, De la Sen M. Positive solutions of fractional integral equations by the technique of measure of noncompactness. J Inequal Appl 2017; 2017:225. [PMID: 28983180 PMCID: PMC5602433 DOI: 10.1186/s13660-017-1497-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/04/2017] [Accepted: 08/30/2017] [Indexed: 06/07/2023]
Abstract
In the present study, we work on the problem of the existence of positive solutions of fractional integral equations by means of measures of noncompactness in association with Darbo's fixed point theorem. To achieve the goal, we first establish new fixed point theorems using a new contractive condition of the measure of noncompactness in Banach spaces. By doing this we generalize Darbo's fixed point theorem along with some recent results of (Aghajani et al. (J. Comput. Appl. Math. 260:67-77, 2014)), (Aghajani et al. (Bull. Belg. Math. Soc. Simon Stevin 20(2):345-358, 2013)), (Arab (Mediterr. J. Math. 13(2):759-773, 2016)), (Banaś et al. (Dyn. Syst. Appl. 18:251-264, 2009)), and (Samadi et al. (Abstr. Appl. Anal. 2014:852324, 2014)). We also derive corresponding coupled fixed point results. Finally, we give an illustrative example to verify the effectiveness and applicability of our results.
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Affiliation(s)
- Hemant Kumar Nashine
- Department of Mathematics, Texas A&M University, Kingsville, Texas 78363-8202 USA
| | - Reza Arab
- Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
| | - Ravi P Agarwal
- Department of Mathematics, Texas A&M University, Kingsville, Texas 78363-8202 USA
| | - Manuel De la Sen
- Institute of Research and Development of Processes IIDP Faculty of Science and Technology, University of the Basque Country, Leioa, Spain
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12
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Xu R, Ma X. Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two variables and their applications. J Inequal Appl 2017; 2017:187. [PMID: 28860688 PMCID: PMC5557940 DOI: 10.1186/s13660-017-1460-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2017] [Accepted: 07/24/2017] [Indexed: 05/31/2023]
Abstract
In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.
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Affiliation(s)
- Run Xu
- Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165 People’s Republic of China
| | - Xiangting Ma
- Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165 People’s Republic of China
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13
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Abstract
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of linear-nonlinear equations (SLNE) with respect to intensities and frequencies of the discrete spectral lines. The SLNE is linear with respect to lines' intensities and nonlinear with respect to the lines' frequencies. The integral approximation algorithm is proposed for the solution of this SLNE. The algorithm combines solution of linear integral equations with solution of a system of linear algebraic equations and avoids nonlinear equations. Numerical examples of the application of the technique, both to synthetic and experimental spectra, demonstrate the efficacy of the proposed approach in enabling an effective enhancement of the spectrometer's resolution.
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Affiliation(s)
| | - Denis Sidorov
- 2 Energy Systems Institute SB RAS, Irkutsk National Research Technical University, Irkutsk, Russia
- 3 Hunan University, Changsha, China
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14
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Dyer KM, Perkyns JS, Pettitt BM. Dielectric behavior for saline solutions from renormalized diagrammatically proper interaction site model theory. J Phys Condens Matter 2016; 28:414006. [PMID: 27546725 PMCID: PMC5340275 DOI: 10.1088/0953-8984/28/41/414006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We consider the dielectric response of angularly dependent site-site theories for models of aqueous saline solutions. We find that we can use relatively low order approximations of the angularly dependent correlation functions with correct long ranged behavior to obtain good estimates of the dielectric constant for three site water models and simple 1-1 salts. We find that the solution thermodynamics results for this level of theory, as measured by the Kirkwood G integrals and the excess chemical potentials, are in good quantitative agreement with simulation even when the details of the short ranged structure is not as accurately determined. We find that the dielectric constant predictions of both the pure fluid and the salt-water mixtures are similarly predictive, in comparison to both simulation and experiment.
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Affiliation(s)
- Kippi M Dyer
- Department of Biochemistry and Molecular Biology, Sealy Center for Structural Biology and Molecular Biophysics, UTMB-Galveston, 301 University Boulevard, Galveston, TX 77555-03004, USA
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15
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Brink WM, Remis RF, Webb AG. A theoretical approach based on electromagnetic scattering for analysing dielectric shimming in high-field MRI. Magn Reson Med 2015; 75:2185-94. [PMID: 26125996 DOI: 10.1002/mrm.25783] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Revised: 04/15/2015] [Accepted: 05/02/2015] [Indexed: 11/12/2022]
Abstract
PURPOSE In this study, we analyzed dielectric shimming by formulating it as an electromagnetic scattering problem using integral equations. METHODS Three-dimensional simulations of the radiofrequency field in two configurations using different materials were analyzed in terms of induced currents and secondary fields. A two-dimensional integral equation method with different backgrounds was used to identify the underlying physical mechanisms. This framework was then used to develop an inversion method for the design of dielectric pads. RESULTS The effects of a dielectric pad can be attributed to the interference of a secondary field that is produced by the currents induced in the dielectric pad, radiating in an inhomogeneous background. The integral equation method with inhomogeneous background reduces the complexity of the forward and inverse problem significantly and can be used to optimize the permittivity distribution for a desired B1+ field. Agreement with experimental B1+ maps was obtained in a cylindrical phantom, demonstrating the validity of the method. CONCLUSIONS The integral equation method with inhomogeneous background yields an efficient numerical framework for the analysis and inverse design of dielectric shimming materials.
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Affiliation(s)
- Wyger M Brink
- C. J. Gorter Center for High Field MRI, Department of Radiology, Leiden University Medical Center, Leiden, Netherlands
| | - Rob F Remis
- Circuits and Systems Group, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands
| | - Andrew G Webb
- C. J. Gorter Center for High Field MRI, Department of Radiology, Leiden University Medical Center, Leiden, Netherlands
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16
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Sergiievskyi VP, Jeanmairet G, Levesque M, Borgis D. Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections. J Phys Chem Lett 2014; 5:1935-1942. [PMID: 26273876 DOI: 10.1021/jz500428s] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.
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Affiliation(s)
- Volodymyr P Sergiievskyi
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Guillaume Jeanmairet
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Maximilien Levesque
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Daniel Borgis
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
- ‡Maison de la Simulation, CNRS USR 3441, CEA Saclay, 91191 Gif-sur-Yvette, France
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Krumin M, Reutsky I, Shoham S. Correlation-based analysis and generation of multiple spike trains using hawkes models with an exogenous input. Front Comput Neurosci 2010; 4:147. [PMID: 21151360 PMCID: PMC2995522 DOI: 10.3389/fncom.2010.00147] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2009] [Accepted: 10/25/2010] [Indexed: 11/14/2022] Open
Abstract
The correlation structure of neural activity is believed to play a major role in the encoding and possibly the decoding of information in neural populations. Recently, several methods were developed for exactly controlling the correlation structure of multi-channel synthetic spike trains (Brette, 2009; Krumin and Shoham, 2009; Macke et al., 2009; Gutnisky and Josic, 2010; Tchumatchenko et al., 2010) and, in a related work, correlation-based analysis of spike trains was used for blind identification of single-neuron models (Krumin et al., 2010), for identifying compact auto-regressive models for multi-channel spike trains, and for facilitating their causal network analysis (Krumin and Shoham, 2010). However, the diversity of correlation structures that can be explained by the feed-forward, non-recurrent, generative models used in these studies is limited. Hence, methods based on such models occasionally fail when analyzing correlation structures that are observed in neural activity. Here, we extend this framework by deriving closed-form expressions for the correlation structure of a more powerful multivariate self- and mutually exciting Hawkes model class that is driven by exogenous non-negative inputs. We demonstrate that the resulting Linear–Non-linear-Hawkes (LNH) framework is capable of capturing the dynamics of spike trains with a generally richer and more biologically relevant multi-correlation structure, and can be used to accurately estimate the Hawkes kernels or the correlation structure of external inputs in both simulated and real spike trains (recorded from visually stimulated mouse retinal ganglion cells). We conclude by discussing the method's limitations and the broader significance of strengthening the links between neural spike train analysis and classical system identification.
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Affiliation(s)
- Michael Krumin
- Faculty of Biomedical Engineering, Technion - Israel Institute of Technology Haifa, Israel
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Abstract
We propose a simple, two-site model of water, using the familiar three-site Simple Point Charge (SPC) model as a guide. We briefly examine the resulting dielectric and solvation properties of the bulk fluid, both pure and in a three component mixture of apolar or ionic simple fluid solutes, using integral equation methods. The results confirm a practical utility of this simplified model, and the essential predictive properties of the site-renormalised molecular fluid theory.
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Affiliation(s)
- Kippi M. Dyer
- Chemistry Department, University of Houston, Houston, TX 77004-5003, USA
| | - John S. Perkyns
- Chemistry Department, University of Houston, Houston, TX 77004-5003, USA
| | - George Stell
- Chemistry Department, SUNY-Stony Brook, Stony Brook, NY 11794, USA
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Dyer K, Perkyns J, Pettitt B, Stell G. An angle dependent site-renormalized theory for the conformations of n-butane in a simple fluid. Condens Matter Phys 2007; 10:331-342. [PMID: 20664717 PMCID: PMC2909681 DOI: 10.5488/cmp.10.3.331] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
The angular dependent site-renormalized integral equation theory is developed to compute the dihedral conformation distribution and intermolecular pair distributions of n-butane at infinite dilution in a Lennard-Jones solvent. The equations take advantage of the topological diagrammatic expansion of the full angular dependent molecular system by resumming the series in conjunction with the intramolecular degree of freedom. To first order in an angular basis set, the numerical results of these site-renormalized equations are a systematic quantitative improvement over previous methods. In particular, the thermodynamics and conformational distribution of the solute are essentially indistinguishable from simulation.
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Affiliation(s)
- K Dyer
- Chemistry Department, University of Houston, Houston, TX 77204-5003
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