17 results on '"LAPLACE"'
Search Results
2. Gradient Regularization as Approximate Variational Inference
- Author
-
Ali Unlu and Laurence Aitchison
- Subjects
variational inference ,Laplace ,Bayes ,Bayesian neural networks ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
We developed Variational Laplace for Bayesian neural networks (BNNs), which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The Variational Laplace objective is simple to evaluate, as it is the log-likelihood plus weight-decay, plus a squared-gradient regularizer. Variational Laplace gave better test performance and expected calibration errors than maximum a posteriori inference and standard sampling-based variational inference, despite using the same variational approximate posterior. Finally, we emphasize the care needed in benchmarking standard VI, as there is a risk of stopping before the variance parameters have converged. We show that early-stopping can be avoided by increasing the learning rate for the variance parameters.
- Published
- 2021
- Full Text
- View/download PDF
3. Solution of DGLAP evolution equation for gluon fragmentation in LO and NLO
- Author
-
G R Boroun and S Zarrin
- Subjects
Fragmentation ,Evolution ,Laplace ,Physics ,QC1-999 - Abstract
In this work, we calculate DGLAP evolution equation at LO and NLO by Laplace method for fragmentation function of gluon to meson or baryon. To prove the validity of this method, we evolve the fragmentation functions of andby using this method. In this method, it is not necessary to calculate these functions in Laplace space. This method is just used for simplifing the equations
- Published
- 2017
4. Entropy, Information Theory, Information Geometry and Bayesian Inference in Data, Signal and Image Processing and Inverse Problems
- Author
-
Ali Mohammad-Djafari
- Subjects
Bayes ,Laplace ,entropy ,Bayesian inference ,maximum entropy principle ,information theory ,Kullback–Leibler divergence ,Fisher information ,geometrical science of information ,inverse problems ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
The main content of this review article is first to review the main inference tools using Bayes rule, the maximum entropy principle (MEP), information theory, relative entropy and the Kullback–Leibler (KL) divergence, Fisher information and its corresponding geometries. For each of these tools, the precise context of their use is described. The second part of the paper is focused on the ways these tools have been used in data, signal and image processing and in the inverse problems, which arise in different physical sciences and engineering applications. A few examples of the applications are described: entropy in independent components analysis (ICA) and in blind source separation, Fisher information in data model selection, different maximum entropy-based methods in time series spectral estimation and in linear inverse problems and, finally, the Bayesian inference for general inverse problems. Some original materials concerning the approximate Bayesian computation (ABC) and, in particular, the variational Bayesian approximation (VBA) methods are also presented. VBA is used for proposing an alternative Bayesian computational tool to the classical Markov chain Monte Carlo (MCMC) methods. We will also see that VBA englobes joint maximum a posteriori (MAP), as well as the different expectation-maximization (EM) algorithms as particular cases.
- Published
- 2015
- Full Text
- View/download PDF
5. Spherical One-Way Wave Equation
- Author
-
Oskar Bschorr and Hans-Joachim Raida
- Subjects
1st order partial differential equation (PDE) ,QC1-999 ,impulse flow equilibrium ,MathematicsofComputing_GENERAL ,transversal wave propagation ,Near and far field ,two-way wave equation ,one-way wave equation ,longitudinal wave propagation ,monopole ,spherical wave propagation ,symbols.namesake ,Operator (computer programming) ,spherical coordinates ,Nabla symbol ,force equilibrium ,Physics ,Laplace transform ,2nd order partial differential equation (PDE) ,Mathematical analysis ,Laplace ,spherical Bessel functions ,Spherical coordinate system ,General Medicine ,Wave equation ,inverse distance law ,point source ,gradient ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Amplitude ,impedance ,symbols ,Nabla operator ,wattless near field ,divergence ,spherical waves ,Bessel function - Abstract
The coordinate-free one-way wave equation is transferred in spherical coordinates. Therefore it is necessary to achieve consistency between gradient, divergence and Laplace operators and to establish, beside the conventional radial Nabla operator ∂Φ/∂r, a new variant ∂rΦ/r∂r. The two Nabla operator variants differ in the near field term Φ/r whereas in the far field r≫0 there is asymptotic approximation. Surprisingly, the more complicated gradient ∂rΦ/r∂r results in unexpected simplifications for – and only for – spherical waves with the 1/r amplitude decrease. Thus the calculation always remains elementary without the wattless imaginary near fields, and the spherical Bessel functions are obsolete.
- Published
- 2021
6. Kant-Laplace Cosmogonic Hypothesis
- Author
-
Le Gars, Stéphane, Gargaud, Muriel, editor, Irvine, William M., editor, Amils, Ricardo, editor, Cleaves, Henderson James (Jim), II, editor, Pinti, Daniele L., editor, Quintanilla, José Cernicharo, editor, Rouan, Daniel, editor, Spohn, Tilman, editor, Tirard, Stéphane, editor, and Viso, Michel, editor
- Published
- 2015
- Full Text
- View/download PDF
7. Gradient Regularization as Approximate Variational Inference
- Author
-
Laurence Aitchison and Ali Unlu
- Subjects
variational inference ,Laplace ,Bayes ,Bayesian neural networks ,Laplace transform ,Calibration (statistics) ,Science ,Physics ,QC1-999 ,General Physics and Astronomy ,Inference ,Sampling (statistics) ,Variance (accounting) ,Astrophysics ,Regularization (mathematics) ,Article ,QB460-466 ,Bayes' theorem ,Maximum a posteriori estimation ,Applied mathematics ,Mathematics - Abstract
We developed Variational Laplace for Bayesian neural networks (BNNs), which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The Variational Laplace objective is simple to evaluate, as it is the log-likelihood plus weight-decay, plus a squared-gradient regularizer. Variational Laplace gave better test performance and expected calibration errors than maximum a posteriori inference and standard sampling-based variational inference, despite using the same variational approximate posterior. Finally, we emphasize the care needed in benchmarking standard VI, as there is a risk of stopping before the variance parameters have converged. We show that early-stopping can be avoided by increasing the learning rate for the variance parameters.
- Published
- 2021
8. Schrodinger's original quantum-mechanical solution for hydrogen
- Author
-
James Freericks, Jeremy Canfield, Anna Galler, Centre de Physique Théorique [Palaiseau] (CPHT), and Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
- Subjects
Differential equation ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,General Physics and Astronomy ,FOS: Physical sciences ,01 natural sciences ,Schrödinger equation ,Set (abstract data type) ,symbols.namesake ,[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] ,0103 physical sciences ,Calculus ,010306 general physics ,Quantum ,Mathematical Physics ,Physics ,Quantum Physics ,Series (mathematics) ,atom ,05 social sciences ,quantum mechanics ,Laplace ,050301 education ,differential equations ,Mathematical Physics (math-ph) ,Eigenfunction ,Laplace's method ,hydrogen ,symbols ,Frobenius ,Schroedinger equation ,Quantum Physics (quant-ph) ,0503 education ,Schrödinger's cat ,mechanics ,energy - Abstract
In 1926, Erwin Schrodinger wrote a series of papers that invented wave mechanics and set the foundation for much of the single-particle quantum mechanics that we teach today. In his first paper, he solved the Schrodinger equation using the Laplace method, which is a technique that is quite powerful, but rarely taught. This is unfortunate, because it opens the door to examining quantum mechanics from a complex-analysis perspective. Gaining this experience with complex analysis is a useful notion to consider when teaching quantum mechanics, as these techniques can be widely used outside of quantum mechanics, unlike the standard Frobenius summation method, which is normally taught, but rarely used elsewhere. The Laplace method strategy is subtle and no one has carefully gone through the arguments that Schrodinger did in this first paper, instead it is often just stated that the solution was adopted from Schlesinger's famous differential equation textbook. In this work, we show how the Laplace method can be used to solve for the quantum-mechanical energy eigenfunctions of the hydrogen atom, following Schrodinger's original solution, with all the necessary details, and illustrate how it can be taught in advanced instruction; it does require familiarity with intermediate-level complex analysis, which we also briefly review., Comment: 22 pages, 8 figures
- Published
- 2020
- Full Text
- View/download PDF
9. Doubly-hidden scalar heavy molecules and tetraquarks states from QCD at NLO
- Author
-
G. Randriamanatrika, A. Rabemananjara, D. Rabetiarivony, R.M. Albuquerque, Stephan Narison, Laboratoire Univers et Particules de Montpellier (LUPM), and Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Montpellier 2 - Sciences et Techniques (UM2)
- Subjects
Quark ,Particle physics ,High Energy Physics::Lattice ,hadron: exotic ,Scalar (mathematics) ,FOS: Physical sciences ,01 natural sciences ,gluon: condensation ,tetraquark: mass ,High Energy Physics - Experiment ,bottom ,High Energy Physics - Experiment (hep-ex) ,sum rule: spectral ,High Energy Physics - Lattice ,High Energy Physics - Phenomenology (hep-ph) ,0103 physical sciences ,radiative correction ,[PHYS.HEXP]Physics [physics]/High Energy Physics - Experiment [hep-ex] ,quantum chromodynamics: perturbation theory ,Strong Interactions ,010306 general physics ,Quantum chromodynamics ,Physics ,[PHYS.HLAT]Physics [physics]/High Energy Physics - Lattice [hep-lat] ,010308 nuclear & particles physics ,High Energy Physics::Phenomenology ,High Energy Physics - Lattice (hep-lat) ,higher-order: 1 ,Laplace ,Perturbative QCD ,hadron: molecule ,Gluon condensate ,Exotic hadron ,stability ,LHC-B ,heavy quark: mass ,3. Good health ,High Energy Physics - Phenomenology ,[PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph] ,Tetraquark ,High Energy Physics::Experiment ,Sum rule in quantum mechanics ,charm - Abstract
Alerted by the recent LHCb discovery of exotic hadrons in the range (6.2 -- 6.9) GeV, we present new results for the doubly-hidden scalar heavy $(\bar QQ) (Q\bar Q)$ charm and beauty molecules using the inverse Laplace transform sum rule (LSR) within stability criteria and including the Next-to-Leading Order (NLO) factorized perturbative and $\langle G^3\rangle$ gluon condensate corrections. We also critically revisit and improve existing Lowest Order (LO) QCD spectral sum rules (QSSR) estimates of the $({ \bar Q \bar Q})(QQ)$ tetraquarks analogous states. In the example of the anti-scalar-scalar molecule, we separate explicitly the contributions of the factorized and non-factorized contributions to LO of perturbative QCD and to the $\langle\alpha_sG^2\rangle$ gluon condensate contributions in order to disprove some criticisms on the (mis)uses of the sum rules for four-quark currents. We also re-emphasize the importance to include PT radiative corrections for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at LO in the literature. Our LSR results for tetraquark masses summarized in Table II are compared with the ones from ratio of moments (MOM) at NLO and results from LSR and ratios of MOM at LO (Table IV). The LHCb broad structure around (6.2 --6.7) GeV can be described by the $\overline{\eta}_{c}{\eta}_{c}$, $\overline{J/\psi}{J/\psi}$ and $\overline{\chi}_{c1}{\chi}_{c1}$ molecules or/and their analogue tetraquark scalar-scalar, axial-axial and vector-vector lowest mass ground states. The peak at (6.8--6.9) GeV can be likely due to a $\overline{\chi}_{c0}{\chi}_{c0}$ molecule or/and a pseudoscalar-pseudoscalar tetraquark state. Similar analysis is done for the scalar beauty states whose masses are found to be above the $\overline\eta_b\eta_b$ and $\overline\Upsilon(1S)\Upsilon(1S)$ thresholds., Comment: 18 pages, 16 Figures, 4 Tables. version published in Phys. Rev. D
- Published
- 2020
- Full Text
- View/download PDF
10. Principles of Physics in Surgery: The Laws of Mechanics and Vectors Physics for Surgeons-Part 2.
- Author
-
Srivastava, Anurag, Sood, Akshay, Joy, Parijat, Mandal, Shubhyan, Panwar, Rajesh, Ravichandran, Suresh, Sarangi, Sasmit, and Woodcock, John
- Subjects
- *
HERNIA , *PHYSICS , *OPERATIVE surgery , *PLASTIC surgery , *SURGICAL dressings , *SUTURES , *WOUND healing - Abstract
In this sequel, to an earlier article, we discuss the laws of Mechanics, Thermodynamics and Vectors as they apply to soft and bony tissues. These include the Laplace's Law as applied to colonic perforation, compression therapy, parturition, variceal rupture, disc herniations etc. The Pascal's Law finds use in hernia repair and the Heimlich maneuver. Trigonometrically derived components of forces, acting after suturing, show ways to reduce cut-through; the thickness and the bite of suture determines the extent of tissue reaction. The heating effect of current explains the optimum gap between the prongs of a bipolar cautery and the use of law of transfer of heat in determining relation between healthy wound healing and ambient temperature. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
11. Interaction of a Guided Wave with a Crack in an Embedded Multilayered Anisotropic Plate: Global Matrix with Laplace Transform Formalism
- Author
-
Marc Deschamps, Pierric Mora, and Eric Ducasse
- Subjects
Physics ,Global Matrix ,Laplace transform ,Boundary Element Method ,transient wave ,Mathematical analysis ,Laplace ,embedded plate ,Inverse Laplace transform ,Physics and Astronomy(all) ,anisotropic ,Green's function for the three-variable Laplace equation ,Finite element method ,horizontal crack ,symbols.namesake ,Fourier transform ,Green function ,Laplace transform applied to differential equations ,symbols ,Boundary value problem ,Boundary element method - Abstract
We solve the problem of the interaction of a transient guided elastic wave by a planar crack with an indirect Boundary Element approach in the Laplace domain ( t → s ). The originality of this work is to use the numerical Green function of the layered plate rather than the analytical Green function of each layer. As a consequence, the BEM matrices are small. To obtain the Green function in the (x,z,s) domain we first solve the equations in the Fourier transform (k,z,s) domain with a Global Matrix approach, and then perform a numerical inverse FFT. Comparisons with finite element show excellent agreement. This approach is fast and low memory consuming for planar defects in arbitrary layered media, and can be extended to arbitrary shapes and boundary conditions for a higher computational cost. It is valid in 3D, however only the 2D case is considered in this work.
- Published
- 2015
12. Combined Laplacian-equivolumic model for studying cortical lamination with ultra high field MRI (7 T)
- Author
-
Denis Rivière, Dominique Hasboun, Fabrice Poupon, Cyril Poupon, Yann Leprince, Thierry Delzescaux, Service NEUROSPIN (NEUROSPIN), Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Université Paris-Sud - Paris 11 (UP11), Service MIRCEN (MIRCEN), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut de Biologie François JACOB (JACOB), Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Algorithms, models and methods for images and signals of the human brain (ARAMIS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut du Cerveau et de la Moëlle Epinière = Brain and Spine Institute (ICM), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Ministère de l'enseignement supérieur et de la recherche, CEA, IEEE, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Institut de Biologie François JACOB (JACOB), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-CHU Pitié-Salpêtrière [AP-HP], Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-CHU Pitié-Salpêtrière [AP-HP], Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Université Paris-Saclay-Institut de Biologie François JACOB (JACOB), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], and Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
cytoarchitecture ,[SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging ,advection ,brain ,column ,MESH: Imaging, Three-Dimensional ,Lamination (topology) ,Curvature ,computer.software_genre ,MESH: Magnetic Resonance Imaging ,Bok ,Nuclear magnetic resonance ,Voxel ,Cortex (anatomy) ,medicine ,lamination ,ACM: I.: Computing Methodologies/I.6: SIMULATION AND MODELING/I.6.5: Model Development ,[INFO.INFO-IM]Computer Science [cs]/Medical Imaging ,MESH: Neuroimaging ,Image resolution ,Physics ,ACM: I.: Computing Methodologies/I.4: IMAGE PROCESSING AND COMPUTER VISION ,Resolution (electron density) ,layer ,Laplace ,Human brain ,MESH: Cerebral Cortex ,medicine.anatomical_structure ,cortex ,equivolumic ,Cerebral cortex ,[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] ,high-field MRI ,Biological system ,computer - Abstract
International audience; The fine spatial resolution and novel contrasts offered by high-field magnetic resonance allow in vivo detection of histological layers in the cerebral cortex. This opens the way to in vivo analysis of cortical lamination, but the comparison of lamination profiles has proved challenging because the layers’ geometry is strongly influenced by cortical curvature. This paper introduces a model of the micro-structural organization of the cortex, which can compensate for the effect of cortical curvature. Layers are modelled by an equivolumic principle, while the vertical structure of the cortex is represented with a Laplacian model. In this framework, lamination profiles can be represented in a way that preserves the original voxel sampling of the acquisition. This model is validated on a magnetic resonance image of a post-mortem human brain acquired on a human 7 T scanner at 0.35 mm resolution.
- Published
- 2015
13. Science, Print, and Crossing Borders: Importing French Science Books into Britain, 1789–1815
- Author
-
Topham, Jonathan R., editor
- Published
- 2011
- Full Text
- View/download PDF
14. Statistical concepts in philosophy of science
- Author
-
Suppes, Patrick
- Published
- 2007
- Full Text
- View/download PDF
15. Kvantfysikens Matematiska Grunder
- Author
-
Israelsson, Anders
- Subjects
Planck ,Hilbertspace ,Hermitian ,Lower Bound Estimate ,Self-adjoint ,Obestämdhetsrelation ,Väteatom ,Schrödinger ,Dynamik ,Hilbertrum ,Kvantmekanik ,Nedåtbegränsning ,Commutator ,Fysik ,Quantum Mechanics ,Matematik ,Functional ,Hydrogen Atom ,Physics ,Analys ,Uncertainty Principle ,Laplace ,Kommutator ,Självadjungerad ,Dynamics ,Hamiltonian ,Heisenberg ,Funktional ,Hermitisk ,Operator ,Laplacian ,Kvantfysik ,Mathematics - Published
- 2013
16. Structure of the two-dimensional relaxation spectra seen within the eigenmode perturbation theory and the two-site exchange model
- Author
-
Dimitri Bytchenkoff, Stéphane Rodts, Laboratoire Navier (navier umr 8205), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS), Physique des milieux poreux, and Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Nuclear and High Energy Physics ,Magnetic Resonance Spectroscopy ,NMR Relaxation ,Diagonal ,Biophysics ,02 engineering and technology ,01 natural sciences ,Biochemistry ,Spectral line ,Porous system ,Diffusion ,[PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] ,Nuclear magnetic resonance ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,Normal mode ,0103 physical sciences ,Computer Simulation ,Statistical physics ,010306 general physics ,Physics ,Laplace transform ,Laplace ,Inverse Laplace transform ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,[PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] ,Porous ,Models, Chemical ,Homogeneous space ,0210 nano-technology ,Exchange model ,[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing ,[PHYS.COND.CM-SCM]Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft] ,Algorithms - Abstract
The form of the two-dimensional (2D) NMR-relaxation spectra – which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice ( T 1 ) and spin-spin ( T 2 ) relaxation times – has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T 1 - and T 2 -eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them – the presence of negative peaks – underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data.
- Published
- 2010
17. Structural properties of 2D NMR relaxation spectra of diffusive systems
- Author
-
Dimitri Bytchenkoff, Stéphane Rodts, Physique des milieux poreux, Laboratoire Navier (navier umr 8205), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS), ANR-08- ECOT-009, ANR-06-JCJC-0106,ANR-08- ECOT-009, and ANR-06-JCJC-0106
- Subjects
Nuclear and High Energy Physics ,Relaxation ,Diagonal ,Biophysics ,010402 general chemistry ,01 natural sciences ,Biochemistry ,Spectral line ,Diffusion ,[PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] ,Nuclear magnetic resonance ,0103 physical sciences ,Computer Simulation ,Statistical physics ,010306 general physics ,Physics ,Models, Statistical ,Laplace transform ,Laplace ,Condensed Matter Physics ,Magnetic Resonance Imaging ,[PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] ,0104 chemical sciences ,Porous ,Formalism (philosophy of mathematics) ,Inverse laplace transformation ,Data Interpretation, Statistical ,Homogeneous space ,[PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci] ,[PHYS.PHYS.PHYS-CHEM-PH]Physics [physics]/Physics [physics]/Chemical Physics [physics.chem-ph] ,Two-dimensional nuclear magnetic resonance spectroscopy ,Porosity ,Algorithms - Abstract
International audience; Much has been learnt and speculated about the form of 2D NMR relaxation spectra of diffusive systems. Herein we show that the eigen-modes formalism can help to establish a number of fundamental structural properties, i.e. symmetries, overall intensities, signs and relative intensities of the diagonal and cross components, of such spectra, on which one can safely rely in analysing experimental data. More specifically, we prove that the correlation T1–T2 spectra will always have negative peaks, thus making questionable the nowadays wide spread strategy in developing inverse Laplace transformation algorithms.
- Published
- 2010
Catalog
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.