A unified approach to dynamic NMR based on a physical interpretation of the transition probability

1996 ◽  
Vol 74 (6) ◽  
pp. 819-824 ◽  
Author(s):  
Alex D. Bain ◽  
G.J. Duns
Keyword(s):  
General Theory ◽  
Chemical Exchange ◽  
Transition Probability ◽  
Spin Coherence ◽  
Unified Approach ◽  
Classic Problem ◽  
Initial Magnetization ◽  
Two Factors ◽  
Ab Spin System ◽  
Exchange Kinetics

A general theory of the effect of dynamics (relaxation and (or) exchange) on NMR spectra is presented. This theory is based on a reexamination of the transition probability. The classic expression for this is as the square of the transition moment, but we feel it is useful to separate the square into two separate terms. In the generalization presented here, we show that one of these terms corresponds to the share of the initial magnetization that each spin coherence receives at the start of the experiment. The second term is how much that coherence contributes to the total detected signal. The final intensity is the product of these two factors. For a static spectrum, these two terms are complex conjugates, so the product is real and we recover the standard transition probability. When there is dynamics, the product becomes complex, so the time evolution includes oscillatory and dispersive terms. This means that a dynamic spectrum is still a sum of individual transitions, but the lineshapes are distorted in phase, intensity, position, and linewidth by the dynamic process. In this paper we develop the general theory, and illustrate it with a calculation of the classic problem of mutual exchange in an AB spin system. Key words: NMR spectroscopy, transition probability, chemical exchange, kinetics.

scholarly journals On the theory of the catalysis of the ortho-para transformation by paramagnetic gases

1935 ◽  
Vol 150 (871) ◽  
pp. 520-533 ◽  
Keyword(s):  
Nuclear Spin ◽  
Transition Probability ◽  
Electronic Configuration ◽  
Statistical Weight ◽  
Quantum Numbers ◽  
Symmetry Properties ◽  
Two Factors ◽  
Paramagnetic Molecules ◽  
The One ◽  
The Magnetic Field

According to quantum statistics, there exists for a diatomic molecule containing similar atoms an important difference between states with even and uneven rotational quantum numbers j . These two kinds of states have different statistical weights in the ratio of (S + 1)/S or S/(S + 1) where S is the nuclear spin. Whether the states of larger statistical weight possess even or uneven values of j depends on the symmetry properties of the electronic configuration and on the nuclear statistics. The states with the larger weight are called the ortho-states, those with the smaller weight the para-states. Under normal conditions, the transition probability between ortho-and para-states is zero. There are, however, two ways of inducing an ortho-para transformation. The one consists in dissociating the molecules, after which the atoms will recombine at random. The other possibility is to introduce a perturbation which depends both on the spins and on the positions of the nuclei. Under such conditions a transition may take place for the following reason: the unperturbed eigenfunction can be written as a product of two factors Ψ = ψ ( q 1 , q 2 ) ψ (s 1 , s 2 ) depending respectively on the space-co-ordinates q and the spin-vectors s of the two nuclei. Now, in order that an ortho-para transition may take place, it is necessary that the symmetry properties with respect to a permutation of the nuclei shall be changed in both factors. A simultaneous transition in ψ( q 1 , q 2 ) and ψ(s 1 , s 2 ) can, however, only occur if the perturbation contains a term depending both on q and s. It is due to a perturbation of this kind that the ortho-para hydrogen transformation is catalysed by paramagnetic gases as was found by Farkas and Sachsse. The interaction between the magnetic field of the paramagnetic molecules and the magnetic moment of the H-nuclei depends on the nuclear spin and, as the field is inhomogeneous, it also involves the nuclear positions. The theory of this catalysis was given by Wigner.

scholarly journals On the figure of elastic planets I: gravitational collapse and infinitely many equilibria

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180815
Author(s):  
Fei Jia ◽  
Ousmane Kodio ◽  
S. Jon Chapman ◽  
Alain Goriely
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Gravitational Collapse ◽  
Gravitational Force ◽  
Large Deformations ◽  
Elastic Model ◽  
Initial Radius ◽  
Elastic Deformations ◽  
Classic Problem ◽  
Elastic Forces

A classic problem of elasticity is to determine the possible equilibria of an elastic planet modelled as a homogeneous compressible spherical elastic body subject to its own gravitational field. In the absence of gravity, the initial radius is given and the density is constant. With gravity and for small planets, the elastic deformations are small enough so that the spherical equilibria can be readily obtained by using the theory of linear elasticity. For larger or denser planets, large deformations occur and the general theory of nonlinear elasticity is required to obtain the solution. Depending on the elastic model, we show that there may be parameter regimes where there exist no equilibrium or arbitrarily many equilibria. Yet, at most two of them are dynamically stable with respect to radial disturbances. In some of these models, there is a critical initial radius at which spherical solutions cease to exist. For planets with larger initial radii, there is no spherical solution as the elastic forces are not sufficient to balance the gravitational force. Therefore, the system undergoes gravitational collapse, an unexpected phenomenon within the framework of classical continuum mechanics.

A general theory for skid steering of tracked vehicles on firm ground

2001 ◽  
Vol 215 (3) ◽  
pp. 343-355 ◽  
Author(s):  
J Y Wong ◽  
C F Chiang
Keyword(s):  
General Theory ◽  
Close Agreement ◽  
The Other ◽  
Unified Approach ◽  
Tracked Vehicles ◽  
Strong Resemblance ◽  
Turning Resistance ◽  
Skid Steering ◽  
Turning Radius ◽  
The Moment

A general theory for skid steering of tracked vehicles under steady state conditions on firm ground, taking into account the shear stress-shear displacement relationship on the track-ground interface, is presented. The steering behaviour predicted using the general theory bears a strong resemblance to that observed in the field. The variations of sprocket torques for the outer and inner tracks with turning radius predicted by the general theory are in reasonably close agreement with available experimental data. On the other hand, predictions based on Steeds’ theory developed earlier differ greatly from measured results. Using the general theory, the lateral coefficient of friction used in the conventional method for predicting the moment of turning resistance of the track can be quantitatively determined as a function of turning radius. It is believed that the new theory presented in this paper provides a unified approach to the study of the mechanics of skid steering of tracked vehicles and that it may be extended to the study of transient handling behaviour of tracked vehicles.

scholarly journals If Only There Were a Blueprint! Factors for Success and Failure of UN Peace-Building Operations

2009 ◽  
Vol 13 (1-2) ◽  
pp. 45-71 ◽  
Author(s):  
Jaïr van der Lijn
Keyword(s):  
General Theory ◽  
Case Studies ◽  
Use Of Force ◽  
Fine Tuning ◽  
Peace Building ◽  
Substantial Body ◽  
Peacekeeping Operations ◽  
Un Peacekeeping ◽  
Two Factors ◽  
The Subject

AbstractIn spite of the fact that UN peacekeeping operations are a relative new field for scholarly research, the literature on the subject has grown into a substantial body. This article distils from this body of scholarly literature eleven clusters of factors for success and failure for UN peacekeeping operations in general and tests these on four case studies – Cambodia, Mozambique, Rwanda and El Salvador – of one particular type of UN peacekeeping operation: the UN peace-building operations. It concludes that although the results of the four cases of UN peace-building operations largely confirm the factors for success and failure as found in literature for UN peacekeeping operations in general, theory on UN peace-building operations still needs adjustment and fine tuning. Amongst others, it appears from the cases that two factors that receive a lot of attention in literature – the non-use of force by the operation and the need for a clear and detailed mandate – are less important.

scholarly journals Binding site exchange kinetics revealed through efficient spin–spin dephasing of hyperpolarized 129Xe

2021 ◽  
Vol 12 (1) ◽  
pp. 158-169
Author(s):  
Martin Kunth ◽  
Leif Schröder
Keyword(s):  
Binding Site ◽  
Chemical Exchange ◽  
Spin Dephasing ◽  
Hyperpolarized 129Xe ◽  
Site Exchange ◽  
Exchange Kinetics ◽  
Displacement Assays

Localized detection of hyperpolarized, exchanging Xe spins enables quantitative insights at unprecedented sensitivity for characterizing chemical exchange kinetics in various contexts such as host–guest interactions and displacement assays.

Studies of the chemical exchange kinetics of glycinate ions in mixed ligand complexes of copper (II) and glycylglycine

1982 ◽  
Vol 19 (1-2) ◽  
pp. 131-133 ◽  
Author(s):  
A. V. Zakharov ◽  
E. L. Gogolashvili
Keyword(s):  
Chemical Exchange ◽  
Mixed Ligand ◽  
Mixed Ligand Complexes ◽  
Exchange Kinetics ◽  
Kinetics Of

The Reduction of Occupational Stress among Elderly Lawyers: The Creation of a Functional Niche

1981 ◽  
Vol 13 (3) ◽  
pp. 209-219 ◽  
Author(s):  
Michael W. Meltzer
Keyword(s):  
Job Satisfaction ◽  
General Theory ◽  
Occupational Stress ◽  
Work Stress ◽  
High Stress ◽  
Legal Profession ◽  
Work Role ◽  
Retirement Behavior ◽  
Two Factors ◽  
Stratified Sample

The question of how older lawyers function in the context of what is generally a high stress occupation is examined from data drawn from a random stratified sample of 130 members of the legal profession. It is shown that elderly lawyers are able to reduce work stress (largely deriving from volume, responsibility, clients, and trials) by control over the quantity and focus of their work, as well as through client selection. Elderly lawyers are able to create a relatively stress free work role, which is in fact a functional niche for them within the profession. The result is high job satisfaction and low rates of retirement among elderly practitioners. Two factors: work role compensation and work role autonomy, are isolated from the legal data and proposed as important variables in a general theory of retirement behavior.

scholarly journals Mapping of Absolute Host Concentration and Exchange Kinetics of Xenon Hyper-CEST MRI Agents

2021 ◽  
Vol 14 (2) ◽  
pp. 79 ◽  
Author(s):  
Martin Kunth ◽  
Christopher Witte ◽  
Leif Schröder
Keyword(s):  
Spin Exchange ◽  
Chemical Exchange ◽  
Chemical Exchange Saturation Transfer ◽  
Planar Imaging ◽  
Internal Reference ◽  
Cest Mri ◽  
Exchange Kinetics ◽  
Magnetic Resonance Imaging Mri ◽  
Echo Planar

Xenon magnetic resonance imaging (MRI) provides excellent sensitivity through the combination of spin hyperpolarization and chemical exchange saturation transfer (CEST). To this end, molecular hosts such as cryptophane-A or cucurbit[n]urils provide unique opportunities to design switchable MRI reporters. The concentration determination of such xenon binding sites in samples of unknown dilution remains, however, challenging. Contrary to 1H CEST agents, an internal reference of a certain host (in this case, cryptophane-A) at micromolar concentration is already sufficient to resolve the entire exchange kinetics information, including an unknown host concentration and the xenon spin exchange rate. Fast echo planar imaging (EPI)-based Hyper-CEST MRI in combination with Bloch–McConnell analysis thus allows quantitative insights to compare the performance of different emerging ultra-sensitive MRI reporters.

Family-Based Selection

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
General Theory ◽  
Plant Breeding ◽  
Relative Effectiveness ◽  
Index Selection ◽  
Family Selection ◽  
Selection Decisions ◽  
Two Factors ◽  
The Mean ◽  
Family Based ◽  
Weighted Combination

A number of selection schemes (especially in plant breeding) are based on using family information. Individuals may be chosen based on the mean of their families (among-family selection), on their standing within their family (either strict within-family selection or family-deviations selection), or on some weighted combination of these two factors (family index selection). This chapter reviews the general theory of response in such settings and examines the relative effectiveness of a number of different family-based selection decisions.

Sign in / Sign up

Export Citation Format

Share Document