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•A method for determining of the exchange coefficients by a direct analysis of T2- data in the time domain is proposed.•Significantly reduced both the time of the experiment and the ...time of computer processing of the results.•Relaxation experiments of 35Cl NQR for KClO3 and 1H NMR for rubber are performed.•The method is useful for the T2-exchange relaxometry, which provides information on molecular dynamics.
The paper proposes a new method for quantitative assessment of the constant exchange of magnetization between different states without registration of cross peaks on the T2-T2 topogram which significantly reduced both the experimental time and the time of computer processing of the results.
The natural frequency and transient response of FGM cylindrical shells under arbitrary boundary conditions are performed in present work. A novel semi-analytical method, which integrates Durbin’s ...inverse Laplace transform and the differential quadrature method, is developed to analyze the dynamical behavior of cylindrical shells. Durbin’s numerical inversion method is selected to gain time domain solutions. The trigonometric series expansion is used in the circumferential direction whereas the use of differential quadrature method provides numerical solutions in terms of axial direction. Comparisons show that the calculated natural frequencies are in good agreement with results in the literature. Convergence study illustrates that the developed method is rapidly convergent with the increase of sampling points, and the calculated transient response of the cylindrical shell is validated by comparing with Navier’s solution. The influences of boundary conditions, material graded indexes, temperature changes, elastic foundation coefficients and geometric parameters on transient response are analyzed. Numerical results indicate that the peak displacement of cylindrical shells increases with the increase of temperature changes and length-radius ratios or the decrease of elastic foundation coefficients and thickness-radius ratios.
Frequency–time conversion is a crucial step in grounded electrical-source transient electromagnetic response calculation, and the performance of the algorithm is directly related to the overall ...accuracy and speed of forward modeling. In mainstream algorithms, algorithms with high accuracy often have slow computation speed while algorithms with high efficiency have unsatisfactory accuracy, especially when facing inversion problems that are difficult to meet requirements. This paper introduces three inverse Laplace transform algorithms for this problem: the Gaver–Stehfest algorithm, the Euler algorithm, and the Talbot algorithm. The performance of each algorithm in forward modeling was analyzed using half-space and layered models, and the optimal selection schemes for algorithm weight coefficients were provided. The numerical calculation results show that the Gaver–Stehfest algorithm has a unique advantage in computational efficiency, while the Talbot algorithm and Euler algorithm meet the accuracy requirements. After considering both accuracy and efficiency, the Talbot algorithm is selected to replace conventional algorithms for calculation of grounded electrical-source transient electromagnetic forward modeling. In addition, this paper combines the characteristics of the Gaver–Stehfest algorithm and the Talbot algorithm to implement an adaptive hybrid algorithm. This algorithm uses the Gaver–Stehfest algorithm for forward modeling in the early times and the Talbot algorithm to compensate for the decrease in accuracy in the later times. Through the comparison of forward modeling calculations, it can be seen that the hybrid algorithm proposed in this paper fully utilizes the advantages of both algorithms. The hybrid algorithm greatly improves computational speed while meeting accuracy requirements, and has significant advantages over conventional algorithms.
•Compared and analyzed the characteristics of three inverse Laplace transform algorithms.•The optimal selection for the number of nodes with inverse Laplace transform algorithms coefficients is provided.•The Talbot algorithm has been selected as the most suitable algorithm for forward modeling of grounded electrical-source TEM.•Proposed an adaptive hybrid algorithm and verified its advantages.
This paper provides a new tauberian approach to the study of quantitative time asymptotics of collisionless transport semigroups with general diffuse boundary operators. We obtain an (almost) optimal ...algebraic rate of convergence to equilibrium under very general assumptions on the initial datum and the boundary operator. The rate is prescribed by the maximal gain of integrability that the boundary operator is able to induce. The proof relies on a representation of the collisionless transport semigroups by a (kind of) Dyson-Phillips series and on a fine analysis of the trace on the imaginary axis of Laplace transform of remainders (of large order) of this series. Our construction is systematic and is based on various preliminary results of independent interest.
► Error analysis and numerical experiments demonstrate the efficiency of our method for time fractional diffusion equations. ► Our method avoids costly convolution integral calculation and dilemmatic ...selection of time step size. ► A truly boundary-only meshless method is applied to Laplace-transformed inhomogeneous problem. ► Our method effectively simulates 3D long time-history fractional diffusion systems.
This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.
This paper introduces a computational approach for transient analysis of extensive scattering problems. This novel method is based on the combination of physical optics (PO) and the fast inverse ...Laplace transform (FILT). PO is a technique for analyzing electromagnetic scattering from large-scale objects. We modify PO for application in the complex frequency domain, where the scattered fields are evaluated. The complex frequency function is efficiently transformed into the time domain using FILT. The effectiveness of this combination is demonstrated through large-scale analysis and transient response for a short pulse incidence. The accuracy is investigated and validated by comparison with reference solutions.
The object of this paper is to provide a new and systematic tauberian approach to quantitative long time behaviour of
C
0
C_{0}
-semigroups
(
V
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)
)
t
⩾
0
\left (\mathcal {V}(t)\right )_{t ...\geqslant 0}
in
L
1
(
T
d
×
R
d
)
L^{1}(\mathbb {T}^{d}\times \mathbb {R}^{d})
governing conservative linear kinetic equations on the torus with general scattering kernel
k
(
v
,
v
′
)
\boldsymbol {k}(v,v’)
and degenerate (i.e. not bounded away from zero) collision frequency
σ
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v
)
=
∫
R
d
k
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v
′
,
v
)
m
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d
v
′
)
\sigma (v)=\int _{\mathbb {R}^{d}}\boldsymbol {k}(v’,v)\boldsymbol {m}(\mathrm {d}v’)
, (with
m
(
d
v
)
\boldsymbol {m}(\mathrm {d}v)
being absolutely continuous with respect to the Lebesgue measure). We show in particular that if
N
0
N_{0}
is the maximal integer
s
⩾
0
s \geqslant 0
such that
1
σ
(
⋅
)
∫
R
d
k
(
⋅
,
v
)
σ
−
s
(
v
)
m
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d
v
)
∈
L
∞
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R
d
)
,
\begin{equation*} \frac {1}{\sigma (\cdot )}\int _{\mathbb {R}^{d}}\boldsymbol {k}(\cdot ,v)\sigma ^{-s}(v)\boldsymbol {m}(\mathrm {d}v) \in L^{\infty }(\mathbb {R}^{d}), \end{equation*}
then, for initial datum
f
f
such that
∫
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×
R
d
|
f
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x
,
v
)
|
σ
−
N
0
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)
d
x
m
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d
v
)
>
∞
\displaystyle \int _{\mathbb {T}^{d}\times \mathbb {R}^{d}}|f(x,v)|\sigma ^{-N_{0}}(v)\mathrm {d}x\boldsymbol {m}(\mathrm {d}v) >\infty
it holds
‖
V
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t
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f
−
ϱ
f
Ψ
‖
L
1
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T
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×
R
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=
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f
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(
1
+
t
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N
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−
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,
ϱ
f
≔
∫
R
d
f
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x
,
v
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d
x
m
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v
)
,
\begin{equation*} \left \|\mathcal {V}(t)f-\varrho _{f}\Psi \right \|_{L^{1}(\mathbb {T}^{d}\times \mathbb {R}^{d})}=\dfrac {{\varepsilon }_{f}(t)}{(1+t)^{N_{0}-1}}, \qquad \varrho _{f}≔\int _{\mathbb {R}^{d}}f(x,v)\mathrm {d}x\boldsymbol {m}(\mathrm {d}v), \end{equation*}
where
Ψ
\Psi
is the unique invariant density of
(
V
(
t
)
)
t
⩾
0
\left (\mathcal {V}(t)\right )_{t \geqslant 0}
and
lim
t
→
∞
ε
f
(
t
)
=
0
\lim _{t\to \infty }{\varepsilon }_{f}(t)=0
. We in particular provide a new criteria of the existence of invariant density. The proof relies on the explicit computation of the time decay of each term of the Dyson-Phillips expansion of
(
V
(
t
)
)
t
⩾
0
\left (\mathcal {V}(t)\right )_{t \geqslant 0}
and on suitable smoothness and integrability properties of the trace on the imaginary axis of Laplace transform of remainders of large order of this Dyson-Phillips expansion. Our construction resorts also on collective compactness arguments and provides various technical results of independent interest. Finally, as a by-product of our analysis, we derive essentially sharp “subgeometric” convergence rate for Markov semigroups associated to general transition kernels.
Purpose
A combined diffusion‐relaxometry MR acquisition and analysis pipeline for in vivo human placenta, which allows for exploration of coupling between T2* and apparent diffusion coefficient (ADC) ...measurements in a sub 10‐minute scan time.
Methods
We present a novel acquisition combining a diffusion prepared spin echo with subsequent gradient echoes. The placentas of 17 pregnant women were scanned in vivo, including both healthy controls and participants with various pregnancy complications. We estimate the joint T2*‐ADC spectra using an inverse Laplace transform.
Results
T2*‐ADC spectra demonstrate clear quantitative separation between normal and dysfunctional placentas.
Conclusions
Combined T2*‐diffusivity MRI is promising for assessing fetal and maternal health during pregnancy. The T2*‐ADC spectrum potentially provides additional information on tissue microstructure, compared to measuring these two contrasts separately. The presented method is immediately applicable to the study of other organs.
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•A new spatially-resolved T1-T2 measurement is introduced.•An adiabatic inversion pulse is employed for slice-selection.•The selective pulse can select a quasi-rectangular slice, on ...the order of 1 mm.•The method can be employed to characterize oil–water mixtures and other fluids.
A novel slice-selective T1-T2 measurement is proposed to measure spatially resolved T1-T2 distributions. An adiabatic inversion pulse is employed for slice-selection. The slice-selective pulse is able to select a quasi-rectangular slice, on the order of 1 mm, at an arbitrary position within the sample.The method does not employ conventional selective excitation in which selective excitation is often accomplished by rotation of the longitudinal magnetization in the slice of interest into the transverse plane, but rather a subtraction based on CPMG data acquired with and without adiabatic inversion slice selection. T1 weighting is introduced during recovery from the inversion associated with slice selection. The local T1-T2 distributions measured are of similar quality to bulk T1-T2 measurements.
The new method can be employed to characterize oil–water mixtures and other fluids in porous media. The method is beneficial when a coarse spatial distribution of the components is of interest.
•Algorithm for fast calculation of energization overvoltage of hybrid overhead line-cable transmission lines is proposed.•Algorithm is based on full frequency-dependent parameters and modal ...theory.•Relative errors of the obtained results are less than 0.261 %.•Time consumed by proposed method is only about 32.7 % – 58.6 % of PSCAD/EMTDC.
This paper addresses the challenges associated with the time-consuming and complex nature of using electromagnetic transient (EMT) simulation software, such as PSCAD/EMTDC, for calculating transient overvoltages in complex power grids. To overcome these challenges, we propose a novel algorithm for fast calculation of energization overvoltages in hybrid overhead and cable transmission lines. The proposed algorithm begins by calculating the frequency-dependent parameters of the transmission lines in the full frequency domain. These parameters are then decoupled using phase-mode transformation. Subsequently, the algorithm derives the boundary conditions of the transmission line based on its topology, leading to corresponding complex frequency-domain voltage expressions. To obtain the calculation results of energization overvoltages along the hybrid transmission lines, the algorithm applies mode-phase transformation and an improved numerical inverse Laplace transform (NILT). To verify the accuracy and speed of the proposed algorithm, it is applied to a 330 kV hybrid overhead line and cable transmission system with a length of 56.8 km. The results demonstrate that the proposed algorithm achieves a maximum relative error of less than 0.261 % compared to the frequency-dependent phase model (FDPM) used in PSCAD. Additionally, the calculation time of the proposed algorithm is shown to be only 32.654 % – 58.649 % of the FDPM's calculation time.
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