tensor model
Recently Published Documents


TOTAL DOCUMENTS

302
(FIVE YEARS 116)

H-INDEX

23
(FIVE YEARS 6)

2022 ◽  
Vol 12 (2) ◽  
pp. 846
Author(s):  
Oleksandr Lemeshko ◽  
Jozef Papan ◽  
Maryna Yevdokymenko ◽  
Oleksandra Yeremenko

The advanced tensor solution to the problem of inter-domain routing with normalized Quality of Service under hierarchical coordination in a communication network is proposed in the paper. The novelty of the method based on the tensor model lies in the more flexible load balancing over the network due to the presence of requirements to average end-to-end delay of packets. The framework of the method comprises a decomposed flow-based routing model that includes the inter-domain routing interaction conditions and ensures the normalized Quality of Service derived from the tensor model. Considering the mentioned above, the advanced inter-domain Quality of Service routing task was formulated in the optimization form, using the quadratic optimality criterion. The conducted analysis of the numerical research results confirmed the efficiency and adequacy of the proposed method when the desired solutions were obtained during the finite number of iterations under a provision of the normalized Quality of Service. It should be noted that the reduced number of such iterations during the operation of the method will decrease the amount of service traffic transmitted over the network needed for obtaining the final solution in the process of inter-domain routing with normalized Quality of Service.


2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Fengchang Bu ◽  
Lei Xue ◽  
Mengyang Zhai ◽  
Xiaolin Huang ◽  
Jinyu Dong ◽  
...  

AbstractAcoustic emission (AE) characterization is an effective technique to indirectly capture the failure process of quasi brittle rock. In previous studies, both experiments and numerical simulations were adopted to investigate the AE characteristics of rocks. However, as the most popular numerical model, the moment tensor model (MTM) cannot be constrained by the experimental result because there is a gap between MTM and experiments in principle, signal processing and energy analysis. In this paper, we developed a particle-velocity-based model (PVBM) that enabled direct monitoring and analysis of the particle velocity in the numerical model and had good robustness. The PVBM imitated the actual experiment and could fill in gaps between the experiment and MTM. AE experiments of marine shale under uniaxial compression were carried out, and the results were simulated by MTM. In general, the variation trend of the experimental result could be presented by MTM. Nevertheless, the magnitudes of AE parameters by MTM presented notable differences of more than several orders of magnitude compared with those by the experiment. We sequentially used PVBM as a proxy to analyse these discrepancies and systematically evaluate the AE characterization of rocks from the experiment to numerical simulation, considering the influence of wave reflection, energy geometrical diffusion, viscous attenuation, particle size and progressive deterioration of rock material. The combination of MTM and PVBM could reasonably and accurately acquire AE characteristics of the actual AE experiment of rocks by making full use of their respective advantages.


Author(s):  
Valentin Bonzom ◽  
Victor Nador ◽  
Adrian Tanasa

Abstract We study the double scaling limit of the O(N)3-invariant tensor model, initially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). This model has an interacting part containing two types of quartic invariants, the tetrahedric and the pillow one. For the 2-point function, we rewrite the sum over Feynman graphs at each order in the 1/N expansion as a finite sum, where the summand is a function of the generating series of melons and chains (a.k.a. ladders). The graphs which are the most singular in the continuum limit are characterized at each order in the 1/N expansion. This leads to a double scaling limit which picks up contributions from all orders in the 1/N expansion. In contrast with matrix models, but similarly to previous double scaling limits in tensor models, this double scaling limit is summable. The tools used in order to prove our results are combinatorial, namely a thorough diagrammatic analysis of the Feynman graphs, as well as an analytic analysis of the singularities of the relevant generating series.


Author(s):  
Andrew D Davis ◽  
Stefanie Hassel ◽  
Stephen R Arnott ◽  
Geoffrey B Hall ◽  
Jacqueline K Harris ◽  
...  

Abstract Clinically oriented studies commonly acquire diffusion MRI (dMRI) data with a single non-zero b-value (i.e. single-shell) and diffusion weighting of b=1000 s/mm2. To produce microstructural parameter maps, the tensor model is usually used, despite known limitations. Although compartment models have demonstrated improved fits in multi-shell dMRI data, they are rarely used for single-shell parameter maps, where their effectiveness is unclear from the literature. Here, various compartment models combining isotropic balls and symmetric tensors were fitted to single-shell dMRI data to investigate model fitting optimization and extract the most information possible. Full testing was performed in 5 subjects, and 3 subjects with multi-shell data were included for comparison. The results were tested and confirmed in a further 50 subjects. The Markov chain Monte Carlo (MCMC) model fitting technique outperformed non-linear least squares. Using MCMC, the 2-fibre-orientation mono-exponential ball & stick model (BSME 2) provided artifact-free, stable results, in little processing time. The analogous ball & zeppelin model (BZ2) also produced stable, low-noise parameter maps, though it required much greater computing resources (50 000 burn-in steps). In single-shell data, the gamma-distributed diffusivity ball & stick model (BSGD 2) underperformed relative to other models, despite being an often-used software default. It produced artifacts in the diffusivity maps even with extremely long processing times. Neither increased diffusion weighting nor a greater number of gradient orientations improved BSGD 2 fits. In white matter (WM), the tensor produced the best fit as measured by Bayesian information criterion. This result contrasts with studies using multi-shell data. However, in crossing fibre regions the tensor confounded geometric effects with fractional anisotropy (FA): the planar/linear WM FA ratio was 49%, while BZ2 and BSME 2 retained 76% and 83% of restricted fraction, respectively. As a result, the BZ2 and BSME 2 models are strong candidates to optimize information extraction from single-shell dMRI studies.


2021 ◽  
Author(s):  
Qing Liu ◽  
Xiangfang Li ◽  
Jian Yang ◽  
Sen Feng ◽  
Minxia He ◽  
...  

Abstract Unconventional fractured ultra-low-permeability reservoirs play an important role in continental sedimentary basins in China, and their formation characteristics and seepage laws are greatly different from that of traditional reservoirs. In this paper, the influence of microfractures and unsteady waterflooding on the productivity of fractured ultra-low permeability reservoirs are studied deeply. The reservoir parameters used in the study are from an actual fractured ultra-low-permeability reservoir in Ordos Basin, where microfractures are developed but macroscopic fractures are not. The microfractures have a small opening and are widely distributed in the reservoir, so the reservoir numerical simulation model adopts the equivalent continuous matrix model to simulate waterflooding. On one hand, the physical model of micro-fractured reservoir and the permeability tensor model of the equivalent continuous matrix are established. The results show that the existence of microfractures can increase the permeability of matrix by 1.4 times. On the other hand, an ideal heterogeneous numerical simulation model composed of pure matrix and equivalent continuous matrix considering microfracture is established according to actual geological parameters of the fractured ultra-low-permeability reservoir. To simulate and compare the unsteady waterflooding and continuous waterflooding development in 10-year development under the condition of constant annual injection rate, the results indicate that unsteady waterflooding development make higher productivity and lower water cut and lower formation water saturation than that of continuous waterflooding. By conducting unsteady waterflooding development simulation for sensitivity analysis, the results demonstrate that the greater the capillary force, the better the role of capillary imbibition in a certain range, meanwhile, the unsteady waterflooding has the best exploitation effect when the value of water injection cycle time is 100 days and the fluctuation amplitude of water injection rate is 1. At the above situation, the displacement and capillary imbibition and pressure disturbance achieve the desired effect of reducing water cut and increasing oil production.


Author(s):  
Naoki Sasakura

In this paper, to understand space–time dynamics in the canonical tensor model of quantum gravity for the positive cosmological constant case, we analytically and numerically study the phase profile of its exact wave function in a coordinate representation, instead of the momentum representation analyzed so far. A saddle point analysis shows that Lie group symmetric space–times are strongly favored due to abundance of continuously existing saddle points, giving an emergent fluid picture. The phase profile suggests that spatial sizes grow in “time,” where sizes are measured by the tensor-geometry correspondence previously introduced using tensor rank decomposition. Monte Carlo simulations are also performed for a few small N cases by applying a re-weighting procedure to an oscillatory integral which expresses the wave function. The results agree well with the saddle point analysis, but the phase profile is subject to disturbances in a large space–time region, suggesting existence of light modes there and motivating future computations of primordial fluctuations from the perspective of canonical tensor model.


2021 ◽  
Author(s):  
Benjamin C. Tendler ◽  
Feng Qi ◽  
Sean Foxley ◽  
Menuka Pallebage‐Gamarallage ◽  
Ricarda A. L. Menke ◽  
...  
Keyword(s):  

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 302
Author(s):  
Dennis Obster ◽  
Naoki Sasakura

Tensor rank decomposition is a useful tool for geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able to estimate how many tensor rank decompositions can approximate a given tensor. More precisely, finding an approximate symmetric tensor rank decomposition of a symmetric tensor Q with an error allowance Δ is to find vectors ϕi satisfying ∥Q−∑i=1Rϕi⊗ϕi⋯⊗ϕi∥2≤Δ. The volume of all such possible ϕi is an interesting quantity which measures the amount of possible decompositions for a tensor Q within an allowance. While it would be difficult to evaluate this quantity for each Q, we find an explicit formula for a similar quantity by integrating over all Q of unit norm. The expression as a function of Δ is given by the product of a hypergeometric function and a power function. By combining new numerical analysis and previous results, we conjecture a formula for the critical rank, yielding an estimate for the spacetime degrees of freedom of the CTM. We also extend the formula to generic decompositions of non-symmetric tensors in order to make our results more broadly applicable. Interestingly, the derivation depends on the existence (convergence) of the partition function of a matrix model which previously appeared in the context of the CTM.


Sign in / Sign up

Export Citation Format

Share Document