Identifying the initial state for a parabolic diffusion from their time averages with fractional derivative

Author(s):  
Tran Ngoc Thach ◽  
Nguyen Huu Can ◽  
Vo Viet Tri
Author(s):  
F. I. Grace

An interest in NiTi alloys with near stoichiometric composition (55 NiTi) has intensified since they were found to exhibit a unique mechanical shape memory effect at the Naval Ordnance Laboratory some twelve years ago (thus refered to as NITINOL alloys). Since then, the microstructural mechanisms associated with the shape memory effect have been investigated and several interesting engineering applications have appeared.The shape memory effect implies that the alloy deformed from an initial shape will spontaneously return to that initial state upon heating. This behavior is reported to be related to a diffusionless shear transformation which takes place between similar but slightly different CsCl type structures.


2012 ◽  
Vol 8 (1) ◽  
pp. 37-48
Author(s):  
S. Chehaibi ◽  
K. Abrougui ◽  
F. Haouala

The effects of mechanical perforation densities by extracting soil cores through an aerator Vertidrain with a working width of 1.6 m and equipped with hollow tines spaced of 65 mm, were studied on a sandy soil of a grassy sward in the Golf Course El Kantaoui in Sousse (Tunisia). The mechanical aeration was performed at two densities: 250 and 350 holes/m2. The cone penetration resistance and soil water infiltration were measured. These parameters were performed at initial state before aeration (E0) and then on the 10th, 20th and 30th day after aeration. These results showed that perforation density of 350 holes/m2 had a positive effect on the soil by reducing its cone resistance to penetration compared to the initial state (Rp = 14.8 daN/cm2). At 5 cm depth the decrease in resistance to penetration was 34% and 43% on the 10th and 20th day after aeration, respectively. However, on the 30th day after aeration the soil resistance to penetration tended to grow and its value compared to the initial state decreased only by 21 and 26%, respectively, at 5 and 15 cm of depth only by 10% and 9% with 250 holes/m2 density. The soil water infiltration made a good improvement after aeration compared to the initial state. This parameter increased from 4.8 cm/h to 8.3, 10.9 and 13.1 cm/h with 250 holes/m2 density and to 10, 12.9 and 14.8 cm/h with 350 holes/m2 density on the 10th, 20th and 30th day following the aeration.


2014 ◽  
Vol 62 (1) ◽  
pp. 129-137
Author(s):  
A. Sawicki ◽  
J. Mierczyński

Abstract A basic set of experiments for the determination of mechanical properties of sands is described. This includes the determination of basic physical and mechanical properties, as conventionally applied in soil mechanics, as well as some additional experiments, which provide further information on mechanical properties of granular soils. These additional experiments allow for determination of steady state and instability lines, stress-strain relations for isotropic loading and pure shearing, and simple cyclic shearing tests. Unconventional oedometric experiments are also presented. Necessary laboratory equipment is described, which includes a triaxial apparatus equipped with local strain gauges, an oedometer capable of measuring lateral stresses and a simple cyclic shearing apparatus. The above experiments provide additional information on soil’s properties, which is useful in studying the following phenomena: pre-failure deformations of sand including cyclic loading compaction, pore-pressure generation and liquefaction, both static and caused by cyclic loadings, the effect of sand initial anisotropy and various instabilities. An important feature of the experiments described is that they make it possible to determine the initial state of sand, defined as either contractive or dilative. Experimental results for the “Gdynia” model sand are shown.


2020 ◽  
Author(s):  
Zhengqing Tong ◽  
Margaret S. Cheung ◽  
Barry D. Dunietz ◽  
Eitan Geva ◽  
Xiang Sun

The nonequilibrium Fermi’s golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions, when the nuclear degrees of freedom start out in a <i>nonequilibrium</i> state. In this letter, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer rates in the carotenoid-porphyrin-C<sub>60</sub> molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground-state to the ππ* state, and the porphyrin-to-C<sub>60</sub> and the carotenoid-to-C<sub>60</sub> charge transfer rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C<sub>60</sub> CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.


Author(s):  
T. Mamatov ◽  
R. Sabirova ◽  
D. Barakaev

We study mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The main interest being in the evaluation of the latter for the mixed fractional derivative in the cases Hölder class defined by usual Hölder condition


Sign in / Sign up

Export Citation Format

Share Document