Memory effect in time fractional Schrödinger equation

A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploration of the time fractional Schrodinger equation within the context of a non-Markovian environment.By leveraging a two-level atom as an illustrative case,we find that the choice to raise i to the order of the time derivative is inappropriate.In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment,the time fractional Schrodinger equation,when devoid of fractional-order operations on the imaginary unit i,emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects.Meanwhile,we also prove that it is meaningless to study the memory of time fractional Schrodinger equation with time derivative 1<α≤2.It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrodinger equation.This will be the focus of future research.Our study might provide a new perspective on the role of time fractional Schrodinger equation.

Influence of recovery heating rate on shape memory effect in up-quenched Cu-Al-Mn alloy

The effect of recovery heating rate on shape memory effect of the up-quenched Cu-8.88Al-10.27Mn（mass fraction, %） alloy was investigated by optical microscopy, electron transmission microscopy（TEM） and electrical resistivity measurement. It is found that the shape recovery rate decreases as the heating rate decreases. It can reach 75% when the heating rate is 20 ℃/min, while it is only 8% when the heating rate is 1 ℃/min. In situ microstructure observation indicates that the dependence of shape memory effect on recovery heating rate is caused by the stabilization of twinned martensite induced by deformation. The analysis of electrical resistivity shows that the stabilization of twinned martensite may be ascribed to formation of compound defects of vacancies and dislocations at the boundaries of twinned martensite during the slow heating. The compound defects prevent the reverse transformation of twinned martensite.

Role of thermal martensite in shape memory effect of CoAl and CoNi alloys

To address the role of the HCP martensite in CoAl and CoNi shape memory alloys, the relationship between the shape memory effect （SME） and the content of the thermal and stress-induced HCP martensite was investigated in the solution-treated CoAl and CoNi alloys. In-situ optical observations were employed to investigate the contents of thermal HCP martensite before and after deep cooling and its influence on the stress-induced HCP martensite transformation and SME. The results show that the SME in both the CoAl and the CoNi alloys results from the stress-induced HCP martensite. The role of the thermal HCP martensite in both of them is the strengthening of the matrix. The much higher yield strength in the solution-treated CoAl alloy due to solution strengthening of Al is responsible for its better SME compared with the CoNi alloy.

Memory effect on the pressure-temperature condition and induction time of gas hydrate nucleation

The focus of this study is to investigate the influence of memory effect and the relation of its existence with the dissociation temperature,using gas hydrate formation and dissociation experiments.This is beneficial because memory effect is considered as an effective approach to promote the thermodynamic and dynamic conditions of gas hydrate nucleation.Seven experimental systems （twenty tests in total） were performed in a 1 L pressure cell.Three types of hydrate morphology,namely massive,whiskery and jelly crystals were present in the experiments.The pressures and temperatures at the time when visual hydrate crystals appeared were measured.Furthermore,the influence of memory effect was quantified in terms of pressure-temperature-time （p-T-t） relations.The results revealed that memory effect could promote the thermodynamic conditions and shorten the induction time when the dissociation temperature was not higher than 25℃.In this study,the nucleation superpressure and induction time decrease gradually with time of tests,when the earlier and the later tests are compared.It is assumed that the residual structure of hydrate dissociation,as the source of the memory effect,provides a site for mass transfer between host and guest molecules.Therefore,a driving force is created between the residual structures and its surrounding bulk phase to promote the hydrate nucleation.However,when the dissociation temperature was higher than 25 ℃,the memory effect vanished.These findings provide references for the application of memory effect in hydrate-based technology.

SHAPE MEMORY EFFECT OF PU IONOMERS WITH IONIC GROUPS ON HARD-SEGMENTS

SMPU （shape memory polyurethane） non-ionomers and ionomers, synthesized with poly（c-caprolactone） （PCL）, 4, 4＇-diphenylmethane diisocyanate （MDI）, 1,4-butanediol （BDO）, dimethylolpropionic acid （DMPA） were measured with cyclic tensile test and strain recovery test. The relations between the structure and shape memory effect of these two series were studied with respect to the ionic group content and the effect of neutralization. The resulting data indicate that, with the introduction of asymmetrical extender, the stress at 100% elongation is decreased for PU non-ionomer and ionomer series, especially lowered sharply for non-ionomer series; the fixation ratio of ionomer series is not affected obviously by the ionic group content; the total recovery ratio of ionomer series is decreased greatly. After sufficient relaxation time for samples stretched beforehand, the switching temperature is raised slightly, whereas the recovery ratio measured with strain recovery test method is lowered with increased DMPA content. The characterization with FT-IR, DSC, DMA elucidated that, the ordered hard domain of the two series is disrupted with the introduction of DMPA which causes more hard segments to dissolve in soft phase; ionic groups on hard segment enhance the cohesion between hard segments especially at high ionic group content and significantly facilitate the phase separation compared with the corresponding non-ionomer at moderate ionic group content.

A macroscopic multi-mechanism based constitutive model for the thermo-mechanical cyclic degeneration of shape memory effect of NiTi shape memory alloy

A macroscopic based multi-mechanism constitutive model is constructed in the framework of irreversible thermodynamics to describe the degeneration of shape memory effect occurring in the thermo-mechanical cyclic deformation of NiTi shape memory alloys (SMAs). Three phases, austenite A, twinned martensite and detwinned martensite , as well as the phase transitions occurring between each pair of phases (, , , , and are considered in the proposed model. Meanwhile, two kinds of inelastic deformation mechanisms, martensite transformation-induced plasticity and reorientation-induced plasticity, are used to explain the degeneration of shape memory effects of NiTi SMAs. The evolution equations of internal variables are proposed by attributing the degeneration of shape memory effect to the interaction between the three phases (A, , and and plastic deformation. Finally, the capability of the proposed model is verified by comparing the predictions with the experimental results of NiTi SMAs. It is shown that the degeneration of shape memory effect and its dependence on the loading level can be reasonably described by the proposed model.

Compressive mechanical properties and shape memory effect of NiTi gradient lattice structures fabricated by laser powder bed fusion

Laser additive manufacturing (AM) of lattice structures with light weight, excellent impact resistance, and energy absorption performance is receiving considerable attention in aerospace, transportation, and mechanical equipment application fields. In this study, we designed four gradient lattice structures (GLSs) using the topology optimization method, including the unidirectional GLS, the bi-directional increasing GLS, the bi-directional decreasing GLS and the none-GLS. All GLSs were manufactureed by laser powder bed fusion (LPBF). The uniaxial compression tests and finite element analysis were conducted to investigate the influence of gradient distribution features on deformation modes and energy absorption performance of GLSs. The results showed that, compared with the 45° shear fracture characteristic of the none-GLS, the unidirectional GLS, the bi-directional increasing GLS and the bi-directional decreasing GLS had the characteristics of the layer-by-layer fracture, showing considerably improved energy absorption capacity. The bi-directional increasing GLS showed a unique combination of shear fracture and layer-by-layer fracture, having the optimal energy absorption performance with energy absorption and specific energy absorption of 235.6 J and 9.5 J g-1 at 0.5 strain, respectively. Combined with the shape memory effect of NiTi alloy, multiple compression-heat recovery experiments were carried out to verify the shape memory function of LPBF-processed NiTi GLSs. These findings have potential value for the future design of GLSs and the realization of shape memory function of NiTi components through laser AM.

Buckling-controlled two-way shape memory effect in a ring-shaped bilayer

Shape memory polymers(SMPs)usually have a one-way shape memory effect.In this paper,an easy-operating method to realize a two-way shape memory effect was demonstrated in a ring-shaped bilayer structure where the two layers are SMPs with different thermal transition temperatures.By designing specific thermomechanical processes,the mismatched deformation between the two layers leads to a morphology change of ring-shaped bilayer structures from a smooth ring to a gear-like buckling shape under cooling and a reversible recovery to the smooth shape under heating.Such a morphology change is ascribed to occurrence and recovery of thermoelastic buckling.This method was validated by finite element simulation.We experimentally investigated the influence of pre-strain on buckling,and it was found that both the buckling occurrence and recovery temperature vary with pre-strain.Furthermore,considering a ring-shaped SMP-SMP bilayer structure,finite element analysis was conducted to study the influence of film thickness and modulus ratio of two layers on buckling behavior.The results showed that the critical buckling wavelength was greatly influenced by film thickness and modulus ratio.W e made a theoretical analysis that accorded well with the numerical results.

The regulation of memory effect and its influence on discharge properties of a dielectric barrier discharge driven by bipolar pulse at atmospheric-pressure nitrogen

The regulation of memory effect that the residual charges generated during and after discharge act on the initiation and development of subsequent discharge is explored by adjusting the pulse parameters,which have an influence on the discharge characteristics.The memory effect is quantified by the measurement of‘wall voltage’through a series of reference capacitors.The influences of memory effect on the discharge properties corresponding to rising/falling time50–500 ns,pulse width 0.5–1.5μs,and frequency 200–600 Hz are analyzed.It is found that the‘wall voltage’increases from 1.4 kV to 2.4 kV with rising/falling time from 50 ns to 500 ns,it varies in the range of 0.18 kV with frequency of 200–600 Hz,and 0.17 k V with pulse width of 0.5–1.5μs.The propagation velocity of wavelike ionization under the negative pulse slows down from 2184 km s-1to 1026 km s-1 as the rising/falling time increases from 50 ns to 500 ns due to the weakening of the electric field by the surface memory effect.More intense and uniform emission can be achieved through faster rising/falling time and higher frequency based on the volume memory effect,while pulse width has less influence on the emission uniformity.Furthermore,similar laws are obtained for spectral and discharge intensity.Therefore,the memory effect is most effectively regulated by rising/falling time,and the discharge properties are affected by the surface and volume memory effect.

Surface traps-related nonvolatile resistive switching memory effect in a single SnO2:Sm nanowire

For nanostructure SnO2,it is very difficult for its electric properties to accurately control due to the presence of abundant surface states.The introduction of Sm can improve the traps in surface space charge region of SnO2 nanowires,resulting in a controllable storage charge effect.For the single nanowire-based two-terminal device,two surface state-related back-to-back diodes are formed.At a relatively large voltage,electrons can be injected into the traps in surface space charge region from negative electrode,resulting in a decrease of surface barrier connected with negative electrode,and contrarily electrons can be extracted from the traps in surface space charge region into positive electrode,resulting in an increase of surface barrier connected with positive electrode.The reversible injection and extraction induce a nonvolatile resistive switching memory effect.

Shape Memory Effect of As-aged Fe-14Mn-5Si-8Cr-4Ni-0.2C Alloy

The effects of aging temperature on shape memory effect, mechanical properties and microstruc-ture of Fe-14Mn-5Si-8Cr-4Ni-0.2C shape memory alloy have been studied. The results showed that the second phase particles rich in chromium, manganese and silicon precipitate during aging, and thereby increase the hardness and strength of the alloy. The shape recovery ratio can be remarkably improved by aging and a maximum value can be obtained at 1223 K, which is 68% higher than that of the specimen in solid solution state. When the aging temperature is below 1223 K, the amount of second phase particles increases as the aging temperature increases. The size of austenite grain increases with increasing aging temperature. When the temperature is over 1223 K, the second phase particles can not precipitate. The lack of second phase particles and the increase of grain size make the hardness and shape recovery ratio drastically decrease, when the temperature is over 1223 K.

Microstructure,compression property and shape memory effect of Ru-Nb high temperature shape memory alloy

The microstructure,phase transformation,compression property and strain recovery characteristics of equiatomic Ru-Nb high temperature shape memory alloy were investigated by means of optical microscope,X-ray diffraction(XRD),differential scanning calorimetry(DSC),compression tests and transmission electron microscopy(TEM).When cooling the alloy specimen from high temperature to room temperature,β(parent phase)→β’(interphase)→β″(martensite) two step phase transformation occurs.The microstructure at room temperature shows regularly arranged band morphology with the monoclinic crystal structure.The twinning relationship between the martensite bands was determined to be(101) Type I.Reorientation and of the martensite bands inside the variant and dislocation were found during compression at room temperature.The maximum complete recovery strain is about 1.5%.

Effect of heat treatment on the transformation behavior and temperature memory effect in TiNiCu wires

The effect of heat treatment on the phase transformation behavior of TiNiCu shape memory alloy wires and the temperature memory effect in this alloy were investigated by the resistance method. These results showed that with increasing annealing temperature and annealing time, the phase transformation temperatures of TiNiCu wires were shifted to higher temperatures in the heating and cooling process. It was also found that incomplete thermal cycles, upon heating the TiNiCu wires, which were arrested at a temperature between the start and finish temperatures of the reverse martensite transformation, could induce a kinetic stop in the next complete thermal cycle. The kinetic stop temperature was closely related to the previous arrested temperature. This phenomenon was defined as the temperature memory effect. The result of this study was consistent with the previous report on the phenomenon obtained using the differential scanning calorimetry method, indicating that temperature memory effect was a common phenomenon in shape memory alloys.

Effect of Training on Two-way Shape Memory Effect and Its Stability in a Ti-Ni-Hf High Temperature Shape Memory Alloy

The Effect of the thermal cycling training under constant strain on the two-way shape memory effect (TWSME) in a Ti36l\li49Hf15 high temperature shape memory alloy (SMA) has been investigated by bending tests. The results indicated that the training procedure is beneficial to get the better TWSME. The two-way shape memory strain increases with increasing the training strain. And it decreases with increasing the training temperature. The TWSME obtained in the present alloy shows poorer stability compared with that obtained in the TiNi alloys.

Two-way Shape Memory Effect in a Ti-Ni-Nb Shape Memory Alloy with Wide Hysteresis

A two-way shape memory effect (TWSM E) in the Ti46.3Ni44.7Nb9 alloy has been systematically investigated by means of bending test and transmission electron microscopy (TEM ) observations. Based on the analysis of the microstructure after training. the mechanism of TWSME in the Ti46.3 Ni44.7Nb9 alloy has been discussed.

MICROSTRUCTURE AND REVERSE SHAPE MEMORY EFFECT IN A Cu-Zn-Al ALLOY

The bainite structure in a Cu-Zn-A1 alloy related to the reverse shape memory effect has been observed by means of TEM.The reverse memory effect may be improved by up to one order of magnitude under applied constraint stress.The widespread propagation of bainite was confirmed to be the diffusion controlled shear process by the parabolic configuration of side interface of bainite plate and the twisting of intersected bainite plates.

Reaction mechanism between“memory effect”and induction time of gas hydrate formation

Abstract Using visual experimental apparatus, one system （T40, 1×10^-3 mol/L, nonadded with coal） and another system （T40, 2×10^-3 mol/L, added with coal） were experimented with for three times and two times, respectively. Five groups of P-T experimental parameters were obtained using the data logger system and analyzed combined with the video information of the experiments. Major conclustions show that the induction time is shortened by 10-20 times in the experimental system containing residual pentahedral ring structures; ＂memory effect＂ can accelerate the dynamic progress and improve the thermodynamic conditions of gas hydrate formation.

Effect of Thermal Cycling under Load on Martensite Transformation and Two-way Shape Memory Effect in a TiNi Alloy

The effect of thermal cycling under loading on martensitic transformation and two-way shape memory effect was investigated for Ti-49.8 at, pet Ni alloy. It is shown that M(s), and M(f) temperature increase with increasing the number of cycles, while A(s) and A(f) temperature decrease during thermal cycling. The total strain at and permanent strain epsilon (p) increase with increasing applied stress and number of cycles. The two-way shape memory effect can be improved by proper thermal cycling training under loading, while excessively high applied stress results in the deterioration of TWSME. The reason for the changes in martensitic transformation characteristics and two-way shape memory effect during thermal cycling under loading is discussed based on the analysis of microstructure by TEM observations.

Wavelet network based predistortion method for wideband RF power amplifiers exhibiting memory effects

RF power amplifiers (PAs) are usually considered as memoryless devices in most existing predistortion techniques. Nevertheless, in wideband communication systems, PA memory effects can no longer be ignored and memoryless predistortion cannot linearize PAs effectively. After analyzing PA memory effects, a novel predistortion method based on wavelet networks (WNs) is proposed to linearize wideband RF power amplifiers. A complex wavelet network with tapped delay lines is applied to construct the predistorter and then a complex backpropagation algorithm is developed to train the predistorter parameters. The simulation results show that compared with the previously published feed-forward neural network predistortion method, the proposed method provides faster convergence rate and better performance in reducing out-of-band spectral regrowth.

A nonlinear hydroelastic method considering wave memory effect for ship load responses in irregular waves

Since the amplitude and frequency of irregular waves change with time,great difficulties are brought for solving ship load responses in random waves.To take the effect of various frequencies of irregular waves into consideration in load responses of hull,the wave memory effect is necessary.A semi-analytical method is introduced for the time-domain retardation functions,and then a nonlinear hydroelastic method considering memory effect for ships in irregular waves is proposed.Segmented self-propelling model experiments of a container ship were carried out in a towing tank,a ship motion measuring device for self-propelling model test was designed.Whipping responses of the ship in regular and irregular waves are analyzed.Finally,the calculation results are compared with those measured by segmented model experiments,and the result indicates that the memory effect has little effect on load responses of ship in regular waves,but pronounced effect on results in irregular waves.Moreover,the presented method is reasonable for the prediction of ship load responses in irregular waves.