scholarly journals Wegner Estimate for Discrete Alloy-type Models

2010 ◽  
Vol 11 (5) ◽  
pp. 991-1005 ◽  
Author(s):  
Ivan Veselić
Keyword(s):  
2015 ◽  
Vol 27 (04) ◽  
pp. 1550007 ◽  
Author(s):  
Karsten Leonhardt ◽  
Norbert Peyerimhoff ◽  
Martin Tautenhahn ◽  
Ivan Veselić

We study Schrödinger operators on L2(ℝd) and ℓ2(ℤd) with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying but not necessarily of fixed sign. In the continuum setting, we require a generalized step-function shape. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. In the described situation, a Wegner estimate, which is polynomial in the volume of the box and linear in the size of the energy interval, holds. We apply the established Wegner estimate as an ingredient for a localization proof via multiscale analysis.


2002 ◽  
Vol 112 (1) ◽  
pp. 131-146 ◽  
Author(s):  
Werner Kirsch ◽  
Ivan Veselic
Keyword(s):  

2021 ◽  
Vol 868 ◽  
pp. 159233
Author(s):  
Aichi Yamashita ◽  
Tatsuma D. Matsuda ◽  
Yoshikazu Mizuguchi

Metals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 772
Author(s):  
Seunghyun Kim ◽  
Osung Kwon ◽  
Hojeong Ryu ◽  
Sungjun Kim

This work demonstrates the synaptic properties of the alloy-type resistive random-access memory (RRAM). We fabricated the HfAlOx-based RRAM for a synaptic device in a neuromorphic system. The deposition of the HfAlOx film on the silicon substrate was verified by X-ray photoelectron spectroscopy (XPS) analysis. It was found that both abrupt and gradual resistive switching could be implemented, depending on the reset stop voltage. In the reset process, the current gradually decreased at weak voltage, and at strong voltage, it tended to decrease rapidly by Joule heating. The type of switching determined by the first reset process was subsequently demonstrated to be stable switching by successive set and reset processes. A gradual switching type has a much smaller on/off window than abrupt switching. In addition, retention maintained stability up to 2000 s in both switching cases. Next, the multiple current states were tested in the gradual switching case by identical pulses. Finally, we demonstrated the potentiation and depression of the Cu/HfAlOx/Si device as a synapse in an artificial neural network and confirmed that gradual resistive switching was suitable for artificial synapses, using neuromorphic system simulation.


Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 624
Author(s):  
Roman Kolenak ◽  
Igor Kostolny ◽  
Jaromir Drapala ◽  
Paulina Babincova ◽  
Peter Gogola

The aim of the research work was to characterize the soldering alloy type Bi-Ag-Ti and to study the direct soldering of silicon and copper. Bi11Ag1.5Ti solder has a broad melting interval. Its scope depends mainly on the content of silver and titanium. The solder begins to melt at the temperature of 262.5 ∘C and full melting is completed at 405 ∘C. The solder microstructure consists of a bismuth matrix with local eutectics. The silver crystals and titanium phases as BiTi2 and Bi9Ti8 are segregated in the matrix. The average tensile strength of the solder varies around 42 MPa. The bond with silicon is formed due to interaction of active titanium with the silicon surface at the formation of a reaction layer, composed of a new product, TiSi2. In the boundary of the Cu/solder an interaction between the liquid bismuth solder and the copper substrate occurs, supported by the eutectic reaction. The mutual solubility between the liquid bismuth solder is very limited, on both the Bi and the Cu side. The average shear strength in the case of a combined joint of Si/Cu fabricated with Bi11Ag1.5Ti solder is 43 MPa.


2013 ◽  
Vol 197 ◽  
pp. 232-237 ◽  
Author(s):  
Dariusz Kuc ◽  
Eugeniusz Hadasik

The paper presents a model of microstructure changes elaborated for magnesium alloy type AZ31. In previous papers, the function of flow stress was defined on the basis of uniaxial hot compression tests. On the basis of marked relaxation curves and quantitative tests of structure the softening indicators were defined together with elaboration of equations which describe the changes in the grain size. Marked coefficients of equations were introduced in the code of simulation program. Calculations were conducted for given temperature values from 450 ÷ 250°C and strain rate from 0.01 to 10 s-1, which correspond with rolling temperature range of this alloy. Prepared model will allow the proper choice of parameters in hot rolling process of this alloy to achieve the assumed microstructure.


2019 ◽  
Vol 11 ◽  
pp. 46-60 ◽  
Author(s):  
Lichuan Wang ◽  
Jolanta Światowska ◽  
Sirui Dai ◽  
Minglei Cao ◽  
Zhicheng Zhong ◽  
...  

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