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By discovery of carbon nano tubes in 1991 by a Japanese scientist named Iijima, a new window was opened for science. Carbon nano tubes are **one**- **dimensional** **nanostructures**. They are of two types: single-walled and multi-walled with the former having higher purity. These nano-particles, in terms of structure, are divided in two types of metal and semiconductor. The general **properties** of carbon nano tubes are high Young’s modulus, high thermal and **electrical** conductivity due to high aspect ratio, excellent thermal stability and chemical storage of hydrogen and helium and others [7].

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I-V curves of our structures based on the PS, mea- sured at room temperature using AFM probe, are shown in Fig. 4a. The experimental samples were characterized with **nonlinear** I-V curves that can be caused by contact phenomena and electric barriers in the porous layer and on the interfaces of PS–silicon substrate and PS–PGO. Deposition of the RGO on the PS surface led to a change in **electrical** parameters of sandwich structures. We ob- served increase in conductivity and the rectifier-type I-V curves of the PS–RGO structures. Noticeable also is a diode-like nature of the I-V curves of the hybrid PS– RGO structures with ITO contact on surface of porous layer as well (Fig. 4b). Detected increase in electric con- ductivity of experimental structures with ITO contact can be connected with larger area of contact compared to AFM tip.

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In summary, this article provides a comprehensive review on recent developments in synthesis, characterization, transport **properties**, and applications of **one**-**dimensional** manganite oxide **nanostructures** (including nanorods, nanowires, nanotubes, and nanofibers). Nowadays, **one**- **dimensional** manganite oxide **nanostructures** are widely used for applications in nanostructure-based devices because of their fascinating **electrical** and magnetic trans- port **properties**. Although many exciting progresses and potential applications of **one**-**dimensional** manganite oxide **nanostructures** have been made, considerable challenges remain to be resolved. In terms of the fabrication tech- niques, the top-down (physical approach) fabrication technique often requires expensive equipment and com- plicated processing and also usually faces the challenge of structural defects (such as edge roughness) in the litho- graphically patterned **one**-**dimensional** manganite oxide **nanostructures**. In addition, most of the perovskite man- ganite oxide materials need high deposition temperature and the typical electron beam and photo resists are incompatible with this requirement. The bottom-up (chemical approach) synthesis of **one**-**dimensional** man- ganite oxide **nanostructures** with precise and reproducible controls in composition, morphology, and physical prop- erties is challenging for **one**-**dimensional** manganite oxide **nanostructures** used for spintronic devices. In terms of microelectronic devices, there have been some revolution- ary breakthroughs in spintronics, such as spin valves, mag- netic tunneling junctions, and spin field-effect transistors. However, several problems for **one**-**dimensional** manganite oxide **nanostructures** used for spintronic devices remain unresolved and some technical challenges lie ahead. For ex- ample, the spin polarization of manganite oxides decays rapidly with temperature, and the working temperature of the **one**-**dimensional** manganite oxide nanostructure-based spintronic device is often lower than the room temperature. The low-**dimensional** spin-dependent transport exists in the **one**-**dimensional** manganite oxide **nanostructures**, and the physical **properties** of the interfaces within **one**- **dimensional** manganite oxide nanostructure-based devices remain elusive. Furthermore, the defect chemistries and the stoichiometry-property correlations in the **one**-**dimensional** perovskite manganite oxide **nanostructures** are quite com- plex. In addition, new device processing techniques are also urgent to be developed. With the researches into **one**- **dimensional** manganite oxide **nanostructures** spreading their wings and becoming more extensive, it is expected that the fascinating achievements towards the practical

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Variants of these equations (including summation over subbands) are often used for d = 2 or d = 1 to estimate carrier densities in quasi two-**dimensional** systems or nanowires, and the density of states plays a crucial role in all transport and optical **properties** of materials. Indeed, the obvious relevance for **electrical** conductivity **properties** in micro and nanotechnology implies that densities of states for d = 1, 2, or 3 are now commonly discussed in engineering textbooks, but there is another reason why I anticipate that variants of Eq. (1) will become ever more prominent in the technical literature. Densities also play a huge role in data storage, but with us still relying on binary R. Dick ( & )

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Gold **nanostructures** [GNSs] have been attracting much attention because of the high chemical stability coinci- dent with their unique optoelectronic **properties**, which are dependent on the morphology of the GNSs [1-4]. Surface plasmon resonance [SPR] is **one** of the most interesting **properties** of **one**-**dimensional** [1-D] GNSs [2-5]. The wavelength of SPR is affected by the length, diameter, and aspect ratio of the 1-D GNSs [6,7]. Aligned GNSs perform polarization of light [8-10]. Such multi- functionality of the 1-D GNSs opens up new application fields such as wavelength-sensitive **nonlinear** optical devices and polarization filters [8,9,11]. Several methods for synthesizing GNSs including 1-D GNSs have been reported. These methods include photochemical and electrochemical deposition [12,13] and seeding growth methods [14,15]. In these methods, however, the GNSs

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Recently, many researchers have studied different metal oxide morphologies, such as spherical, ordered porous particles, rods, fibers, and hollow structures. The performances of these materials in various applications depend on their chemical composition and surface **properties** as well as on their textural **properties** [ 1- 4]. Specially, microtubes play an important role in the miniaturization of components and devices because of their small diameters and high aspect ratios [5]. As their diameter is in the micrometer range, they are more suitable than nanotubes to load guest species such as biomolecules, catalysts, and nanoparticles, which allows to use them in different applications in drug delivery, catalysis, batteries and so on [6]. Currently, hollow metal oxide structures can be prepared with a template method, dry or wet spinning, electrospinning, and centrifugal spinning [ 7 ].

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Sulphur incorporation at the precursor stage on the growth of CZTS was studied by Chalapathi et al. [15]. Where, the thin films have been prepared in a two-stages process. The elemental composition, structural, microstructural and optical **properties** of these films were analyzed and it was discovered that the lattice parameters were a=0.542 nm and c=1.089 nm. Additionally, at 550 °C for 30 min, distinct and compact grain size of CZTS was obtained with a grain size range of 400-800. A direct band gap between 1.44 eV and 1.56 eV (depending on the annealing temperature and duration) was as well discovered. Furthermore, Dasgupta et al. [16] have also successfully produced pn-junction devices based on layers of Cu 2 ZnSnS 4 (CZTS) and (AgInS 2 @Cu) ternary nanocrystals. From the capacitance–voltage

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3 Interaction between the stationary contact wave and the elementary waves In this section, we only consider the interaction of the stationary contact wave with the rarefaction wave or the shock wave. As for the interaction between the rarefaction wave and the shock wave, we may see [, ] or other related results. Since the speed of **one**- wave (R or S ) is less than zero and that of three-wave (R or S ) is greater than zero, the

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However, **one** has to question the validity of mapping a particular microscopic model of a disordered system onto the NL M. More specifically, this mapping is approximately correct in the case of weak disorder and breaks down totally for strong disorder. Another strict requirement is that the un- derlying geometry allows for a diffusive process—this cer- tainly is not the case for strictly **one**-**dimensional** 共1D兲 ran- dom media. Finally, NL M calculations preassume that the disorder potential is white noise, thus excluding the emerg- ing family of disordered systems with imprinted correlations

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completed in several seconds as well. **One** of the important features of synthesis in RF plasma system is that the growth rate is rather rapid when compared with the con- ventional vapor deposition process. In the experimental process, vapor species were formed due to the high pro- cessing temperature (up to 1.0 9 10 4 K) in the flame zone, and then cooled to form ultrahigh-level supersaturated vapor in the plasma tail, which provides intensive growth driver for ZnS to nucleate and grow. In addition, part of zinc was ionized in the plasma zone, which accelerates the transmittability of electrons from zinc to sulfur. All of these provide intensive growth driver for ZnS to nucleate and grow, and the 1D **nanostructures** were finally formed due to the anisotropic growth habit of ZnS crystals results from the cation- or anion-terminated atomic planes [26]. Different materials were also synthesized by this method in our laboratory (including previous reported ZnO, Zn, AlN, and WO 3 ).

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In this chapter, the solution to **one** **dimensional** coupled Fisher KPP system is successfully approximated by a various numerical ﬁnite diﬀerence schemes. Explicit FTCS is conditionally stable, and we give more attention to parameter R 1 and R 2 , which can be used to stabilized the results as we can see from Figure

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Quasicrystals carry a number of interesting lattice-like **properties** with the obvious exclusion of period- icity, namely self-similarities or relative discreteness and uniform density (Delone property), and possibly others. For years these attributes have been used in modelling quasicrystals. In this article we extend the detailed study of some geometric **properties** of quasicrystals with the golden mean τ = 1 2 (1 + √ 5) published in [?, ?, ?] to other quadratic irrationalities. In [?] a complete description of inflation centers inside and outside of a given quasicrystal in any dimensions was provided. The minimal distances between points of quasicrystals as functions of linear dimensions of the acceptance window were described in [?]. In the third paper of the series [?], sets invariant under a certain binary operation (quasiaddition) are studied and identified with quasicrystals.

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Fan, Jiang and Nakamura [] investigated the uniqueness of the weak solutions of MHD with Lebesgue initial data. Fan, Jiang and Nakamura [] also considered a **one**- **dimensional** plane MHD compressible ﬂow, and proved that as the shear viscosity goes to zero, global weak solutions converge to a solution of the original equations with zero shear viscosity. The uniqueness and continuous dependence of weak solutions for the Cauchy problem have been proved by Hoﬀ and Tsyganov [].

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buckling of columns. In 1889 Friedrich Engesser [71] proposed the tangent modulus approach to the modeling of **nonlinear** inelastic column buckling, and two years later in 1891 Armand Gabriel Consid´ ere [72] proposed the double modulus theory. Just under 20 years later Theodore von K´ arm´ an [73] would publish his reduced modulus theory. In 1946 F. R. Shanley [74] while working for Lockheed Aircraft Coporation published The Column Paradox where in a single page document he laid out the paradoxical nature of the arguments implied by Engesser and Consid´ ere establishing the approximative nature of both approaches with the tangent modulus playing the role of the upper bound and the double modulus the lower bound of the correct solution. A year later [75] he would publish Inelastic Column Theory in which he proposes a means to resolve this problem. After Shanley some important analysis in this field would appear by Duberg and Wilder [76] to then be followed by the well-known method of finite elements. These works concern themselves primarily with plastic behavior of the column material in relation to buckling. There are many works scattered throughout the literature regarding piece-wise approaches to **nonlinear** material behavior and functional approximations of established material behaviors, but there is very little in the engineering literature with regard to undiluted **nonlinear** functions, such as the inverse of (1.7), and nearly all such works which do attempt to address it eventually devolve into some manner of unnecessary simplification. None of them are capable of explicitly defining the distribution of curvature along the length of the member based upon a full implementation of the material expression. There has been some very recent and growing interest in the type of elastic nonlinearity [77, 78] which we hope to address.

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In this work, we combine a systematic experimental investigation of the power- and temperature- dependent evolution of the spatial coherence function, g ð1Þ ðrÞ , in a **one** **dimensional** exciton-polariton channel with a modern microscopic numerical theory based on a stochastic master equation approach. The spatial coherence function g ð1Þ ðrÞ is extracted via high-precision Michelson interferometry, which allows us to demonstrate that in the regime of nonresonant excitation, the dependence g ð1Þ ðrÞ reaches a saturation value with a plateau, which is determined by the intensity of the pump and effective temperature of the crystal lattice. The theory, which was extended to allow for treating incoherent excitation in a stochastic frame, matches the experimental data with good qualitative and quantitative agreement. This allows us to verify the prediction that the decay of the off-diagonal long-range order can be almost fully suppressed in **one** **dimensional** condensate systems.

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The SEM and TEM images of the as-prepared samples are listed in Figure 2. As shown, the three morphologies were successfully obtained by the electrospinning process, and all the samples present a uniform **one**-**dimensional** structure with diameter at 400 ~ 600 nm. The tubular structure can be clearly seen in the insert of Figure 2a; ob- vious holes and phase interface can be found in Figure 2b. Figure 2c,d shows the core-shell structure nanofibers; the boundaries (marked in the line) between two phases of SnO 2 and TiO 2 could be directly observed. For mixed

distributions. This works well in the so-called reaction limited regime when the density of clusters is sufficiently high that each aggregating cluster has a large number of potential partners to with which to aggregate. In the most commonly considered case, in which the trans- port process is simple diffusion, this assumption turns out to be inconsistent for large masses if the spatial di- mension is less than or equal to two. The reason is that in two dimensions and below random walks are recur- rent so that clusters which encounter each other once are highly probable to do so infinitely many times and hence to aggregate. Heavy clusters thereby generate an effective depletion zone around themselves. The dynam- ics thus becomes diffusion limited and dominated by dif- fusive fluctuations making the system much more diffi- cult to analyse. The only case for which a systematic study of the diffusion limited regime has been done is the case of constant kernel in which the aggregation rate is independent of mass (ζ = 0). For the forced case in d < 2, the diffusion limited stationary mass density can be shown to scale as N (m) ∼ m −(2d+2)/(d+2) which is shallower than the corresponding mean-field prediction, N (m) ∼ m −3/2 . Note that the diffusion limited scaling exponent coincides with the reaction limited **one** when d = 2 which reflects the fact that d = 2 is the criti- cal dimension for this model. In addition to having a different value for the scaling exponent of N(m), the sta- tistical **properties** of the diffusion limited regime are also structurally different: higher order correlation functions exhibit multi-scaling in the sense that they do not scale as powers of the corresponding single-point densities as they do in the mean field regime.

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therefore not limited by the diffraction in the collec- tion and excitation optics, which is very customary in all the far-field techniques. Hence, to enhance our understanding regarding the optical **properties** of PS-ZnO composites under irradiation conditions, the PL studies have been complimented by CL analysis. The major reason that very few studies reported CL of PS is due to an extremely weak and unstable data. The inset in Figure 5c shows a strong decrease of the CL emission signal of the PS produced by the electron beam irradiation in SEM. Deposition of AZO layer on the mesoporous silicon layer leads to the stability of the composite structure. As the electron beam can inject into the samples, a strong charge density pro- duces saturation of radiative levels; hence, the lumi- nescence from defects can be explored in detail. Figure 5a shows CL spectra from the non-irradiated (pristine) sample with a broad emission centered at about 2.6 eV, which apparently corresponds to the ZnO defect emission centered at 2.5 eV in PL spectra. The low-intensity CL recorded in the spectra is attrib- uted to the low sensibility of our system at room temperature. As compared to the PL spectra from the pristine sample, the ZnO band edge emission was not resolved in CL spectra, possibly due to presence of a high density of defects in the film-substrate interface. Figure 5b shows the CL spectra from the irradiated ZLP sample, revealing two emissions centered at 3.2 and 2.5 eV, associated to the ZnO band edge and de- fect emission. As commented in the ‘Photoluminescence

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