Heterogeneous reactions in a HFCVD reactor: simulation using a 2D model

• Xochitl Aleyda Morán Martínez,
• José Alberto Luna López,
• Zaira Jocelyn Hernández Simón,
• Gabriel Omar Mendoza Conde,
• José Álvaro David Hernández de Luz and
• Godofredo García Salgado

Beilstein J. Nanotechnol. 2024, 15, 1627–1638, doi:10.3762/bjnano.15.128

• Dirichlet boundary conditions were employed to solve this model numerically. The types of boundaries are listed in Table 1. For the boundary wall on the filaments, we use a constraints boundary condition; for the outlet, a pressure boundary condition was used. For the inlet, we use a mass flow boundary

• condition. The simulations give us a broad overview on the probable reaction mechanisms during the deposition of thin films in the HFCVD reactor. This allows us to get an estimate of the types of species that will be deposited for the growth of thin films, which depend strongly on the parameters and

Exploring surface charge dynamics: implications for AFM height measurements in 2D materials

• Mario Navarro-Rodriguez,
• Andres M. Somoza and
• Elisa Palacios-Lidon

Beilstein J. Nanotechnol. 2024, 15, 767–780, doi:10.3762/bjnano.15.64

• surface between two media. In a previous work, we studied the tip-less case, which we will use as the starting point for our model. Here, we just summarize the main aspects and refer to [78] for further details. Then, we include the tip influence by adding the appropriate boundary condition, which is time

• , y, z, t) is calculated through solving the Laplace equation with the boundary condition V(r∈ tip surface) = Vbias. This term may depend on time if the tip oscillates or if an AC voltage is applied. V1(x′, y′, z′; x, y, z, t) is calculated with the boundary condition V(r∈ tip surface) = 0 and is

Design, fabrication, and characterization of kinetic-inductive force sensors for scanning probe applications

• August K. Roos,
• Ermes Scarano,
• Elisabet K. Arvidsson,
• Erik Holmgren and
• David B. Haviland

Beilstein J. Nanotechnol. 2024, 15, 242–255, doi:10.3762/bjnano.15.23

• either the sideband-resolved or sideband-unresolved regime. For the given thickness, we simulate the eigenfrequencies of the cantilever using the finite-element method (FEM) implemented in COMSOL Multiphysics [31], with the boundary condition of a perfectly rigid clamp along the line where the plate

Spin dynamics in superconductor/ferromagnetic insulator hybrid structures with precessing magnetization

• Yaroslav V. Turkin and
• Nataliya Pugach

Beilstein J. Nanotechnol. 2023, 14, 233–239, doi:10.3762/bjnano.14.22

• of spin current inside the superconducting layer completely agrees with the boundary condition of the zero matrix current at the interface between the free space and superconducting layer at z = 0. Now let us consider the Fourier coefficients for the induced magnetization. Earlier, we have shown that

Characterisation of a micrometer-scale active plasmonic element by means of complementary computational and experimental methods

• Ciarán Barron,
• Giulia Di Fazio,
• Samuel Kenny,
• Silas O’Toole,
• Robin O’Reilly and
• Dominic Zerulla

Beilstein J. Nanotechnol. 2023, 14, 110–122, doi:10.3762/bjnano.14.12

• physical active element was fabricated. The thermal behaviour of the element was simulated for an applied alternating electrical potential with a DC offset through the thin silver layer and compared to experimental findings. A temperature boundary condition was imposed on both the bottom and lateral

Density of states in the presence of spin-dependent scattering in SF bilayers: a numerical and analytical approach

• Tairzhan Karabassov,
• Valeriia D. Pashkovskaia,
• Nikita A. Parkhomenko,
• Anastasia V. Guravova,
• Elena A. Kazakova,
• Boris G. Lvov,
• Alexander A. Golubov and
• Andrey S. Vasenko

Beilstein J. Nanotechnol. 2022, 13, 1418–1431, doi:10.3762/bjnano.13.117

• . To complete the boundary problem, we also set a boundary condition at x = +∞: where the Green’s functions take the well-known bulk BCS form. The Green’s function method allows us to compute the DOS at the outer F boundary by solving the resulting system of equations above. The DOS at the outer F

• superconductor. Hence, the problem can be reduced to the rigid boundary condition when the order parameter in the S layer is set to its bulk value Δ0. We will keep all scattering terms in the solution to obtain a more general result. In this case, we can expand the solution of the Usadel equations up to the

Bending and punching characteristics of aluminum sheets using the quasi-continuum method

• Man-Ping Chang,
• Shang-Jui Lin and
• Te-Hua Fang

Beilstein J. Nanotechnol. 2022, 13, 1303–1315, doi:10.3762/bjnano.13.108

• . The punch is assumed as an ideal rigid Ni with crystal orientation of X[−110]-Y[111]. The dimensions of the Al substrates are 100 Å (width) × 100 Å (height), and the width of the Al workpiece is 200 Å, as shown in Figure 1a. A periodic boundary condition (PBC) was applied for the z-axis of the

Analytical and numerical design of a hybrid Fabry–Perot plano-concave microcavity for hexagonal boron nitride

• Felipe Ortiz-Huerta and
• Karina Garay-Palmett

Beilstein J. Nanotechnol. 2022, 13, 1030–1037, doi:10.3762/bjnano.13.90

• -concave cavity. To achieve a high Purcell factor, and a small NA, R2 must be as small as possible (small W02), while maintaining the lower boundary condition (R2 ≥ L2), therefore the optimal values of R2, for any arbitrary L2, will reside near the vicinity of the minima of the W2 function (Figure 5

Experimental and theoretical study of field-dependent spin splitting at ferromagnetic insulator–superconductor interfaces

• Peter Machon,
• Michael J. Wolf,
• Detlef Beckmann and
• Wolfgang Belzig

Beilstein J. Nanotechnol. 2022, 13, 682–688, doi:10.3762/bjnano.13.60

• effect at a ferromagnetic insulator–superconductor (FI–S) interface. The calculations are based on the boundary condition for diffusive quasiclassical Green’s functions, which accounts for arbitrarily strong spin-dependent effects and spin mixing angles. The resulting phase diagram shows a transition

• on the internal spin-degrees of freedom (spin mixing angles [29]), since the conductance is zero, in contrast to a metallic ferromagnet. The absence of conductance-related parameters (transmission and polarization of each channel) strongly simplifies the boundary condition to a ferromagnetic

• deviation can be explained by Fermi-liquid renormalization of the effective spin splitting near the critical field [49][46], which is not included in our model. Conclusion Based on the general spin-dependent boundary condition [30][31] augmenting the spin-dependent circuit theory [38][50], we investigated

Design aspects of Bi₂Sr₂CaCu₂O_8+δ THz sources: optimization of thermal and radiative properties

• Mikhail M. Krasnov,
• Natalia D. Novikova,
• Roger Cattaneo,
• Alexey A. Kalenyuk and
• Vladimir M. Krasnov

Beilstein J. Nanotechnol. 2021, 12, 1392–1403, doi:10.3762/bjnano.12.103

• low T. The substrate is thermally well anchored with the boundary condition at the bottom surface T = T0. Due to the large κ, temperature variation in the substrate is negligible. Therefore, we use a constant κ = 3000 W·K−1·m−1 for the substrate, corresponding to a monocrystalline sapphire at T ≃ 10 K

A review on slip boundary conditions at the nanoscale: recent development and applications

• Ruifei Wang,
• Jin Chai,
• Bobo Luo,
• Xiong Liu,
• Jianting Zhang,
• Min Wu,
• Mingdan Wei and
• Zhuanyue Ma

Beilstein J. Nanotechnol. 2021, 12, 1237–1251, doi:10.3762/bjnano.12.91

• Development, Zhongyuan Oilfield Company, SINOPEC, Puyang 457001, China 10.3762/bjnano.12.91 Abstract The slip boundary condition for nanoflows is a key component of nanohydrodynamics theory, and can play a significant role in the design and fabrication of nanofluidic devices. In this review, focused on the

• effective slip length. Finally, potential applications of nanofluidics with a tunable slip length are discussed and future directions related to slip boundary conditions for nanoscale flow systems are addressed. Keywords: boundary condition; interfacial properties; nanofluidics; slip length; unconventional

• reservoirs; Introduction A basic postulate in the study and design of macroscopic fluidic systems based on the knowledge of fluid mechanics is that the no-slip boundary condition is valid at the solid–liquid interface [1]. In the last two centuries, this no-slip boundary condition has been successfully

Vibration analysis and pull-in instability behavior in a multiwalled piezoelectric nanosensor with fluid flow conveyance

• Sayyid H. Hashemi Kachapi

Beilstein J. Nanotechnol. 2020, 11, 1072–1081, doi:10.3762/bjnano.11.92

• the system softening in the SS boundary condition (with and without surface/interface and low natural frequency in this case), FC-MWPENS is at a higher critical fluid velocity and lower pull-in voltage than other boundary conditions. After the SS boundary condition, the other boundary conditions CS

Effect of magnetic field, heat generation and absorption on nanofluid flow over a nonlinear stretching sheet

• Santoshi Misra and
• Govardhan Kamatam

Beilstein J. Nanotechnol. 2020, 11, 976–990, doi:10.3762/bjnano.11.82

• distribution θ(η) when ξ = 1.0, M = Q = 0.0, Pr = 2.0, Nb = Nt = 0.5, Le = 5.0, and Fw = 0.2 (due to the boundary condition, the value of ξ is changed). Influence of the stretching parameter n on the concentration distribution ϕ(η) when ξ = 1.0, M = Q = 0.0, Pr = 2.0, Nb = Nt = 0.5, Le = 5.0, and Fw = 0.2 (due

• to the boundary condition, the value of ξ is changed). Influence of the Brownian motion parameter Nb on the temperature distribution, θ(η) when n = 2.0, ξ = 1.0, M = Q = 0.0, Pr = 2.0, Nt = 0.5, Le = 5.0, and Fw = 0.2. Influence of the Brownian motion parameter Nb on the concentration distribution ϕ

A Josephson junction based on a highly disordered superconductor/low-resistivity normal metal bilayer

• Pavel M. Marychev and
• Denis Yu. Vodolazov

Beilstein J. Nanotechnol. 2020, 11, 858–865, doi:10.3762/bjnano.11.71

• equation, Here, js is the superconducting current density, which is determined by the following expression: where ρ is the residual resistivity of the corresponding layer. At the SN-interface we use a boundary condition similar to Equation 4, and for the interfaces with the vacuum we use dϕ/dn = 0. At the

Agglomerates of nanoparticles

• Dieter Vollath

Beilstein J. Nanotechnol. 2020, 11, 854–857, doi:10.3762/bjnano.11.70

• function f(i) with the normalization Furthermore, the number of particles in the ensemble is constant; therefore, the sum of the numbers of particles in the agglomerates is constant. This leads to the boundary condition The system of agglomerates is in thermodynamic equilibrium when the free enthalpy G at

Anomalous current–voltage characteristics of SFIFS Josephson junctions with weak ferromagnetic interlayers

• Tairzhan Karabassov,
• Anastasia V. Guravova,
• Aleksei Yu. Kuzin,
• Elena A. Kazakova,
• Shiro Kawabata,
• Boris G. Lvov and
• Andrey S. Vasenko

Beilstein J. Nanotechnol. 2020, 11, 252–262, doi:10.3762/bjnano.11.19

• corresponds to a rather weak suppression. To calculate the density of states in the S/F bilayer we should set the boundary conditions at the outer boundary of the ferromagnet (x = 0), To complete the boundary problem we also set a boundary condition at x = ±∞, where the Green’s functions acquire the well

An investigation on the drag reduction performance of bioinspired pipeline surfaces with transverse microgrooves

• Weili Liu,
• Hongjian Ni,
• Peng Wang and
• Yi Zhou

Beilstein J. Nanotechnol. 2020, 11, 24–40, doi:10.3762/bjnano.11.3

• factors on the simulation results, the calculations used the same parameter settings, and the specific conditions were set as follows: (1) The periodic boundary condition was adopted along the flow direction to guarantee the turbulent flow was fully developed. The no-slip boundary condition was adopted

• for the wall (as shown in Figure 2). The desired velocity was achieved by adopting a steady mass flow boundary condition. (2) Incompressible water was used as continuous phase medium. The density was 998.2 kg/m3 and the dynamic viscosity was 0.001003 Pa∙s. (3) The pressure-velocity coupling scheme was

Effects of surface charge and boundary slip on time-periodic pressure-driven flow and electrokinetic energy conversion in a nanotube

• Mandula Buren,
• Yongjun Jian,
• Yingchun Zhao,
• Long Chang and
• Quansheng Liu

Beilstein J. Nanotechnol. 2019, 10, 1628–1635, doi:10.3762/bjnano.10.158

• Equation 3, Equation 9 and the boundary condition in Equation 6, we obtain Substituting Equation 10 in Equation 2 yields The streaming current through the channel is equal to The streaming electric field Es generates a reverse conduction current Ic. Due to the electric neutrality of the fluid inside the

Energy distribution in an ensemble of nanoparticles and its consequences

• Dieter Vollath

Beilstein J. Nanotechnol. 2019, 10, 1452–1457, doi:10.3762/bjnano.10.143

• quantities gi−1 and gi−2 stand for the free enthalpy of the particle i in the phases 1 and 2, and |Δgi| stands for the difference of the free enthalpy of the two phases at the temperature Ti. Equation 5 gives the boundary condition for fluctuation, but does not give any information about the probability

The effect of flexible joint-like elements on the adhesive performance of nature-inspired bent mushroom-like fibers

• Elliot Geikowsky,
• Serdar Gorumlu and
• Burak Aksak

Beilstein J. Nanotechnol. 2018, 9, 2893–2905, doi:10.3762/bjnano.9.268

• constant cross-section for the entire composite fiber. Prior to peel, the boundary condition for the fiber is fixed–fixed. Assuming that the problem is linear, and for simplicity that the fiber is tilted but straight, the compatibility equation such that the null slope at the tip due to the fixed boundary

• condition is unchanged becomes Here, L is the effective length of the fiber, θ is the effective tilt angle, Es is the stalk elastic modulus. The first three terms in this equation represent the classical solution for the tip deflection angle and the last term accounts for the rotation of the flexible joint

Au–Si plasmonic platforms: synthesis, structure and FDTD simulations

• Anna Gapska,
• Marcin Łapiński,
• Paweł Syty,
• Wojciech Sadowski,
• Józef E. Sienkiewicz and
• Barbara Kościelska

Beilstein J. Nanotechnol. 2018, 9, 2599–2608, doi:10.3762/bjnano.9.241

• overall simulation time was set to 40 fs, and the grid size was 1 nm (which is less than a third of the smallest nanoparticle in the structure). The perfect matched layer (PML) boundary condition was applied to avoid wave reflections from the system borders. In both cases, results for non-polarized light

Cathodoluminescence as a probe of the optical properties of resonant apertures in a metallic film

• Kalpana Singh,
• Evgeniy Panchenko,
• Babak Nasr,
• Amelia Liu,
• Lukas Wesemann,
• Timothy J. Davis and
• Ann Roberts

Beilstein J. Nanotechnol. 2018, 9, 1491–1500, doi:10.3762/bjnano.9.140

• . A second order scattering boundary condition is used and no backscattering from the boundary into the modelled region was apparent. The far-field spectrum (which excludes evanescent contributions) radiated into a range of angles corresponding to a numerical aperture of 0.95 above the surface of the

Excitation of nonradiating magnetic anapole states with azimuthally polarized vector beams

• Aristeidis G. Lamprianidis and
• Andrey E. Miroshnichenko

Beilstein J. Nanotechnol. 2018, 9, 1478–1490, doi:10.3762/bjnano.9.139

• calculate the elements of the T-matrix [43][44][45]. We are going to employ the semi-analytical extended boundary condition method (EBCM) [39][46], also known as null-field method [42], which was originally introduced by Waterman in 1965 [47]. This method best applies for cases of homogeneous, isotropic

Proximity effect in a two-dimensional electron gas coupled to a thin superconducting layer

• Christopher Reeg,
• Daniel Loss and
• Jelena Klinovaja

Beilstein J. Nanotechnol. 2018, 9, 1263–1271, doi:10.3762/bjnano.9.118

• by In Equation 10, is the Green’s function of the bare superconductor (in the absence of tunneling), which satisfies Imposing a vanishing boundary condition at z = 0 and z = d, we find a solution to Equation 11 given by where = 2ms(μs ± iΩ) − k2 and Ω2 = Δ2 + ω2 [48][54]. The Green’s function of a

Thermoelectric current in topological insulator nanowires with impurities

• Sigurdur I. Erlingsson,
• Jens H. Bardarson and
• Andrei Manolescu

Beilstein J. Nanotechnol. 2018, 9, 1156–1161, doi:10.3762/bjnano.9.107

• chose the coordinate system such that the magnetic field is along the x-axis, B = (B,0,0), the vector potential being A = (0,0,By) = (0,0,BRsinφ). For B = 0 the angular part of the Hamiltonian has eigenfunctions where n are half-integers to fulfill the boundary condition. It is convenient to