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We theoretically illustrate how complex fluids flowing over superhydrophobic surfaces may exhibit giant flow enhancements in the double limit of small solid fractions ($\epsilon\ll1$) and strong shear thinning ($\beta\ll1$, $\beta$ being the ratio of the viscosity at infinite shear rate to that at zero shear rate). Considering a Carreau liquid within the canonical scenario of longitudinal shear-driven flow over a grooved superhydrophobic surface, we show that, as $\beta$ is decreased, the scaling of the effective slip length at small solid fractions is enhanced from the logarithmic scaling $\ln(1/\epsilon)$ for Newtonian fluids to the algebraic scaling $1/\epsilon^{\frac{1-n}{n}}$, attained for $\beta=\mathcal{O}(\epsilon^{\frac{1-n}{n}})$, $n\in(0,1)$ being the exponent in the Carreau model. We illuminate this scaling enhancement and the geometric-rheological mechanism underlying it through asymptotic arguments and numerical simulations.

An unprecedented double-threshold lasing behavior has been observed in a plasmonic random laser composed of Au nanoislands decorated on vertically standing ZnO nanorods, infiltrated with dye-doped polymer matrix. The strong coupling of random laser modes to plasmonic nanocavities results in a dominant absorption of the random laser emission, leading to the first unusual lasing threshold. At higher pump fluences, the nonlinear optical behavior of the Au nanoislands induces a second lasing threshold. Various statistical tools have been employed to analyze the intensity fluctuations of the random laser modes, validating this unique lasing behavior.

Current research work deals with the effect of uniform and non-uniform wall heating on magnetohydrodynamic (MHD) natural convection within a three-dimensional (3D) cavity filled with molten lithium. A new Higher-Order Super Compact (HOSC) finite difference scheme is used to analyze the thermal behavior under both heating scenarios. After the quantitative and qualitative validations, the computed results are analyzed for a range of Hartman number ($Ha = 25, 50, 100, 150$) and Rayleigh number ($Ra = 10^3, 10^4, 10^5$) with fixed $Pr=0.065$ (molten lithium). Three distinct heating scenarios, i.e., uniform heating ($T_h = 1$), $y$-dependent non-uniform heating ($T_h = sin(\pi y$)), and a combination of $y$ and $z$-dependent non-uniform heating ($T_h = sin(\pi y)sin(\pi z)$) are investigated on the left wall ($x=0$) of the cubic cavity. It is found that variations in the $Ha$ and $Ra$, along with distinct thermal boundary conditions, exert significant effects on both the temperature distribution and flow field inside the 3D cubical cavity. Specifically, an increase in $Ra$ corresponds to enhanced heat transfer, highlighting the dominance of convection. Conversely, an increase in $Ha$ leads to a reduction in heat transfer due to the deceleration of fluid velocity. The scenario in which walls are uniformly heated exhibits the most significant total entropy generation. It is observed that with an increase in the $Ra$, the Bejan number ($Be$) decreases, which ultimately leads to an increase in total entropy generation. The implementation of the new HOSC scheme in this analysis showcases its effectiveness in capturing the complexities of 3D MHD-driven natural convection and entropy generation. This study offers significant information that might help improve the optimization and design of relevant engineering systems. Thus, our work stands out as genuinely novel and pioneering in its approach.

This work deals with a novel Gaussian filter-based pressure correction technique with a super compact higher order finite difference scheme for solving unsteady three-dimensional (3D) incompressible, viscous flows. This pressure correction technique offers significant advantages in terms of optimizing computational time by taking minimum iterations to reach the required accuracy, making it highly efficient and cost-effective. Pressure fields often exhibit highly nonlinear behavior, and employing the Gaussian filter can help to enhance their reliability by reducing noise and uncertainties. On the other hand, the super compact scheme uses minimum grid points to produce second-order accuracy in time and fourth-order accuracy in space variables. The main focus of this study is to enhance the accuracy and efficiency and minimize the computational cost of solving complex fluid flow problems. The super compact scheme utilizes 19 grid points at the known time level (i.e., $n^{th}$ time level) and only seven grid points from the unknown time level (i.e., $n + 1$ time level). By employing the above strategies, it becomes possible to notably decrease computational expenses while maintaining the accuracy of the computational scheme for solving complex fluid flow problems. We have implemented our methodology across three distinct scenarios: the 3D Burger's equation having analytical solution, and two variations of the lid-driven cavity problem. The outcomes of our numerical simulations exhibit a remarkable concordance, aligning exceptionally well with both the analytical benchmarks and previously validated numerical findings for the cavity problems.

This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the first ever developed finite difference scheme to solve three-dimensional non-Newtonian flow problem. Not only that, the proposed method is fourth-order accurate in space variables and second-order accurate in time. Also, the proposed scheme utilizes only seven directly adjacent grid points, at the $(n+1)^{th}$ time level, around which the finite difference discretization is made. The governing equations are solved using a time-marching methodology, and pressure is calculated using a pressure-correction strategy based on the modified artificial compressibility method. Using the power-law viscosity model, we tackle the benchmark problem of a 3D lid-driven cavity, systematically analyzing the varied rheological behavior of shear-thinning ($n=0.5$), shear-thickening $(n=1.5)$, and Newtonian $(n=1.0)$ fluids across different Reynolds numbers $(Re= 1, 50, 100, 200)$. Both Newtonian and non-Newtonian results are carefully investigated in terms of streamlines, velocity variation, pressure distributions, and viscosity contours, and the computed results are validated with the existing benchmark results. The findings demonstrate excellent agreement with the existing results. This extensive analysis, using the new HOSC scheme, not only increases our understanding of non-Newtonian fluid behavior but also provides a robust foundation for future research and practical applications.

This article exploits group-IV germanium (Ge) quantum dots (QDs) on Silicon-on-Insulator (SOI) grown by molecular beam epitaxy (MBE) in order to explore its optical behaviour in the Terahertz (THz) regime. In this work, Ge QDs, pumped by an above bandgap near infrared wavelength, exhibit THz amplitude modulation in the frequency range of 0.1-1.0 THz. The epitaxial Ge QDs outperform reference SOI substrate in THz amplitude modulation owing to higher carrier generation in weakly confined dots compared to its bulk counterpart. This is further corroborated using theoretical model based on the non-equilibrium Green's function (NEGF) method. This model enables the calculation of photo carriers generated (PCG) and their confinement in the Ge QD region. Our model also reroutes the calculation from PCG to corresponding plasma frequency and hence to refractive index and THz photo-conductivity. Moreover, the photo-generated confined holes accumulation at the Ge QDs-Si interface is elevated after optical illumination, leading to a decreased THz photo-conductivity. This augmentation in THz photo-conductivity contributes to a significant enhancement of THz modulation depth ~77% at Ge QDs-Si interfaces compared to bare SOI at 0.1 THz., Comment: 15 pages, 5 figures

For Riemannian symmetric spaces $X=G/K$ of noncompact type, we show that for all left $K$-invariant $f\in L^1(X)$, the functions $\|h_t\|_p^{-1}(f\ast h_t-M_p(f)h_t)$ (with $h_t$ being the heat kernel of $X$) converges to zero in $L^p(X)$, $p\in [1,\infty]$, as $t\to\infty$, with the constant $M_p(f)$ depending only on $p$ and $f$. We also prove an analogous result for the fractional heat kernels $h_t^{\alpha}$, $\alpha\in (0,1)$. The above results were earlier proved for the important special cases $p=1$ and $\alpha= 1,\frac 12$ in \cite{Vaz-2, AE, Eff2}., Comment: 35 pages, modified proofs of Proposition 3.2 and Proposition 3.4 of the earlier version

We report Chandra-ACIS observations of SN 2023ixf in M101 on day 13 and 86 since the explosion. The X-rays in both epochs are characterized by high temperature plasma from the forward shocked region as a result of circumstellar interaction. We are able to constrain the absorption column density at both Chandra epochs, which is much larger than that due to the Galactic and host absorption column, and we attribute it to absorption by the circumstellar matter in the immediate vicinity of SN 2023ixf. Combining our column density measurements with the published measurement on day 4, we show that the column density declines as $t^{-2}$ between day 4 to day 13 and then evolves as $t^{-1}$. The unabsorbed $0.3-10$ keV luminosity evolves as $t^{-1}$ during the Chandra epochs. On day 13 Chandra observation we detect the Fe K$\alpha$ fluorescent line at 6.4 keV indicating presence of cold material in the vicinity of the SN. The line is absent on day 86, consistent with the decreased column density by a factor of 7 between the two epochs. Our analysis indicates that during 10 years to 1.5 years before explosion, the progenitor was evolving with a constant mass-loss rate of $5.6\times 10^{-4}$ M$_\odot$ yr$^{-1}$., Comment: Accepted for publication in ApJ Letters

We demonstrate the effectiveness of the logistic function to model the evolution of two economic systems. The first is the GDP and trade growth of the USA, and the second is the revenue and human resource growth of IBM. Our modelling is based on the World Bank data in the case of the USA, and on the company data in the case of IBM. The coupled dynamics of the two relevant variables in both systems - GDP and trade for the USA, and revenue and human resource for IBM - follows a power-law behaviour., Comment: 5 pages, 6 figures, ReVTeX double column format. arXiv admin note: substantial text overlap with arXiv:2109.05262

The main objective of this paper is to study the effect of a cold, vertical, arc-shaped control plate on the flow characteristics and forced convective heat transfer mechanism across a rotary oscillating, isothermally heated circular cylinder. Two-dimensional, unsteady, incompressible, laminar, and viscous flow of a Newtonian, constant property fluid is considered across the cylinder. The simulations are performed with an in-house code for various gap ratios between the control plate and the cylinder ($0\leq d/R_0 \leq 3$), maximum angular velocity ($0.5\leq \alpha_m \leq 4$) and frequency ratio of oscillation ($f/f_0=0.5,\ 3$) at Prandtl number $0.7$ and Reynolds number $150$. Here, $d$ denotes the gap between the surface of the cylinder and the leading surface of the control plate, $R_0$ denotes the radius of the cylinder, $f$ is the frequency of oscillation and $f_0$ is the frequency of natural vortex shedding. $d/R_0=0$ corresponds to the no plate case. Heat transfer and vortex shedding phenomena are discussed in relation to one another. A significant increase in heat transmission is observed for all $\alpha_m$ with the gap ratio of $d/R_0=0.5$ and $f/f_0=0.5$. The heat absorption on the surface of the control plate decreases to zero with increasing gap ratio when $\alpha_m=0.5$ and $f/f_0=0.5$ but never becomes zero when $\alpha_m=4$ and $f/f_0=3$. Additionally, when compared to the no plate case with $(\alpha_m,\ f/f_0)=(0.5,\ 0.5)$, the maximum peak of the drag coefficient is decreased by $9.877\%$ for the gap ratio of $d/R_0=3$. For $\alpha_m=4$ and $f/f_0=3$, the smallest gap ratio of $d/R_0=0.5$ is found to significantly increase the lift coefficient relative to other cases.

The main objective of this paper is to study the flow characteristics of a rotating, isothermally heated circular cylinder with a vertical arc-shaped control plate placed downstream. Stream function-Vorticity ($\psi-\omega$) formulation of two dimensional (2-D) Navier-Stokes (N-S) equations is considered as the governing equation and the simulations are performed for different distances of the control plate ($0.5$, $1$, $2$, $3$), rotational rates ($0.5$, $1$, $2.07$, $3.25$) at Prandtl number $0.7$ and Reynolds number $150$. The governing equations are discretized using the Higher Order Compact (HOC) scheme and the system of algebraic equations, arising from HOC discretization, is solved using the Bi-Conjugate Gradient Stabilized approach. Present computed results show that the vortex shedding plane is shifted upward from the centerline of the flow domain by the cylinder's rotational motion. The structure of the wake varies based on the plate's position. The size of vortices is greatly reduced when the control plate is set at $d/R_0=3$ and the rotational rate is very high. At greater rotational rates, the impact of varied positions of the arc-shaped control plate is very significant. The rotation of the cylinder and the location of the plate can be used to lower or enhance the values of drag and lift coefficients as well as the heat transfer from the surface of the cylinder. The maximum value of the drag coefficient, which is about $3$, is achieved for $d/R_0=2$ and $\alpha=3.25$.

Modelling and forecasting real-life human behaviour using online social media is an active endeavour of interest in politics, government, academia, and industry. Since its creation in 2006, Twitter has been proposed as a potential laboratory that could be used to gauge and predict social behaviour. During the last decade, the user base of Twitter has been growing and becoming more representative of the general population. Here we analyse this user base in the context of the 2021 Mexican Legislative Election. To do so, we use a dataset of 15 million election-related tweets in the six months preceding election day. We explore different election models that assign political preference to either the ruling parties or the opposition. We find that models using data with geographical attributes determine the results of the election with better precision and accuracy than conventional polling methods. These results demonstrate that analysis of public online data can outperform conventional polling methods, and that political analysis and general forecasting would likely benefit from incorporating such data in the immediate future. Moreover, the same Twitter dataset with geographical attributes is positively correlated with results from official census data on population and internet usage in Mexico. These findings suggest that we have reached a period in time when online activity, appropriately curated, can provide an accurate representation of offline behaviour., Comment: Accepted for publication in EPJ Data Science. 20 pages, 7 figures, 1 table