Mean exit time in irregularly-shaped annular and composite disc domains

Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications in biophysics, economics and heat and mass transfer. While many exact results for MET are known for diffusion in simple geometries involving homogeneous materials, calculating MET for diffusion in realistic geometries involving heterogeneous materials is typically limited to repeated stochastic simulations or numerical solutions of the associated boundary value problem (BVP). In this work we derive exact solutions for the MET in irregular annular domains, including some applications where diffusion occurs in heterogenous media. These solutions are obtained by taking the exact results for MET in an annulus, and then constructing various perturbation solutions to account for the irregular geometries involved. These solutions, with a range of boundary conditions, are implemented symbolically and compare very well with averaged data from repeated stochastic simulations and with numerical solutions of the associated BVP. Software to implement the exact solutions is available on \href{https://github.com/ProfMJSimpson/Exit_time}{GitHub}.

Transport and losses of fusion-born alpha particles in the presence of tearing modes using the new Toroidal Accelerated P Article Simulator (TAPAS)

The transport and losses of fusion-born alpha particles is studied in the presence of a single-helicity tearing mode, characterized by (m=2,n=1). The analysis is performed by means of the recently developed Toroidal Accelerated PArticle Simulator (TAPAS). Although such modes have been usually believed to result only in a local flattening of the radial profiles, it is shown that the density profile can exhibit a global modification leading to significant losses of alpha particles. This is due to the fact that, although the magnetic field does not exhibit any chaotic behaviour, the trajectories of alpha particles do, as revealed by their Poincaré maps. Such result is in qualitative agreement with past observations and simulations of energetic particles generated by neutral beam injection in TFTR, DIII-D and AUG tokamaks. In-depth analysis is carried out to characterize the impact of the tearing mode on the transport and losses of fusion-born alpha-particles with a realistic density profile. The impact of the amplitude is evidenced. Moreover, the effect of the island rotation frequency is assessed based on a detailed analysis of the linear resonances in phase-space, in agreement with the simulation results. Finally, the probability density function of the exit time has been computed and the transport of alpha particles has been found to be anomalous.

Closing a Bitcoin Trade Optimally under Partial Information: Performance Assessment of a Stochastic Disorder Model

The Bitcoin market exhibits characteristics of a market with pricing bubbles. The price is very volatile, and it inherits the risk of quickly increasing to a peak and decreasing from the peak even faster. In this context, it is vital for investors to close their long positions optimally. In this study, we investigate the performance of the partially observable digital-drift model of Ekström and Lindberg and the corresponding optimal exit strategy on a Bitcoin trade. In order to estimate the unknown intensity of the random drift change time, we refer to Bitcoin halving events, which are considered as pivotal events that push the price up. The out-of-sample performance analysis of the model yields returns values ranging between 9% and 1153%. We conclude that the return of the initiated Bitcoin momentum trades heavily depends on the entry date: the earlier we entered, the higher the expected return at the optimal exit time suggested by the model. Overall, to the extent of our analysis, the model provides a supporting framework for exit decisions, but is by far not the ultimate tool to succeed in every trade.

Autonomous Gateway Architecture for Security Using OpenCV

Today as we can see security for anything is considered to be a very important part of our livelihood and we need to seek more and more security every day in this fast growing world. As the security of public parking lots increases day by day and to ensure safety, many people are required in this job that increases the cost of security So we have looked into the process and came up with a plan to use computer vision for the security purpose which will reduce the manpower required for work instead with machine intelligence. We are going to use Computer Vision to mask the license plate and save it with the entry and exit time. This research paper will enhance the security provided by a CCTV camera in any public parking and will also keep the record of every car entering and exiting the parking area. Keywords: OpenCV, Machine Learning, EasyOCR, SQLite, Image Contour Processing

A Macroeconomic SIR Model for COVID-19

The COVID-19 pandemic and subsequent lockdowns highlight the close and delicate relationship between a country’s public health and economic health. Models that combine macroeconomic factors with traditional epidemic dynamics to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We developed a macroeconomic SIR model that considers herd immunity, behavior-dependent transmission rates, remote workers, and the indirect externalities of lockdowns. It is formulated as an exit time control problem where a social planner is able to prescribe separate levels of the lockdown low-risk and high-risk portions of the adult population. The model predicts that by considering the possibility of reaching herd immunity, high-risk individuals are able to leave lockdown sooner than in models where herd immunity is not considered. Additionally, a behavior-dependent transmission rate (which represents increased personal caution in response to increased infection levels) can lower both output loss and total mortality. Overall, the model-determined optimal lockdown strategy, combined with individual actions to slow virus transmission, is able to reduce total mortality to one-third of the model-predicted no-lockdown level of mortality.

KEMISKINAN B40 DAN PURATATEMPOH MASA KELUAR (AVERAGE EXIT TIME) DARIPADA KEMISKINAN: KAJIAN KES ISI RUMAH B40 DI DAERAH KUBANG PASU KEDAH

Kajian kes ini mengukur tempoh purata masa keluar daripada kemiskanan (average exit time) dalam kalangan B40 di Daerah Kubang Pasu, Kedah. Data yang digunakan adalah data primer yang dikumpul daripada ketua isi rumah dengan menggunakan borang soal selidik yang berstruktur. Watts indeks diguna pakai bagi mengira tempoh masa keluar daripada kemiskinan. Pengiraan tempoh masa keluar daripada kemiskinan makin pendek sekiranya ketua isi rumah mempunyai pendapatan lain atau pendapatan sampingan dan bayaran pindahan. Bukti menunjukkan bahawa dengan kadar pertumbuhan pendapatan sebanyak lima peratus, tempoh masa untuk keluar daripada kepompong kemiskinan bagi mereka yang mempunyai pendapatan sampingan dan pendapatan daripada bayaran pindahan adalah lebih pendek iaitu 25 tahun berbanding 42 tahun sekiranya mereka tidak mempunyai pendapatan sampingan dan bayaran pindahan. Ini bermakna kedua-dua pendapatan (sampingan dan bayaran pindahan) dapat menjimatkan tempoh masa keluar kemiskinan selama 16 tahun.

On the heat content functional and its critical domains

We study and classify smooth bounded domains in an analytic Riemannian manifold which are critical for the heat content at all times $$t>0$$ t > 0 . We do that by first computing the first variation of the heat content, and then showing that $$\Omega $$ Ω is critical if and only if it has the so-called constant flow property, so that we can use a previous classification result established in [33] and [34]. The outcome is that $$\Omega $$ Ω is critical for the heat content at time t, for all $$t>0$$ t > 0 , if and only if $$\Omega $$ Ω admits an isoparametric foliation, that is, a foliation whose leaves are all parallel to the boundary and have constant mean curvature. Then, we consider the sequence of functionals given by the exit-time moments $$T_1(\Omega ),T_2(\Omega ),\dots $$ T 1 ( Ω ) , T 2 ( Ω ) , ⋯ , which generalize the torsional rigidity $$T_1$$ T 1 . We prove that $$\Omega $$ Ω is critical for all $$T_k$$ T k if and only if $$\Omega $$ Ω is critical for the heat content at every time t, and then we get a classification as well. The main purpose of the paper is to understand the variational properties of general isoparametric foliations and their role in PDE’s theory; in some respects they generalize the properties of the foliation of $$\mathbf{R}^{n}$$ R n by Euclidean spheres.