Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk

In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the heterogeneity of the medium is represented by the selection, at any jump, of a different time-scale for an exponential survival probability. The resulting process is a non-Markovian non-Gaussian random walk. In particular, for a power-law distribution of the time-scales, the resulting random walk corresponds to a time-fractional diffusion process. We relates the power-law of the medium heterogeneity to the fractional order of the diffusion. This relation provides an interpretation and an estimation of the fractional order of derivation in terms of environment heterogeneity. The results are supported by simulations

Langevin equation in complex media and anomalous diffusion

The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle’s dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations.V.S. acknowledges BCAM Internship Program, Bilbao, for the financial support to her internship research period during which she developed her master’s thesis research useful for her master’s degree in Physics at University of Bologna. S.V. acknowledges the University of Bologna for the financial support through the ‘Marco Polo Programme’ for her PhD research period abroad spent at BCAM, Bilbao, useful for her PhD degree in Physics at University of Bologna. P.P. acknowledges financial support from Bizkaia Talent and European Commission through COFUND scheme, 2015 Financial Aid Program for Researchers, project number AYD–000–252 hosted at BCAM, Bilbao

Microwave-assisted vacuum synthesis of tio2 nanocrystalline powders in one-pot, one-step procedure

A new method for fast and simple synthesis of crystalline TiO2 nanoparticles with photocat-alytic activity was developed by carrying out a classic sol–gel reaction directly under vacuum. The use of microwaves for fast heating of the reaction medium further reduces synthesis times. When the solvent is completely removed by vacuum, the product is obtained in the form of a powder that can be easily redispersed in water to yield a stable nanoparticle suspension, exhibiting a comparable photocatalytic activity with respect to a commercial product. The present methodology can, therefore, be considered a process intensification procedure for the production of nanotitania

Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion

We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.”Marco Polo Programme” (University of Bologna

Effect of FCNC mediated Z boson on lepton flavor violating decays

We study the three body lepton flavor violating (LFV) decays $\mu^- \to e^- e^+ e^-$, $\tau^- \to l_i^- l_j^+ l_j^-$ and the semileptonic decay $\tau \to \mu \phi$ in the flavor changing neutral current (FCNC) mediated $Z$ boson model. We also calculate the branching ratios for LFV leptonic B decays, $B_{d,s} \to \mu e$, $B_{d,s} \to \tau e$, $B_{d,s} \to \tau \mu$ and the conversion of muon to electron in Ti nucleus. The new physics parameter space is constrained by using the experimental limits on $\mu^- \to e^- e^+ e^-$ and $\tau^- \to \mu^- \mu^+ \mu^-$. We find that the branching ratios for $\tau \to eee$ and $\tau \to \mu \phi$ processes could be as large as $\sim {\cal O}(10^{-8})$ and ${\rm Br}B_{d,s} \to \tau \mu, \tau e) \sim {\cal O}(10^{-10})$. For other LFV B decays the branching ratios are found to be too small to be observed in the near future.Comment: 15 pages, 8 figures, typos corrected, one more section added, version to appear in EPJ

Impact of the COVID-19 pandemic on ovarian tissue cryopreservation planning in the Bologna clinical center

Introduction: Treatment of patients with COVID-19 has been a priority by competing with the treatment of any other disease due to limited hospital resources. The current pandemic situation has focused the attention of healthcare providers around the world away from all other non-emergency health problems, including oncofertility. The aim of the study was to evaluate the repercussions of the COVID-19 pandemic on the activity levels of ovarian tissue cryopreservation (OTC) in the our center. Methods: The study analyzed the number of patients treated for OTC in our center during three periods: pre-pandemic period: March 2019-February 2020, pandemic period: March 2020-February 2021 and post-pandemic period: March 2021-February 2022. Results: In our center routine hospital operation was completely reorganized, allowing only urgent interventions. Continuing to urgently preserve fertility during the pandemic required rapid changes to our standard practices for the care of these vulnerable patients. Despite the modifications, there was no difference in the number of OTC performed among the periods analyzed. Similarly, the number of patients who did not perform OTC was the same over the three years analyzed. Discussion: Despite the local and national restructuring of care to conserve resources and protect the community, it is significant to continue offering fertility-sparing treatment to cancer patients. This emphasis on the importance of preserving fertility despite the pandemic further highlights the essential and urgent nature of this procedure

Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks

We use the Real Space Renormalization Group (RSRG) method to study extreme value statistics for a variety of Brownian motions, free or constrained such as the Brownian bridge, excursion, meander and reflected bridge, recovering some standard results, and extending others. We apply the same method to compute the distribution of extrema of Bessel processes. We briefly show how the continuous time random walk (CTRW) corresponds to a non standard fixed point of the RSRG transformation.Comment: 24 pages, 5 figure

The Physics of Heavy Flavours at SuperB

This is a review of the SuperB project, covering the accelerator, detector, and highlights of the broad physics programme. SuperB is a flavour factory capable of performing precision measurements and searches for rare and forbidden decays of $B_{u,d,s}$, $D$, $\tau$ and $\Upsilon({\mathrm{nS}})$ particles. These results can be used to test fundamental symmetries and expectations of the Standard Model, and to constrain many different hypothesised types of new physics. In some cases these measurements can be used to place constraints on the existence of light dark matter and light Higgs particles with masses below $10GeV/c^2$. The potential impact of the measurements that will be made by SuperB on the field of high energy physics is also discussed in the context of data taken at both high energy in the region around the \Upsilon({\mathrm{4S}})$, and near charm threshold.Comment: 49 pages, topical review submitted to J. Phys

Muon Physics: A Pillar of the Standard Model

Since its discovery in the 1930s, the muon has played an important role in our quest to understand the sub-atomic theory of matter. The muon was the first second-generation standard-model particle to be discovered, and its decay has provided information on the (Vector -Axial Vector) structure of the weak interaction, the strength of the weak interaction, G_F, and the conservation of lepton number (flavor) in muon decay. The muon's anomalous magnetic moment has played an important role in restricting theories of physics beyond the standard standard model, where at present there is a 3.4 standard-deviation difference between the experiment and standard-model theory. Its capture on the atomic nucleus has provided valuable information on the modification of the weak current by the strong interaction which is complementary to that obtained from nuclear beta decay.Comment: 8 pages, 9 figures. Invited paper for the Journal of Physical Society in Japan (JPSJ), Special Topics Issue "Frontiers of Elementary Particle Physics, The Standard Model and beyond

MFV Reductions of MSSM Parameter Space

The 100+ free parameters of the minimal supersymmetric standard model (MSSM) make it computationally difficult to compare systematically with data, motivating the study of specific parameter reductions such as the cMSSM and pMSSM. Here we instead study the reductions of parameter space implied by using minimal flavour violation (MFV) to organise the R-parity conserving MSSM, with a view towards systematically building in constraints on flavour-violating physics. Within this framework the space of parameters is reduced by expanding soft supersymmetry-breaking terms in powers of the Cabibbo angle, leading to a 24-, 30- or 42-parameter framework (which we call MSSM-24, MSSM-30, and MSSM-42 respectively), depending on the order kept in the expansion. We provide a Bayesian global fit to data of the MSSM-30 parameter set to show that this is manageable with current tools. We compare the MFV reductions to the 19-parameter pMSSM choice and show that the pMSSM is not contained as a subset. The MSSM-30 analysis favours a relatively lighter TeV-scale pseudoscalar Higgs boson and $\tan \beta \sim 10$ with multi-TeV sparticles.Comment: 2nd version, minor comments and references added, accepted for publication in JHE