Boltzmann hierarchy for interacting neutrinos I: formalism

Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used $(c_{\rm eff}^2,c_{\rm vis}^2)$-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles.Comment: 44 pages, 14 figures; included scalar Boltzmann hierarchy in the massless case and plots of integral kernels; accepted by JCA

Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond-fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density of states results have been evaluated for interaction parameters spanning the range from good to poor solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.Comment: 17 pages, 12 figures, to appear in J. Chem. Phy

On the fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media

The fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by $\sigma_{\theta_J}$) decay with the lattice size according to the power-law $\sigma_{\theta_J} \propto L^{-1/ \nu}$. The exponent $\nu$ depends on the dimensionality $D$ of the substrate and the fractal dimension of the set where the RSA process actually takes place ($d_f$) according to $\nu = 2 / (2D - d_f)$.This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers on homogeneous and stochastic fractal substrates. Furthermore, our predictions are in excellent agreement with different previous numerical results. It is also shown that, studying correlated stochastic processes, one can define various fluctuating quantities designed to capture either the underlying physics of individual processes or that of the whole system. So, subtle differences in the definitions may lead to dramatically different physical interpretations of the results. Here, this statement is demonstrated for the case of RSA of dimers on binary alloys.Comment: 20 pages, 8 figure

Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N [subscript G] is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε ε[subscript s] with slow internal dynamics. The cohesion strength ε[subscript s] of this freezing transition depends on N G . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N [subscript G] . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi

Interacting neutrinos in cosmology: exact description and constraints

We consider the impact of neutrino self-interactions described by an effective four-fermion coupling on cosmological observations. Implementing the exact Boltzmann hierarchy for interacting neutrinos first derived in [arxiv:1409.1577] into the Boltzmann solver CLASS, we perform a detailed numerical analysis of the effects of the interaction on the cosmic microwave background (CMB) anisotropies, and compare our results with known approximations in the literature. While we find good agreement between our exact approach and the relaxation time approximation used in some recent studies, the popular $\left( c_{\text{eff}}^2,c_{\text{vis}}^2 \right)$-parameterisation fails to reproduce the correct scale dependence of the CMB temperature power spectrum. We then proceed to derive constraints on the effective coupling constant $G_{\text{eff}}$ using currently available cosmological data via an MCMC analysis. Interestingly, our results reveal a bimodal posterior distribution, where one mode represents the standard $\Lambda$CDM limit with $G_{\rm eff} \lesssim 10^8 \, G_{\rm F}$, and the other a scenario in which neutrinos self-interact with an effective coupling constant $G_{\rm eff} \simeq 3 \times 10^9 \, G_{\rm F}$.Comment: 25 pages, 11 figures; accepted for publication in JCA

Establishing the VR-haptic thinkers group: Insights and progress in dental training technologies

In today’s fast-paced, digitalized world, dental educators and professionals alike need to try and stay up to date on current learning methods to provide the best possible education to the new generations of students. VR-haptic training allows educators to guide students in performing dental exercises within a digital environment using input methods with tactile force feedback features. This can reduce the mental burden of students due to fear of failure, as material losses are no longer a factor. Additionally, students can practice in their own time and pace, outside of teaching hours. Despite being digital, this mode of teaching has been shown to enable skill transfer to the real world, affording educators more flexibility with how to teach their students both before and during traditional methods of practical dental education. To help support the embracement of this new technology, a global VR-Haptic Thinkers Consortium was established in early 2024 and is now formed of 36 partner universities, institutions, and industrial companies. The second VR-Haptic Thinkers Meetup, held in mid-2024, was given the theme of “VR-Haptic Dentistry, Pedagogy, and Curriculum Evolution”. The theme of the meetup was timely as in recent years dental educators have all faced many challenges in education and research and have had to deal with rapid changes in supportive VR-haptic education. A robust program was featured to engage with the dental community members who are curious about the new technological advancements in dental education

Benefits and challenges of the integration of haptics-enhanced virtual reality training within dental curricula

Background: Haptics-enhanced virtual reality (VR-haptic) simulation in dental education has evolved considerably during the past decade, representing a promising resource of simulation-based training opportunities to support conventional practice. We aim to summarize current literature on the applications of VR-haptics in learning, practicing, and teaching dental education. Methods: A literature search was performed using PubMed, focusing on research articles published between January 2010 and January 2024. Out of the 667 articles that matched the search terms (dentistry, education, haptic, teaching, training, virtual reality), 105 were screened, and 42 were eligible for full-text reading and utilization. Findings from an ongoing educator survey on the use of VR-haptics in dental education have also been provided. Results: VR-haptic simulation has been shown to have a supportive role in dental simulation practice. Despite training within a digital world, hand skill transfer to the real world has been demonstrated, which affords educators more flexibility in how to train their students before and during traditional preclinical and clinical practical education. The individualized VR-haptic training and feedback help students in mastering essential working techniques, while also increasing engagement and motivation. Conclusions: VR-haptics-supported dental education can help students effectively address challenges during their preclinical and clinical training, as well as in their subsequent careers, and it may help mitigate some weaknesses of the current educational system. Validation is a key factor for the acceptance of VR-haptic simulators; thus, further research and verification are needed before VR-haptics could be considered a primary hand skill development method of learning in dental education. VR-haptic simulation may in the future be used as an assessment tool for the students’ and clinicians’ credentialing process.publishedVersio

Establishing the VR-haptic thinkers group: Insights and progress in dental training technologies

In today's fast-paced, digitalized world, dental educators and professionals alike need to try and stay up to date on current learning methods to provide the best possible education to the new generations of students. VR-haptic training allows educators to guide students in performing dental exercises within a digital environment using input methods with tactile force feedback features. This can reduce the mental burden of students due to fear of failure, as material losses are no longer a factor. Additionally, students can practice in their own time and pace, outside of teaching hours. Despite being digital, this mode of teaching has been shown to enable skill transfer to the real world, affording educators more flexibility with how to teach their students both before and during traditional methods of practical dental education. To help support the embracement of this new technology, a global VR-Haptic Thinkers Consortium was established in early 2024 and is now formed of 36 partner universities, institutions, and industrial companies. The second VR-Haptic Thinkers Meetup, held in mid-2024, was given the theme of “VR-Haptic Dentistry, Pedagogy, and Curriculum Evolution”. The theme of the meetup was timely as in recent years dental educators have all faced many challenges in education and research and have had to deal with rapid changes in supportive VR-haptic education. A robust program was featured to engage with the dental community members who are curious about the new technological advancements in dental education