A mathematical model of p62-ubiquitin aggregates in autophagy

Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where either aggregates are unstable, or their size saturates at a finite value, or their size grows indefinitely as long as free particles are abundant. The boundaries of these regimes as well as the finite size in the second case can be computed explicitly. The growth in the third case (quadratic in time) can also be made explicit by formal asymptotic methods. In the absence of rigorous results the dynamic stability of these structures has been investigated by numerical simulations. A comparison with recent experimental results permits a partial parametrization of the model.

Black Hole Evaporation: Sparsity in Analogue and General Relativistic Space-Times

<p>Our understanding of black holes changed drastically, when Stephen Hawking discovered their evaporation due to quantum mechanical processes. One core feature of this effect, later named after him, is both its similarity and simultaneous dissimilarity to classical black body radiation as known from thermodynamics: A black hole’s spectrum certainly looks like that of a black (or at least grey) body, yet the number of emitted particles per unit time differs greatly. However it is precisely this emission rate that determines — together with the frequency of the emitted radiation — whether the resulting radiation field behaves classical or non-classical. It has been known nearly since the Hawking effect’s discovery that the radiation of a black hole is in this sense non-classical (unlike the radiation of a classical black or grey body). However, this has been an utterly underappreciated property. In order to give a more readily quantifiable picture of this, we introduced the notion of ‘sparsity’, which is easily evaluated, and interpreted, and agrees with more rigorous results despite a semi-classical, semi-analytical origin. Sadly, and much to relativists’ chagrin, astrophysical black holes (and their Hawking evaporation) have a tendency to be observationally elusive entities. Luckily, Hawking’s derivation lends itself to reformulations that survive outside its astrophysical origin — all one needs, are three things: a universal speed limit (like the speed of sound, the speed of light, the speed of surface waves, . . . ), a notion of a horizon (the ‘black hole’), and lastly a sprinkle of quantum dynamics on top. With these ingredients at hand, the last thirty-odd years have seen a lot of work to transfer Hawking radiation into the laboratory, using a range of physical models. These range from fluid mechanics, over electromagnetism, to Bose–Einstein condensates, and beyond. A large part of this thesis was then aimed at providing electromagnetic analogues to prepare an analysis of our notion of sparsity in this new paradigm. For this, we developed extensively a purely algebraic (kinematical) analogy based on covariant meta-material electrodynamics, but also an analytic (dynamical) analogy based on stratified refractive indices. After introducing these analogue space-time models, we explain why the notion of sparsity (among other things) is much</p>

Black Hole Evaporation: Sparsity in Analogue and General Relativistic Space-Times

<p>Our understanding of black holes changed drastically, when Stephen Hawking discovered their evaporation due to quantum mechanical processes. One core feature of this effect, later named after him, is both its similarity and simultaneous dissimilarity to classical black body radiation as known from thermodynamics: A black hole’s spectrum certainly looks like that of a black (or at least grey) body, yet the number of emitted particles per unit time differs greatly. However it is precisely this emission rate that determines — together with the frequency of the emitted radiation — whether the resulting radiation field behaves classical or non-classical. It has been known nearly since the Hawking effect’s discovery that the radiation of a black hole is in this sense non-classical (unlike the radiation of a classical black or grey body). However, this has been an utterly underappreciated property. In order to give a more readily quantifiable picture of this, we introduced the notion of ‘sparsity’, which is easily evaluated, and interpreted, and agrees with more rigorous results despite a semi-classical, semi-analytical origin. Sadly, and much to relativists’ chagrin, astrophysical black holes (and their Hawking evaporation) have a tendency to be observationally elusive entities. Luckily, Hawking’s derivation lends itself to reformulations that survive outside its astrophysical origin — all one needs, are three things: a universal speed limit (like the speed of sound, the speed of light, the speed of surface waves, . . . ), a notion of a horizon (the ‘black hole’), and lastly a sprinkle of quantum dynamics on top. With these ingredients at hand, the last thirty-odd years have seen a lot of work to transfer Hawking radiation into the laboratory, using a range of physical models. These range from fluid mechanics, over electromagnetism, to Bose–Einstein condensates, and beyond. A large part of this thesis was then aimed at providing electromagnetic analogues to prepare an analysis of our notion of sparsity in this new paradigm. For this, we developed extensively a purely algebraic (kinematical) analogy based on covariant meta-material electrodynamics, but also an analytic (dynamical) analogy based on stratified refractive indices. After introducing these analogue space-time models, we explain why the notion of sparsity (among other things) is much</p>

Thermodynamic Basis of Brine Density on Pressure, Temperature, and Chemical Composition in Ultrahigh Pressure/High Temperature Environments

Summary Temperature change and the pressure/volume/temperature (PVT) response of wellbore annular fluids are the primary variables that control annular pressure buildup in offshore wells. Though the physics of annular pressure buildup is well understood, there is some ambiguity in the PVT models of brines. While custom tests can be performed to determine the PVT response of brines, they are time-consuming and expensive. In this light, our paper presents a method to determine the density of brines from their chemical composition, as a function of pressure and temperature. It compares theoretical predictions with the results of tests on brines used in our industry and available test data from the oil and gas and other industries. In 1987, Kemp and Thomas used the principles of chemical thermodynamics to develop equations for the density of brines as a function of pressure and temperature and their electrolytic actions. However, their paper contained two (inadvertent, and probably typographical) errors. One of the errors lay in the set of the Debye-Hückel parameters, and the other was contained in the coefficients of the series expansion for the infinite dilution molal volume. Furthermore, they (inadvertently) did not mention the role of a crucial parameter that accounts for the interaction between the ionic constituents of the salt. As a result, nearly a generation of engineers in our industry has been unable to reproduce their valuable results or apply their technically rigorous results to other brine chemistries. In this paper, we return to the basic equations of chemical thermodynamics and the principles of stoichiometry and delineate the inadvertent errors that had crept into the Kemp and Thomas equations. We then present the rectified equations and reproduce their example with the corrected results. Further, we compare the predictions from the original Kemp and Thomas work with results from a leading chemical engineering model. Finally, we compare the results of theoretical models with test measurements from the laboratory and characterize the uncertainty inherent in each model. Thereby, we have rendered the Kemp and Thomas (1987) model useful to the well design community.

Vortex reconnections in classical and quantum fluids

We review recent rigorous results on the phenomenon of vortex reconnection in classical and quantum fluids. In the context of the Navier–Stokes equations in $$\mathbb {T}^3$$ T 3 we show the existence of global smooth solutions that exhibit creation and destruction of vortex lines of arbitrarily complicated topologies. Concerning quantum fluids, we prove that for any initial and final configurations of quantum vortices, and any way of transforming one into the other, there is an initial condition whose associated solution to the Gross–Pitaevskii equation realizes this specific vortex reconnection scenario. Key to prove these results is an inverse localization principle for Beltrami fields and a global approximation theorem for the linear Schrödinger equation.

Method to determine fact and place of commercial losses in distribution networks

The improvement of methods to register the commercial losses in electrical distribution networks, and especially in low voltage networks, is one of the most important tasks for power supply providers. It is rather difficult to correctly register the fact of occurrence of such losses in the network. It is objectively impossible to analyze the state of the networks based on data obtained from various points of the specified network with the required accuracy. In this regard, at present no methods have been developed for remote detection of the fact and determination of the place of commercial losses in distribution networks, that could work in the mode of integration with automated information-measuring system of fiscal electricity metering. To solve this problem a method is to be developed that allows us to establish accurately for practical purposes the volume of commercial losses in the network and determine the place of their occurrence. During the research, methods of electric power networks modeling have been used. The assumption has been made about no flow of capacitive leakage currents to ground in the network, about full compliance of the line parameters with their calculated (nominal) values, as well as the basic laws of electrical engineering science. A unique method is proposed to determine the fact and the place of commercial losses in distribution networks. In contrast to the prototypes, it is based on the analysis of data obtained from metering devices, based on the key laws of electrical engineering and it allows us to get reliable arithmetically rigorous results without using fuzzy logic. The authors have proved theoretically and practically the effectiveness of the proposed solutions, and the possibility of their application. A calculation has been made to determine the place of commercial losses in the network using an example. The proposed method to determine the fact and place of commercial losses in distribution networks of low and medium voltage levels solves the problem of inability to effectively identify the points of occurrence of commercial losses in distribution networks. The reliability of the results obtained is confirmed by mathematical rigor of the method and algorithmic nature of the procedure for analyzing the distribution network.

Automated Optimization of Residual Reduction Algorithm Parameters in OpenSim

The residual reduction algorithm (RRA) in OpenSim improves dynamic consistency of movement simulations of musculoskeletal models. RRA requires the user to select numerous tracking weights for the joint kinematics to reduce residual errors. Selection is often performed manually, which can be time-consuming and is unlikely to yield optimal tracking weights. A multi-heuristic optimization algorithm was employed to expedite tracking weight decision making to reduce residual errors. This method produced more rigorous results than manual iterations and although the total computation time was not significantly reduced, this method does not require the user to monitor the algorithm's progress to find a solution, thereby reducing manual tuning. Supporting documentation and code to implement this optimization is freely provided to assist the community with developing movement simulations.

Mathematical study of a system of multi-dimensional non-local evolution equations describing surfactant-laden two-fluid shear flows

This article studies a coupled system of model multi-dimensional partial differential equations (PDEs) that arise in the nonlinear dynamics of two-fluid Couette flow when insoluble surfactants are present on the interface. The equations have been derived previously, but a rigorous study of local and global existence of their solutions, or indeed solutions of analogous systems, has not been considered previously. The evolution PDEs are two-dimensional in space and contain novel pseudo-differential terms that emerge from asymptotic analysis and matching in the multi-scale problem at hand. The one-dimensional surfactant-free case was studied previously, where travelling wave solutions were constructed numerically and their stability investigated; in addition, the travelling wave solutions were justified mathematically. The present study is concerned with some rigorous results of the multi-dimensional surfactant system, including local well posedness and smoothing results when there is full coupling between surfactant dynamics and interfacial motion, and global existence results when such coupling is absent. As far as we know such results are new for non-local thin film equations in either one or two dimensions.

Disentangling how multiple traits drive 2 strain frequencies in SIS dynamics with coinfection

A general theory for competitive dynamics among many strains at the epidemiological level is required to understand polymorphisms in virulence, transmissibility, antibiotic resistance and other biological traits of infectious agents. Mathematical coinfection models have addressed specific systems, focusing on the criteria leading to stable coexistence or competitive exclusion, however, due to their complexity and nonlinearity, analytical solutions in coinfection models remain rare. Here we study a 2-strain SIS compartmental model with co-infection/co-colonization, incorporating multiple fitness dimensions under the same framework: variation in transmissibility, duration of carriage, pairwise susceptibilities to coinfection, coinfection duration, and transmission priority effects from mixed coinfection. Taking advantage of a singular perturbation approach, under the assumption of strain similarity, we expose how strain dynamics on a slow timescale are explicitly governed by a replicator equation which encapsulates all traits and their interplay. This allows us to predict explicitly not only the final epidemiological outcome of a given 2-player competition, but moreover, their entire frequency dynamics as a direct function of their relative variation and of strain-transcending global parameters. Based on mutual invasion fitnesses, we analyze and report rigorous results on transition phenomena in the 2-strain system, strongly mediated via coinfection prevalence. This framework offers a deeper analytical understanding of 2-strain competitive games in coinfection, with applications to virulence, interventions, antibiotic resistance, and social evolution theory.