Conservation Constraints Research Articles

Dynamics of fixed-volume pinned films – dealing with a non-self-adjoint thin-film problem

The use of thin liquid films has expanded beyond lubrication and coatings, and into applications in actuators and adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite or periodic films, these applications are characterized by a finite amount of liquid in an impermeable domain. The global mass conservation constraint, together with common boundary conditions (e.g. pinning), create quantitatively and qualitatively different dynamics than those of infinite films. Mathematically, this manifests itself as a non-self-adjoint problem. This work presents a combined theoretical and experimental study for this problem. We provide a time-dependent closed-form analytical solution for the linearized non-self-adjoint system that arises from these boundary conditions. We highlight that, in contrast to self-adjoint problems, here, special care should be given to deriving the adjoint problem to reconstruct the solution based on the eigenfunctions properly. We compare these solutions with those obtained for permeable and periodic boundary conditions, representing common models for self-adjoint thin-film problems. We show that, while the initial dynamics is nearly identical, the boundary conditions eventually affect the film deformation as well as its response time. To experimentally illustrate the dynamics and to validate the theoretical model, we fabricated an experimental set-up that subjects a thin liquid film to a prescribed normal force distribution through dielectrophoresis, and used high-frame-rate digital holography to measure the film deformation in real time. The experiments agree well with the model and confirm that confined films exhibit a different behaviour which could not be predicted by existing models.

Application of Strength Pareto Evolutionary Algorithm II in Multi-Objective Water Supply Optimization Model Design for Mountainous Complex Terrain

Water distribution networks (WDN) model optimization is an important part of smart water systems to achieve optimal strategies. WDN optimization focuses on the nonlinearity of the discharge head loss equation, the availability of discrete properties of pipe sizes, and the conservation of constraints. Multi-objective evolutionary algorithms (MOEAs) have been proposed and successfully applied in the field of WDN design optimization. Previous studies have focused on comparing the optimization effects of algorithms in water distribution networks, ignoring the problems of unbalanced pressure distribution and water hammer at the nodes of the pipe network caused by the complex terrain in mountainous areas. In this paper, a multi-objective water supply optimization model that integrated cost, reliability, and water quality was established for a mountainous WDN in real engineering. The method of traversing the nodes to solve the water age was introduced to find a more scientific and practical water age solution model, with setting the weight function to evaluate the water age of the water supply model comprehensively. Strength Pareto Evolutionary Algorithm II (SPEA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) were adopted to optimize the WDN design model in the mountainous complex terrain. The significance levels of the number of Pareto solutions (NOPS) and running time are 0.029 and 0.001, respectively, indicating that the two algorithms have significant differences. Compared to NSGA-II, SPEA-II has a better convergence rate and running time in multi-objective water supply optimization design. The solution set distribution of SPEA-II is more concentrated than that of NSGA-II, also the numerical value is better. The number of SPEA-II optimization schemes is larger and the scheme is more effective. Among them, the Pareto solution set of SPEA-II can obtain more desirable optimization results on cost, reliability index (RI) and water age. In summary, the study provides valuable information for decision makers in WDN with complex terrain.

Fast Neutrino Flavor Conversions Can Help and Hinder Neutrino-Driven Explosions.

We present the first simulations of core-collapse supernovae in axial symmetry with feedback from fast neutrino flavor conversion (FFC). Our schematic treatment of FFCs assumes instantaneous flavor equilibration under the constraint of lepton-number conservation individually for each flavor. Systematically varying the spatial domain where FFCs are assumed to occur, we find that they facilitate SN explosions in low-mass (9-12M_{⊙}) progenitors that otherwise explode with longer time delays, whereas FFCs weaken the tendency to explode of higher-mass (around 20M_{⊙}) progenitors.

A physics investigation on impedance matching theory in microwave absorption film. II. Problem analyses

In Part I of this work published previously, it was proved from the transmission-line theory that impedance matching (IM) theory should be replaced by wave cancellation theory, film is different from the material, and the phase effects from interfaces should be considered in quarter wavelength theory. In this Part, it is shown that energy penetration for a film cannot be defined and IM is flawed because it cannot be proved theoretically or shown to be consistent with experimental data. The multi-absorption peaks in a film originate from wave cancellation under the constraint of energy conservation rather than from the resonances from the material.

CT‐value conservation based spatial transformer network for cardiac motion correction

AbstractArtifact correction is a great challenge in cardiac imaging. During the correction of coronary tissue with motion‐induced artifacts, the spatial distribution of CT value not only shifts according to the motion vector field (MVF), but also shifts according to the volume change rate of the local voxels. However, the traditional interpolation method does not conserve the CT value during motion compensation. A new sample interpolation algorithm is developed based on the constraint of conservation of CT value before and after image deformation. This algorithm is modified on the existing interpolation algorithms and can be embedded into neural networks with deterministic back propagation. Comparative experimental results illustrate that the method can not only correct motion‐induced artifacts, but also ensure the conservation of CT value in the region of interest (ROI) area, so as to obtain corrected images with clinically recognized CT value. Both effectiveness and efficiency are proved in forward motion correction process and backward training steps in deep learning. Simultaneously, using the network to learn the MVF making this method more interpretable than the existing image‐based end‐to‐end deep learning method.

An iterative mass-to-drag ratio estimation method for ballistic targets

Ballistic target tracking and identification is a key task for missile defense systems. A vital problem in target track and recognition is how to estimate the target mass-to-drag ratio fast and accurately. Based on the constraints of energy conservation, this paper proposes an iterative mass-to-drag ratio estimation method. This algorithm first estimates the position and velocity of the target using unscented Kalman filter, and then estimates the mass-to-drag ratio of the target by using energy conservation. By iterating, the final value is outputted. The simulation results show that this method can estimate the mass-to-drag ratio of the target at a high altitude, which provides a precise way for mass-to-drag ratio estimation.

Portfolio management for insurers and pension funds and COVID-19: targeting volatility for equity, balanced, and target-date funds with leverage constraints

AbstractInsurers and pension funds face the challenges of historically low-interest rates and high volatility in equity markets, that have been accentuated due to the COVID-19 pandemic. Recent advances in equity portfolio management with a target volatility have been shown to deliver improved on average risk-adjusted return, after transaction costs. This paper studies these targeted volatility portfolios in applications to equity, balanced, and target-date funds with varying constraints on leverage. Conservative leverage constraints are particularly relevant to pension funds and insurance companies, with more aggressive leverage levels appropriate for alternative investments. We show substantial improvements in fund performance for differing leverage levels, and of most interest to insurers and pension funds, we show that the highest Sharpe ratios and smallest drawdowns are in targeted volatility-balanced portfolios with equity and bond allocations. Furthermore, we demonstrate the outperformance of targeted volatility portfolios during major stock market crashes, including the crash from the COVID-19 pandemic.

Modelling crystallization: When the normal growth velocity depends on the supersaturation

The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the material excess, the supersaturation. Using a conservation constraint for the transformation ratio α∈[0,1] as complementing the rescaled supersaturation to 1 and a kinetic law for the normal growth velocity as function of the supersaturation raised to power g, the growth order, we derive an equation for the rate of transformation dα/dt. We integrate it for the six combinations of the three spatial dimensions D = 1, 2, 3 and the two canonical values of g = 1, 2 towards obtaining expressions for αDg. The same equation, with g = 1 and D = n (n is the so called Avrami exponent) is obtained when taking only the linear in α term from the Taylor's expansion around α = 0 of the model equation of Johnson-Mehl-Avrami-Kolmogorov (JMAK). We verify our model by fitting datasets of α21 and α31 (from α = 0 to αupper = 0.999) with JMAK to obtain from the fit n = 1.725, 2.43, resp. We show further how the values of n depend on the value of αupper to which the fit is performed starting always from 0. Towards building a validation protocol, we start with validating α21 with published results.

Equivalence of nonequilibrium ensembles: Two-dimensional turbulence with a dual cascade.

We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two dimensions in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equationin two dimensions by imposing global constraints of energy and enstrophy conservation. A comparative study of the statistical properties of its solutions with those obtained from the standard Navier-Stokes equationsclearly shows that a formally time-reversible system is able to reproduce the features of a two-dimensional turbulent flow. Statistical quantities based on one- and two-point measurements show an excellent agreement between the two systems for the inverse- and direct-cascade regions. Moreover, we find that the conjecture holds very well for two-dimensional turbulent flows with both conserved energy and enstrophy at finite Reynolds number.

Cored dark matter halos in the cosmic neutrino background

We study the impact of the interaction between DM and the cosmic neutrino background on the evolution of galactic dark matter halos. The energy transfer from the cosmic background neutrinos to galactic dark matter can heat the center of the galaxy and make it cored. The core formation is efficient for the small galaxies such as the satellite galaxies of the Milky Way and we can put a conservative constraint on the non-relativistic elastic scattering cross section as σχν ≲ 10-31 cm2 for 0.1 keV dark matter.

Variable-stiffness composites optimisation under multiple design requirements and loads

The aim of this paper is twofold. On the one hand, it presents a methodology for the deterministic optimisation of a general class of variable-stiffness composite (VSC) structures, including a solution obtained by using laminæ with a curvilinear fibres-path and variable-thickness, by considering different design requirements under multiple load cases. The considered framework is the multi-level design methodology based on the polar parameters (PPs) to describe the macroscopic behaviour of the VSC structure. Particularly, only the first-level problem is addressed in this work: the design variables are, thus, the PPs and the thickness of the VSC laminate, whose spatial distribution is described via basis spline (B-spline) surfaces. The goal is to minimise the mass of the VSC structure subject to design requirements on feasibility, strength, first buckling load and maximum curvature of the fibres-path. This latter is formulated as an equivalent (conservative) constraint in the PPs space, regardless of the fibres-path within each lamina. Moreover, a general formulation of the gradient of the requirements related to buckling load and strength is proposed, which takes advantage from the main properties of B-spline entities and PPs. On the other hand, this paper aims to propose a new benchmark problem that is representative of a panel belonging to the fuselage of a standard civil aircraft subjected to multiple loading conditions. To this end, a wide campaign of numerical tests has been performed by considering a sensitivity analysis of the optimised solution to: (a) the integer parameters involved in the definition of the B-spline entities describing the distribution of the PPs and, possibly, of the thickness, (b) the type of VSC structure, (c) the type of deterministic optimisation algorithm. The results can be used as a database to assess the effectiveness of different design strategies against the optimised solutions presented in this paper.

Minimax Flow Over Acyclic Networks: Distributed Algorithms and Microgrid Application

Given a flow network with variable suppliers and fixed consumers, the minimax flow problem consists in minimizing the maximum flow between nodes, subject to flow conservation and capacity constraints. We solve this problem over acyclic graphs in a distributed manner by showing that it can be recast as a consensus problem between the maximum downstream flows, which we define here for the first time. Additionally, we present a distributed algorithm to estimate these quantities. Finally, exploiting our theoretical results, we design an online distributed controller to prevent overcurrent in microgrids consisting of loads and droop-controlled inverters. Our results are validated numerically on the CIGRE benchmark microgrid.

A Single-Tube Robust Model Predictive Control Method Based on ε-Approximation

This paper aims to solve the problem of the robust model predictive control, the contradiction of the system robustness, and the conservative terminal constraint set range. A robust model predictive control (RMPC) method based on an ε-approximation single-tube set is proposed. We construct a single-tube RMPC structure for linear discrete time invariant systems with additive disturbances. To this structure, we add the state estimation and state feedback to improve the convergence rate. Furthermore, we use the ε-approximation to estimate the terminal constraint set with less conservatism, thus improving the robustness. Then, we conduct a stability analysis of the ε-approximation single-tube RMPC system. The simulation results demonstrate the stability and interference allowance advantages of the proposed method.

Aberrantly Expressed Hsa_circ_0060762 and CSE1L as Potential Peripheral Blood Biomarkers for ALS.

Amyotrophic lateral sclerosis (ALS) is a rapidly progressive adult-onset neurodegenerative disease that is often diagnosed with a delay due to initial non-specific symptoms. Therefore, reliable and easy-to-obtain biomarkers are an absolute necessity for earlier and more accurate diagnostics. Circular RNAs (circRNAs) have already been proposed as potential biomarkers for several neurodegenerative diseases. In this study, we further investigated the usefulness of circRNAs as potential biomarkers for ALS. We first performed a microarray analysis of circRNAs on peripheral blood mononuclear cells of a subset of ALS patients and controls. Among the differently expressed circRNA by microarray analysis, we selected only the ones with a host gene that harbors the highest level of conservation and genetic constraints. This selection was based on the hypothesis that genes under selective pressure and genetic constraints could have a major role in determining a trait or disease. Then we performed a linear regression between ALS cases and controls using each circRNA as a predictor variable. With a False Discovery Rate (FDR) threshold of 0.1, only six circRNAs passed the filtering and only one of them remained statistically significant after Bonferroni correction: hsa_circ_0060762 and its host gene CSE1L. Finally, we observed a significant difference in expression levels between larger sets of patients and healthy controls for both hsa_circ_0060762 and CSE1L. CSE1L is a member of the importin β family and mediates inhibition of TDP-43 aggregation; the central pathogenicity in ALS and hsa_circ_0060762 has binding sites for several miRNAs that have been already proposed as biomarkers for ALS. In addition, receiver operating characteristics curve analysis showed diagnostic potential for CSE1L and hsa_circ_0060762. Hsa_circ_0060762 and CSE1L thus represent novel potential peripheral blood biomarkers and therapeutic targets for ALS.

Effects of impact ionization and Auger recombination on hot-carrier solar cells and hot-carrier photocatalysts

We applied hot-carrier extraction to solar cells and photocatalysts used for artificial photosynthesis including water splitting and CO2 reduction, and elucidated the differences between these two applications: hot-carrier solar cells (HC-SCs) and hot-carrier photocatalysts (HC-PCs) by detailed balance calculations. The hot-carrier effect in the photocatalysts is less significant than that in the solar cells, because of the larger bandgaps required for generating sufficiently high-energy carriers consumed for the reactions. On the other hand, impact ionization and Auger recombination (IA) improves the efficiency of the HC-PCs more notably, because the IA functions like photon upconverters and hence narrows the optimal bandgap. Furthermore, the IA improves the spectral robustness by eliminating the constraint of the particle-number conservation for both the HC-SCs and HC-PCs. These benefits of the IA are contrasting with the well-recognized fact that the IA only reduces the carrier number and consequently lowers the efficiency of the conventional counterparts.

On strictly enforced mass conservation constraints for modelling the Rainfall‐Runoff process

AbstractIt has been proposed that conservation laws might not be beneficial for accurate hydrological modelling due to errors in input (precipitation) and target (streamflow) data (particularly at the event time scale), and this might explain why deep learning models (which are not based on enforcing closure) can out‐perform catchment‐scale conceptual and process‐based models at predicting streamflow. We test this hypothesis with two forcing datasets that disagree in total, long‐term precipitation. We analyse the roll of strictly enforced mass conservation for matching a long‐term mass balance between precipitation input and streamflow output using physics‐informed (mass conserving) machine learning and find that: (1) enforcing closure in the rainfall‐runoff mass balance does appear to harm the overall skill of hydrological models; (2) deep learning models learn to account for spatiotemporally variable biases in data (3) however this ‘closure’ effect accounts for only a small fraction of the difference in predictive skill between deep learning and conceptual models.

Orbital evolution of satellite galaxies in self-interacting dark matter models

Dark matter self-interactions can leave distinctive signatures on the properties of satellite galaxies around Milky Way--like hosts through their impact on tidal stripping, ram pressure, and gravothermal collapse. We delineate the regions of self-interacting dark matter parameter space---specified by interaction cross section and a velocity scale---where each of these effects dominates and show how the relative mass loss depends on the satellite's initial mass, density profile, and orbit. We obtain novel, conservative constraints in this parameter space using Milky Way satellite galaxies with notably high central densities and small pericenter distances. Our results for self-interacting dark matter models, in combination with constraints from clusters of galaxies, favor either velocity-dependent cross sections that lead to gravothermal core collapse in the densest satellites or small cross sections which more closely resemble cold and collisionless dark matter.

On a Phase Field Model for RNA-Protein Dynamics

A phase field model which describes the formation of protein-RNA complexes subject to phase segregation is analyzed. A single protein, two RNA species, and two complexes are considered. Protein and RNA species are governed by coupled reaction-diffusion equations which also depend on the two complexes. The latter ones are driven by two Cahn-Hilliard equations with Flory-Huggins potential and reaction terms depending on the solution variables. The resulting nonlinear coupled system is equipped with no-flux boundary conditions and suitable initial conditions. The former ones entail some mass conservation constraints which are also due to the nature of the reaction terms. The existence of global weak solutions in a bounded (two- or) three-dimensional domain is established. In dimension two, some weighted-in-time regularity properties are shown. In particular, the complexes instantaneously get uniformly separated from the pure phases. Taking advantage of this result, a unique continuation property is proven. Among the many technical difficulties, the most significant one arises from the fact that the two complexes are initially nonexistent, so their initial conditions are zero i.e., they start from a pure phase. Thus we must solve, in particular, a system of two coupled Cahn-Hilliard equations with singular potential and nonlinear sources without the usual assumption on the initial datum, i.e., the initial phase cannot be pure. This novelty requires a new approach to estimate the chemical potential in a suitable $L^p(L^2)$-space with $p\in(1,2)$. This technique can be extended to other models like, for instance, the well-known Cahn-Hilliard-Oono equation.

Neural Joint Space Implicit Signed Distance Functions for Reactive Robot Manipulator Control

In this letter, we present an approach for learning a neural implicit signed distance function expressed in joint space coordinates, that efficiently computes distance-to-collisions for arbitrary robotic manipulator configurations. Computing such distances is a long standing problem in robotics as approximate representations of the robot and environment geometry can lead to overly conservative constraints, numerical instabilities and expensive computations – limiting real-time reactive control and task success. Leveraging GPU parallelization and the differentiable nature of the proposed distance function allows for fast calculation of gradients with respect to the neural network inputs, providing a continuous repulsive vector field directly in joint space. We show that the learned high-resolution collision representation can be used to achieve real-time reactive control by i) formulating it as a collision-avoidance constraint for a quadratic programming (QP) inverse kinematics (IK), and ii) introducing it as a collision cost in a sampling-based joint space model predictive controller (MPC). For a reaching benchmark task with a 7DoF robot and dynamic obstacles intentionally obstructing the robot's path we achieve average 250 Hz control frequency with QP-IK and 92 Hz with MPC, showing an accelerated performance of 15% for QP-IK and 40% for MPC over baseline distance computation techniques.

Model Constraints Based on the IceCube Neutrino Nondetection of GRB 221009A

GRB 221009A is a bright gamma-ray burst (GRB) with isotropic energy larger than 1054 erg. Its fairly low redshift makes it a promising candidate for high-energy neutrino detection. However, a neutrino search for this GRB reported by the IceCube collaboration yielded a null result. In this paper, we utilize the upper limit from the IceCube observation to test different GRB prompt emission models. We find that, at least for this specific burst, the dissipative photosphere model could be ruled out in a large parameter space. The internal-shock model can survive only with a large bulk motion Lorentz factor Γ, where the most stringent and conservative constraints are Γ > ∼ 450 and Γ > ∼ 200, respectively. Also, the ratio of the total dissipated energy that goes into the protons and electrons (ϵ p /ϵ e ) can be constrained with a given Γ. For Γ < 400, ϵ p /ϵ e < 10 is required. For the Internal-collision-induced Magnetic Reconnection and Turbulence (ICMART) model, the constraint from GRB 221009A is modest. Under the ICMART model, only for extreme situations when most dissipated energy deposit into protons and all accelerated protons are suitable for producing neutrinos, a slightly large bulk motion (Γ > ∼ 250) is required.