Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders

The numerical solution of partial differential equations in unbounded domains requires a finite computational domain. Often one obtains a finite domain by introducing an artificial boundary and imposing boundary conditions there. This paper derives exact boundary conditions at an artificial boundary for partial differential equations in cylinders. An abstract theory is developed to analyze the general linear problem. Solvability requirements and estimates of the solution of the resulting finite problem are obtained by use of the notions of exponential and ordinary dichotomies. Useful representations of the boundary conditions are derived using separation of variables for problems with constant tails. The constant tail results are extended to problems whose coefficients obtain limits at infinity by use of an abstract perturbation theory. The perturbation theory approach is also applied to a class of nonlinear problems. General asymptotic formulas for the boundary conditions are derived and displayed in detail

The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations

Traveling wave solutions have been studied for a variety of nonlinear parabolic problems. In the initial value approach to such problems the initial data at infinity determines the wave that propagates. The numerical simulation of such problems is thus quite difficult. If the domain is replaced by a finite one, to facilitate numerical computations, then appropriate boundary conditions on the "artificial" boundaries must depend upon the initial data in the discarded region. In this work we derive such boundary conditions, based on the Laplace transform of the linearized problems at ±∞, and illustrate their utility by presenting a numerical solution of Fisher’s equation which has been proposed as a model in genetics

The Effect of Resistance Training in Healthy Adults on Body Fat Percentage, Fat Mass and Visceral Fat: A Systematic Review and Meta-Analysis

Background: Resistance training is the gold standard exercise mode for accrual of lean muscle mass, but the isolated effect of resistance training on body fat is unknown. Objectives: This systematic review and meta-analysis evaluated resistance training for body composition outcomes in healthy adults. Our primary outcome was body fat percentage; secondary outcomes were body fat mass and visceral fat. Design: Systematic review with meta-analysis. Data Sources: We searched five electronic databases up to January 2021. Eligibility Criteria: We included randomised trials that compared full-body resistance training for at least 4 weeks to no-exercise control in healthy adults. Analysis: We assessed study quality with the TESTEX tool and conducted a random-effects meta-analysis, with a subgroup analysis based on measurement type (scan or non-scan) and sex (male or female), and a meta-regression for volume of resistance training and training components. Results: From 11,981 records, we included 58 studies in the review, with 54 providing data for a meta-analysis. Mean study quality was 9/15 (range 6–15). Compared to the control, resistance training reduced body fat percentage by − 1.46% (95% confidence interval − 1.78 to − 1.14, p < 0.0001), body fat mass by − 0.55 kg (95% confidence interval − 0.75 to − 0.34, p < 0.0001) and visceral fat by a standardised mean difference of − 0.49 (95% confidence interval − 0.87 to − 0.11, p = 0.0114). Measurement type was a significant moderator in body fat percentage and body fat mass, but sex was not. Training volume and training components were not associated with effect size. Summary/Conclusions: Resistance training reduces body fat percentage, body fat mass and visceral fat in healthy adults. Study Registration: osf.io/hsk32

Would You Choose to be Happy? Tradeoffs Between Happiness and the Other Dimensions of Life in a Large Population Survey

A large literature documents the correlates and causes of subjective well-being, or happiness. But few studies have investigated whether people choose happiness. Is happiness all that people want from life, or are they willing to sacrifice it for other attributes, such as income and health? Tackling this question has largely been the preserve of philosophers. In this article, we find out just how much happiness matters to ordinary citizens. Our sample consists of nearly 13,000 members of the UK and US general populations. We ask them to choose between, and make judgments over, lives that are high (or low) in different types of happiness and low (or high) in income, physical health, family, career success, or education. We find that people by and large choose the life that is highest in happiness but health is by far the most important other concern, with considerable numbers of people choosing to be healthy rather than happy. We discuss some possible reasons for this preference

Null infinity waveforms from extreme-mass-ratio inspirals in Kerr spacetime

We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large- and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.Comment: 14 pages, 7 figure

Plagiocephaly Perception and Prevention: A Need to Intervene Early to Educate Parents

Background: Plagiocephaly is a condition where the cranium has been malformed because of external forces or premature cranial suture fusion. This study’s objective was to gather and examine data regarding parent and caregiver awareness of plagiocephaly and its potential impact on development as well as to determine their rate of concern for positional flattening. Method: A cross-sectional survey study was conducted. Categorical variables were described by frequency and proportions. The study was conducted across eight outpatient pediatric sites. Approximately 1,100 parents and caregivers were targeted. Inclusion criteria required participants to be willing to answer the questionnaire, to be 18 years of age or older, and to have an infant 12 months of age or younger. Results: There were 404 participants, most of whom were female (89.8%) and 30–39 years of age (61.1%). Nineteen children (4.7%) were reported to have plagiocephaly, torticollis, and/or muscle weakness (PTM). A greater percentage of the participants with a child with PTM knew of positional flattening or plagiocephaly (73.3%) compared to those without (53.8%). The respondents with a child with PTM had a greater concern about plagiocephaly than those without (p = .03). Many of the respondents (65.3%) would use a device designed to prevent plagiocephaly. Conclusion: Many parents and caregivers were unaware of plagiocephaly and its potential impact on facial symmetry. A greater percentage of the participants with a child with PTM knew of positional flattening and also had a greater concern about plagiocephaly than those without

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson

The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f_0(v), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of f_0. We prove that for each f_0 there is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0$is unstable. When$f_0$ is perturbed by an area preserving rearrangement, f_0 will always be stable if the continuous spectrum is only of positive signature, where the signature of the continuous spectrum is defined as in previous work. If there is a signature change, then there is a rearrangement of f_0 that is unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is analogous to Krein's theorem for the continuous spectrum. We prove that if a discrete mode embedded in the continuous spectrum is surrounded by the opposite signature there is an infinitesimal perturbation in C^n norm that makes f_0 unstable. If f_0 is stable we prove that the signature of every discrete mode is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36 pages, 12 figure