The philosophical problem of free will has endured through centuries of enquiry. There is reason to believe that new factors must be integrated into the analysis in order to make progress. In the current physicalist approach, emergence and the physical limits of information representation are found to play crucial roles in the ontological dependence of volitional processes on their neural basis. The commonly invoked characterization of free will as ‘being able to act differently’ is shown to be problematic and is reframed as a more precise explicatum conducive to formal analysis. Subsequently, it is found that the mind operates as an ontologically open system — a causal high-level entity whose dynamics resist reduction to the states of its associated low-level neural systems, even under conditions of physical closure. An affirmative stance on free will for conscious agents is outlined.

Flipped classroom pedagogics has become a widely used approach within blended learning. The aim of the present study is to add students’ perspectives on the flipped classroom as used as a pedagogical method in a Swedish upper secondary school. In this qualitative study, eight students participated in focus group interviews. Problems were found both for neurotypical students as well as for a neurodiverse student. Unless special care is taken, students with neurodiversity may not be given equal opportunities for learning, in conflict with Swedish school legislation. Issues are discussed that need to be addressed when introducing flipped classroom course design at high school level.

A fully spectral multi-domain method has been developed and applied to three applications within ideal MHD, compressible Navier-Stokes, and a two-fluid plasma turbulence model named the Weiland model. The time-spectral method employed is the Generalized Weighted Residual Method (GWRM), where all domains such as space, time, and parameter space are spectrally decomposed with Chebyshev polynomials. The spectral decomposition of the temporal domain allows the GWRM to reach spectral accuracy in all dimensions. The GWRM linear/nonlinear algebraic equations are solved using an Anderson Acceleration (AA) method and a newly developed Quasi Semi-Implicit root solver (Q-SIR). Up to 85% improved convergence rate was obtained for Q-SIR as compared to AA and in certain cases only Q-SIR converged. In the most challenging simulations, featuring steep gradients, the GWRM converged for time intervals roughly two times larger than typical time steps for explicit time-marching schemes, being limited by the CFL condition. Time intervals up to 70 times larger than those of explicit time-marching schemes were used in smooth regions. Furthermore, the most computationally expensive algorithm, namely the product of two Chebyshev series, has been GPU accelerated with speedup gains of several thousands compared to a CPU.

Time-spectral methods may feature substantial advantages over time-stepping solvers for solution of initial-value ODEs and PDEs, but their efficiency depends on the smoothness of the solution. We present two methods to overcome this problem. The first involves transforming the differential equation to an equation for a new variable, related to the time-integrated solution, before applying the solution algorithm. In the second method, a procedure for transformation to exact differential equations of a running average is outlined. Examples of solution of stiff problems and problems with multiple time scales are presented, employing the time-spectral Generalized Weighted Residual Method (GWRM). It is found that the smoothing algorithms have a significant positive effect on convergence.

The mind–body problem is analyzed in a physicalist perspective. By combining the concepts of emergence and algorithmic information theory in a thought experiment, employing a basic nonlinear process, it is shown that epistemologically emergent properties may develop in a physical system. Turning to the signi cantly more com- plex neural network of the brain it is subsequently argued that consciousness is epis- temologically emergent. Thus reductionist understanding of consciousness appears not possible; the mind–body problem does not have a reductionist solution. The ontologically emergent character of consciousness is then identi ed from a com- binatorial analysis relating to universal limits set by quantum mechanics, implying that consciousness is fundamentally irreducible to low-level phenomena.

The mind-body problem is one of the most enigmatic issues in philosophy that has yet to be resolved. Professor Jan Scheffel from KTH Royal Institute of Technology, Sweden analyses the mind–body problem from a physicalist perspective. He finds that consciousness is epistemologically emergent and shows that this result overlaps with the problem of free will. If a theory for consciousness could be constructed, free will would not exist. Professor Scheffel discloses that the mind–body problem cannot be solved reductionistically and evolves the notion of emergence in an argument for free will.

Läroböcker i vektoranalys är ofta kortfattade. Denna bok, som kan användas för såväl grundläggande som mer avancerade kurser, behandlar ämnet mer utförligt.

Bokens pedagogiska idé skiljer sig markant från liknande böcker. Återkommande inslag är tydligt formulerade problem som fångar det centrala i vektoranalysen. Syftet med problemen är dels att väcka intresse för den teori och de metoder som behandlas, dels att stimulera till aktivt lärande. 

Boken innehåller genomarbetade och lättillgängliga teoriavsnitt - som börjar med grundläggande vektoralgebra och slutar med kartesiska tensorer och en härledning av vektoranalysens huvudsats. Dessutom ingår ett stort antal konkreta exempel och många tillämpningar. Sist i varje kapitel finns en sammanfattning av den viktigaste teorin och övningsuppgifter med svar. Ledningar och fullständiga lösningar finns på Libers webbplats. Där finns även ett Appendix med tillämpningar.

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling. Program summary: Program Title: Time-adaptive GWRM Lorenz 1984 Program Files doi: http://dx.doi.org/10.17632/4nxfyjj7nv.1 Licensing provisions: MIT Programming language: Maple Nature of problem: Ordinary differential equations with varying degrees of complexity are routinely solved with numerical methods. The set of ODEs pertaining to chaotic systems, for instance those related to numerical weather prediction (NWP) models, are highly sensitive to initial conditions and unwanted errors. To accurately solve ODEs such as the Lorenz equations (E. N. Lorenz, Tellus A 36 (1984) 98–110), small time steps are required by traditional time-stepping methods, which can be a limiting factor regarding the efficiency, accuracy, and stability of the computations. Solution method: The Generalized Weighted Residual Method, being a time-spectral algorithm, seeks to increase the time intervals in the computation without degrading the efficiency, accuracy, and stability. It does this by postulating a solution ansatz as a sum of weighted Chebyshev polynomials, in combination with the Galerkin method, to create a set of linear/non-linear algebraic equations. These algebraic equations are then solved iteratively using a Semi Implicit Root solver (SIR), which has been chosen due to its enhanced global convergence properties. Furthermore, to achieve a desired accuracy across the entire domain, a time-adaptive algorithm has been developed. By evaluating the magnitudes of the Chebyshev coefficients in the time dimension of the solution ansatz, the time interval can either be decreased or increased.

We analyse a novel subdomain scheme for time-spectral solution of initial-value partial differential equations. In numerical modelling spectral methods are commonplace for spatially dependent systems, whereas finite difference schemes are typically applied for the temporal domain. The Generalized Weighted Residual Method (GWRM) is a fully spectral method that spectrally decomposes all specified domains, including the temporal domain, using multivariate Chebyshev polynomials. The Common Boundary-Condition method (CBC) here proposed is a spatial subdomain scheme for the GWRM. It solves the physical equations independently from the global connection of subdomains in order to reduce the total number of modes. Thus, it is a condensation procedure in the spatial domain that allows for a simultaneous global temporal solution. It is here evaluated against the finite difference methods of Crank-Nicolson and Lax-Wendroff for two example linear PDEs. The CBC-GWRM is also applied to the linearised ideal magnetohydrodynamic (MHD) equations for a screw pinch equilibrium. The growth rate of the most unstable mode was efficiently computed with an error <0.1%.