Motion Capture of Phase Change Transitions During Insight Problem Solving

Insight problem solving refers to the phenomenon of experiencing a sudden flash of insight when discovering novelproblem solving strategies. This sudden transition in thinking suggests a phase change in human cognition as an emergentproperty of the self-organizing complex system of coupled neural activations. In our study, we developed a method of measuringthis phase change within an embodied cognition paradigm. We used 3D motion capture to measure the precise body movementsof 21 participants at 120 Hz resolution while they solved 3 different types of insight problems. We analyzed a sliding time seriesof postural sway and head displacement using recurrence quantification and spectral analyses to determine changes in entropyin the participants’ movements. These measures allow us to make inferences about changes in level of self-organization as theparticipant’s neural activation transitions from one state to another

Mapping Atomic Motions with Electrons: Toward the Quantum Limit to Imaging Chemistry

Recent advances in ultrafast electron and X-ray diffraction have pushed imaging of structural dynamics into the femtosecond time domain, that is, the fundamental time scale of atomic motion. New physics can be reached beyond the scope of traditional diffraction or reciprocal space imaging. By exploiting the high time resolution, it has been possible to directly observe the collapse of nearly innumerable possible nuclear motions to a few key reaction modes that direct chemistry. It is this reduction in dimensionality in the transition state region that makes chemistry a transferable concept, with the same class of reactions being applicable to synthetic strategies to nearly arbitrary levels of complexity. The ability to image the underlying key reaction modes has been achieved with resolution to relative changes in atomic positions to better than 0.01 Å, that is, comparable to thermal motions. We have effectively reached the fundamental space-time limit with respect to the reaction energetics and imaging the acting forces. In the process of ensemble measured structural changes, we have missed the quantum aspects of chemistry. This perspective reviews the current state of the art in imaging chemistry in action and poses the challenge to access quantum information on the dynamics. There is the possibility with the present ultrabright electron and X-ray sources, at least in principle, to do tomographic reconstruction of quantum states in the form of a Wigner function and density matrix for the vibrational, rotational, and electronic degrees of freedom. Accessing this quantum information constitutes the ultimate demand on the spatial and temporal resolution of reciprocal space imaging of chemistry. Given the much shorter wavelength and corresponding intrinsically higher spatial resolution of current electron sources over X-rays, this Perspective will focus on electrons to provide an overview of the challenge on both the theory and the experimental fronts to extract the quantum aspects of molecular dynamics

Bubble Expansion and the Viability of Singlet-Driven Electroweak Baryogenesis

The standard picture of electroweak baryogenesis requires slowly expanding bubbles. This can be difficult to achieve if the vacuum expectation value of a gauge singlet scalar field changes appreciably during the electroweak phase transition. It is important to determine the bubble wall velocity in this case, since the predicted baryon asymmetry can depend sensitively on its value. Here, this calculation is discussed and illustrated in the real singlet extension of the Standard Model. The friction on the bubble wall is computed using a kinetic theory approach and including hydrodynamic effects. Wall velocities are found to be rather large ($v_w \gtrsim 0.2$) but compatible with electroweak baryogenesis in some portions of the parameter space. If the phase transition is strong enough, however, a subsonic solution may not exist, precluding non-local electroweak baryogenesis altogether. The results presented here can be used in calculating the baryon asymmetry in various singlet-driven scenarios, as well as other features related to cosmological phase transitions in the early Universe, such as the resulting spectrum of gravitational radiation.Comment: v2: matches version published in JHE

Ultra-relativistic oscillon collisions

In this short note we investigate the ultra-relativistic collisions of small amplitude oscillons in 1+1 dimensions. Using the amplitude of the oscillons and the inverse relativistic boost factor $\gamma^{-1}$ as the perturbation variables, we analytically calculate the leading order spatial and temporal phase shifts, and the change in the amplitude of the oscillons after the collisions. At leading order, we find that only the temporal phase shift receives a nonzero contribution, and that the collision is elastic. This work is also the first application of the general kinematic framework for understanding ultra-relativistic collisions (arXiv:1308.0606) to intrinsically time-dependent solitons.Comment: 12 pages, 3 figures, version 2, added one reference and matching the version to appear on PR

Bringing forth mathematical concepts: signifying sensorimotor enactment in fields of promoted action

Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the methodological utility of design-research as an approach to such theory development. Building on constructs from ecological psychology, cultural anthropology, studies of motor-skill acquisition, and somatic awareness practices, we develop the notion of an “instrumented field of promoted action”. Children operating in this field first develop environmentally coupled motor-action coordinations. Next, we introduce into the field new artifacts. The children adopt the artifacts as frames of action and reference, yet in so doing they shift into disciplinary semiotic systems. We exemplify our thesis with two selected excerpts from our videography of Grade 4–6 volunteers participating in task-based clinical interviews centered on the Mathematical Imagery Trainer for Proportion. In particular, we present and analyze cases of either smooth or abrupt transformation in learners’ operatory schemes. We situate our design framework vis-à-vis seminal contributions to mathematics education research

Deconstructing the glass transition through critical experiments on colloids

The glass transition is the most enduring grand-challenge problem in contemporary condensed matter physics. Here, we review the contribution of colloid experiments to our understanding of this problem. First, we briefly outline the success of colloidal systems in yielding microscopic insights into a wide range of condensed matter phenomena. In the context of the glass transition, we demonstrate their utility in revealing the nature of spatial and temporal dynamical heterogeneity. We then discuss the evidence from colloid experiments in favor of various theories of glass formation that has accumulated over the last two decades. In the next section, we expound on the recent paradigm shift in colloid experiments from an exploratory approach to a critical one aimed at distinguishing between predictions of competing frameworks. We demonstrate how this critical approach is aided by the discovery of novel dynamical crossovers within the range accessible to colloid experiments. We also highlight the impact of alternate routes to glass formation such as random pinning, trajectory space phase transitions and replica coupling on current and future research on the glass transition. We conclude our review by listing some key open challenges in glass physics such as the comparison of growing static lengthscales and the preparation of ultrastable glasses, that can be addressed using colloid experiments.Comment: 137 pages, 45 figure

Dynamics of viscoelastic snap-through

We study the dynamics of snap-through when viscoelastic effects are present. To gain analytical insight we analyse a modified form of the Mises truss, a single-degree-of-freedom structure, which features an `inverted' shape that snaps to a `natural' shape. Motivated by the anomalously slow snap-through shown by spherical elastic caps, we consider a thought experiment in which the truss is first indented to an inverted state and allowed to relax while a specified displacement is maintained; the constraint of an imposed displacement is then removed. Focussing on the dynamics for the limit in which the timescale of viscous relaxation is much larger than the characteristic elastic timescale, we show that two types of snap-through are possible: the truss either immediately snaps back over the elastic timescale or it displays `pseudo-bistability', in which it undergoes a slow creeping motion before rapidly accelerating. In particular, we demonstrate that accurately determining when pseudo-bistability occurs requires the consideration of inertial effects immediately after the indentation force is removed. Our analysis also explains many basic features of pseudo-bistability that have been observed previously in experiments and numerical simulations; for example, we show that pseudo-bistability occurs in a narrow parameter range at the bifurcation between bistability and monostability, so that the dynamics is naturally susceptible to critical slowing down. We then study an analogous thought experiment performed on a continuous arch, showing that the qualitative features of the snap-through dynamics are well captured by the truss model. In addition, we analyse experimental and numerical data of viscoelastic snap-through times reported in the literature. Combining these approaches suggests that our conclusions may also extend to more complex viscoelastic structures used in morphing applications.Comment: Main text 37 pages, Appendices 13 page