Cartesian Modes Research Articles

Religious Reformation and Ethical Transformation in the Hatata of Zera Yaeqob and Welda Heywat

Abstract The Hatatas of Zera Yaeqob and Welda Heywat are seen as the precursors of a written Ethiopian philosophy. Commentators on these texts such as Claude Sumner and Teodros Kiros argue that, one is able to locate the Cartesian mode of subjectivity in the Hatatas. Against this, this paper argues that the form of subjectivity found in the Hatatas of Zera Yaeqob and Welda Heywat is not fully demythologized and dwells in the background of religious authority, and therefore should not be identified with the Cartesian conception of the human subject. Alternatively, I argue that the goal of the Hatatas is attaining religious reformation. The form of subjectivity found in the Hatatas is founded on communal life and religious experience. The paper concludes that the Hatatas of Zera Yaeqob and Welda Heywat should be read as a call for religious renewal and ethical transformation.

Recipe for Inferring Subsurface Solar Magnetism via Local Mode Coupling Using Slepian Basis Functions

Direct seismic imaging of subsurface flow, sound speed, and magnetic field is crucial for predicting flux-tube emergence on the solar surface, an important ingredient for space weather. The sensitivity of helioseismic mode-amplitude cross-correlation to p- and f-mode oscillations enables formal inversion of such subphotospheric perturbations. It is well known that such problems are written in the form of an integral equation that connects the perturbations to the observations via sensitivity kernels. While the sensitivity kernels for flow and sound speed have been known for decades and have been used extensively, formulating kernels for general magnetic perturbations had been elusive. A recent study proposed sensitivity kernels for Lorentz stresses corresponding to global magnetic fields of general geometry. The present study is devoted to proposing kernels for inferring Lorentz stresses as well as the solenoidal magnetic field in a local patch on the Sun via Cartesian mode coupling. Moreover, for the first time in solar physics, Slepian functions are employed to parameterize perturbations in the horizontal dimension. This is shown to increase the number of data constraints in the inverse problem, implying an increase in the precision of inferred parameters. This paves the path to reliably imaging subsurface solar magnetic features in, e.g., supergranules and (emerging) active regions.

Beckett and Buddhism

Beckett and Buddhism

On Being a Thomist: Cornelius Ernst's Meta-Theology

AbstractThomism is a contested category that exhibits considerable plasticity in its application. An examination of the role played by such invocations of proper names in contemporary theological discourse indicates the importance of textual accessibility and engagement. The role played by texts is examined in terms of an often-elided distinction between ‘intelligibility’ and ‘readability’, with the former aligned with propositional contents and the latter a more expansive attentiveness to the text's performative operations. The historical remoteness of Aquinas coupled with the importation into theology of secularised reading strategies is seen to have alienated the full readability of Aquinas's texts. Acting against Cartesian modes of reading, Cornelius Ernst's re-performance of Thomistic pedagogy as ‘engaged contemplation’ is concerned to enact a horizon of meaning within which Aquinas's texts retain enduring readability. This article develops Ernst's Thomistic meta-theology into an account of Thomism as ‘meta-reading’. On this account, authentic Thomism involves the intentional cultivation of a total human culture, within which the inherently theological discipline of textual engagement exercises a quasi-liturgical function.

Sampling microcanonical ensembles of trajectories using harmonic approximation in internal coordinates.

In this paper, we modify quasiclassical harmonic sampling of microcanonical ensembles of trajectories by using the curvilinear internal coordinates. The harmonic approximation in the curvilinear normal coordinates provides a more realistic description of the PES than in the conventional rectilinear ones at finite displacements. Therefore, the sampling of vibrations in the internal coordinates significantly improves the quality of the sampling in a block-box fashion, providing more realistic displacements and reducing the errors in the potential energy. In particular, the sampling of large-amplitude torsion vibrations, which is non-realistic in the Cartesian modes, becomes accurate or acceptable in the curvilinear modes.

Cartesian Modes and The Simplicity of Mind

AbstractMalebranche argues that we lack a clear idea of the mind because we cannot, even in principle, derive all the possible modes of mind solely from the idea of thought. But we can, in principle, derive all the possible modes of body from the idea of extension. Therefore, there is epistemic asymmetry between our ideas of mind and body. I offer a defense of Descartes whereby he can assert that we have a clear idea of mind despite this asymmetry. I argue that he can do this by distinguishing the simplicity of mind from the divisibility of body.

Optimized Torsion-Angle Normal Modes Reproduce Conformational Changes More Accurately Than Cartesian Modes

We present what to our knowledge is a new method of optimized torsion-angle normal-mode analysis, in which the normal modes move along curved paths in Cartesian space. We show that optimized torsion-angle normal modes reproduce protein conformational changes more accurately than Cartesian normal modes. We also show that orthogonalizing the displacement vectors from torsion-angle normal-mode analysis and projecting them as straight lines in Cartesian space does not lead to better performance than Cartesian normal modes. Clearly, protein motion is more naturally described by curved paths in Cartesian space.

Effect of variable fishing strategy on fisheries under changing effort and pressure: An agent-based model application

An agent-based model was used to evaluate the response of a two-species fish community to fishing boat exploration strategies, namely: boats following high-yield boats (Cartesian); boats fishing at random sites (stochast-random); and boats fishing at least exploited sites (stochast-pressure). At low fishing pressure, the stochast-random mode yielded a high average catch per boat while sustaining fish biomass. At high fishing pressure, the Cartesian mode was more effective. For the Cartesian strategy, fish biomass exhibited four distinct behaviors with increasing number of boats. In the first phase, the fish biomass dropped with increasing number of boats due to a corresponding rise in biomass extraction. Rapid exploitation occurred in the second phase, when two or more boats occupied the same initial area, that led to the faster abandonment of those sites which then underwent biomass recovery. In the third phase, adding more boats resulted in a fluctuating stock biomass, where the combined effects of initial spatial distribution of boats and rapid localization led to either full stock recovery when boats were eventually confined to a single location due to spillovers, or stock extirpation when the entire area became fully occupied. Beyond the third phase, stock extirpation was assured. In order to break the pattern of localization (bandwagon effect), we introduced stochast-random intruders in a Cartesian-dominated fishery. Adding a single intruder changed the patchy-structured stock biomass pattern of a purely Cartesian fishery to a uniformly explored stock biomass pattern because of the additional spatial information provided by the intruder. Consequently, the average catch per boat increased but at the expense of a disproportionate decline in equilibrium biomass.

Bias-free separation of internal and overall motion of biomolecules.

Collective internal motions are known to be important for the function of biological macromolecules. It has been discussed in the past whether the application of superimposing algorithms to remove the overall motion from a structural ensemble introduces artificial correlations between distant atoms. Here we present a new method to eliminate residual rotation and translation from cartesian modes derived from a normal mode analysis or from a principal component analysis. Bias-free separation is based on the idea that the addition of modes of pure rotation/translation can compensate the residual overall motion. Removal of overall motion must reduce the "total amount of motion" (TAM) in the mode. Our algorithm allows to back-calculate revised covariance matrices. The approach was applied to two model systems that show residual overall motion, when analyzed using all atoms as reference for the superimposing algorithm. In both cases, our algorithm was capable of eliminating residual covariances caused by the overall motion, while retaining internal covariances even for very distant atoms. A structural ensemble obtained for a 13-ns molecular dynamics simulation of the protein Ribonuclease T1 showed a covariance matrix of the corrected modes with significantly sharper contours after applying the bias-free separation.

An efficient method to analyze the H-plane waveguide junction circulator with a ferrite sphere

This paper presents an approximate, but efficient field treatment of the new easy-to-fabricate ferrite-sphere-based H-plane waveguide circulator for potentially low-cost millimeter-wave communication systems. A new three-dimensional modeling strategy using a self-inconsistent mixed-coordinates-based mode-matching technique is developed, i.e., the solutions of the Helmholtz wave equations in the ferrite sphere and in the surrounding areas are deduced in the form of infinite summation of spherical, cylindrical, and general Cartesian modes, respectively. The point-matching method is then used on the interface between the ferrite sphere and air within the cylindrical junction, as well as the interface between the junction and waveguides to numerically obtain the coefficients of different orders of basis functions of the field. Therefore, the field distributions, as well as the characteristics of the circulator, are numerically calculated and good agreement is observed between the numerical results and measured data.

Analysis of the H-Plane T-Junction Millimeter Wave Waveguide Circulator with a Ferrite Sphere

This paper presents an approximate but efficient field treatment of the new easy-to-fabricate ferrite sphere based H-plane waveguide circulator for potentially low-cost millimeter wave communication systems. A new three-dimension modeling strategy using a self-inconsistent mixed coordinates based mode matching technique is developed, i.e. the solutions of the Helmholz wave equations in the ferrite sphere and in the surrounding areas are deduced in the form of infinite summation of spherical, cylindrical and general Cartesian modes respectively. The point matching method is then used on the interface to numerically obtain the coefficients of different orders basis functions of the field. Therefore, the field distributions as well as the characteristics of the circulator are numerically calculated and the good agreement is observed between the numerical results and the measured data.

Bodies of Knowledge: Beyond Cartesian Views of Persons, Selves and Mind

In this piece, I argue against the Cartesian trend of seeing persons, selves and mind as something distinct from the body. It is claimed that Descartes realized the importance of the link between body and mind, but never pursued this connection, and this then becomes the aim of the paper. Another effect of Cartesian modes of thinking is to divorce human knowledge from its material contexts, driving a wedge between mind and matter. Some forms of social constructionism appear to fall into this latter trap and instead I argue for a view of persons as embodied beings whose selves are intimately connected to the body. Using the work of Bourdieu, Elias, Merleau‐Ponty, and Ilyenkov, I also suggest that thought cannot be disengaged from a human body active in its world and that knowledge not only partly separates us from the materiality of existence, but connects us to it in deeper ways, as another dimension of human existence. Human beings can then be regarded as bodies of knowledge – active thinkers and persons engaged with the multi‐dimensional world around them and capable of producing change.

Stochastic dynamics of n-nonane and related molecules in solution compared with nuclear magnetic resonance coupled relaxation times

The motion of chain molecules in solution has been analyzed using both generalized Langevin equation (GLE) and ordinary Langevin equation (OLE) simulations. A numerical algorithm for solving the GLEs is developed in which the integrations over various forces have been performed explicitly. It is shown in the GLE simulations that the motion of chain segments is correlated closely with solvent relaxation giving significantly reduced friction forces. At temperatures higher than 233 K, a hydrodynamic description with a structure relaxation mode in the solvent (diglyme) is sufficient to yield Cartesian correlation times in good agreement with the NMR coupled relaxation results on n-nonane. The relative contributions of both overall tumbling and internal motion to the Cartesian and end-to-end direction relaxation and the possible couplings of these two motions are analyzed by calculating apparent activation energies for various motional modes and by using a harmonic approximation. It is found that the OLE model underestimates the contribution of internal motion to the relaxation of local Cartesian modes. The finite structural relaxation rate in the solvent can substantially alter not only the correlation times, but the dynamic features of the relevant relaxation processes in a full GLE calculation. In particular, it is shown that the short-time decay of the Cartesian correlation functions is underdamped oscillation in contrast with the overdamped behavior found from the OLE simulations.

Power Output of a Point Source Exciting a Single Cartesian Mode

When a point source radiates steadily in a rectangular enclosure and excites one mode only, its power output W depends strongly on its position. Distribution functions for W are found when the source is positioned randomly, and an axial, tangential, or oblique mode is excited. The functions for these three cases form a consistent family of curves, whose shapes are controlled by the mode shapes. The space-averaged value of W, i.e., the average for all source positions in the enclosure, does not equal the free-field value W0, but depends on the modal damping. The value of W0 can be derived from sound-pressure measurements, however. The results are derived theoretically, and checked by a Monte Carlo procedure. Some experimental data which confirm the theoretical results are given for a small source driving an axial mode in a reverberation chamber. The work has application to standard methods of measuring the sound power output of a source.