The Lanczos potential for Weyl-candidate tensors exists only in four dimensions

We prove that a Lanczos potential L_abc for the Weyl candidate tensor W_abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for L_abc and W_abcd, then this system's integrability conditions should be checked; and so on. When we find a non-trivial condition involving only W_abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L_abc.Comment: 11 pages, LaTeX, Heavily revised April 200

On the Modulation Equations and Stability of Periodic GKdV Waves via Bloch Decompositions

In this paper, we complement recent results of Bronski and Johnson and of Johnson and Zumbrun concerning the modulational stability of spatially periodic traveling wave solutions of the generalized Korteweg-de Vries equation. In this previous work it was shown by rigorous Evans function calculations that the formal slow modulation approximation resulting in the Whitham system accurately describes the spectral stability to long wavelength perturbations. Here, we reproduce this result without reference to the Evans function by using direct Bloch-expansion methods and spectral perturbation analysis. This approach has the advantage of applying also in the more general multi-periodic setting where no conveniently computable Evans function is yet devised. In particular, we complement the picture of modulational stability described by Bronski and Johnson by analyzing the projectors onto the total eigenspace bifurcating from the origin in a neighborhood of the origin and zero Floquet parameter. We show the resulting linear system is equivalent, to leading order and up to conjugation, to the Whitham system and that, consequently, the characteristic polynomial of this system agrees (to leading order) with the linearized dispersion relation derived through Evans function calculation.Comment: 19 pages

A hardware DC motor emulator

Much work have been done lately to develop complex motor control systems. However they always rely on a physical drive/motor/encoder setup for experimental results. This paper presents a hardware DC motor emulator that can be synthesized to FPGAs. The emulator is intended to replace an actual DC motor during the development phase of motor controllers. A torque based input is required and incremental encoder output is provided, so this model can replace both the DC motor, and its power driver without modifications to the motor control system. The proposed emulator is able to reach a clock frequency of hundreds of megahertz and uses very few logic resources in current FPGA technologies. The hardware can be parameterized at synthesis time to make the model suitable for specific needs

A local potential for the Weyl tensor in all dimensions

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late

Generalized hydrodynamics and extended irreversible thermodynamics

The thermodynamic implications of the first deviations with respect to the classical hydrodynamic behavior in high-frequency, short-wavelength phenomena are examined. The constitutive equations arising from an extended irreversible-thermodynamic formalism taking into account spatial inhomogeneities in the space of state variables are compared with those used in generalized hydrodynamics. The so-called exponential model for the memory function of the transverse-velocity correlation function is derived under the assumptions of extended irreversible thermodynamics only. Furthermore, it is also shown how more complicated memory functions can be derived. The results are carefully analyzed and compared with some microscopic derivations

A digital health intervention for cardiovascular disease management in primary care (CONNECT) randomized controlled trial

Digital health applications (apps) have the potential to improve health behaviors and outcomes. We aimed to examine the effectiveness of a consumer web-based app linked to primary care electronic health records (EHRs). CONNECT was a multicenter randomized controlled trial involving patients with or at risk of cardiovascular disease (CVD) recruited from primary care (Clinical Trial registration ACTRN12613000715774). Intervention participants received an interactive app which was pre-populated and refreshed with EHR risk factor data, diagnoses and, medications. Interactive risk calculators, motivational messages and lifestyle goal tracking were also included. Control group received usual health care. Primary outcome was adherence to guideline-recommended medications (≥80% of days covered for blood pressure (BP) and statin medications). Secondary outcomes included attainment of risk factor targets and eHealth literacy. In total, 934 patients were recruited; mean age 67.6 (±8.1) years. At 12 months, the proportion with >80% days covered with recommended medicines was low overall and there was no difference between the groups (32.8% vs. 29.9%; relative risk [RR] 1.07 [95% CI, 0.88–1.20] p = 0.49). There was borderline improvement in the proportion meeting BP and LDL targets in intervention vs. control (17.1% vs. 12.1% RR 1.40 [95% CI, 0.97–2.03] p = 0.07). The intervention was associated with increased attainment of physical activity targets (87.0% intervention vs. 79.7% control, p = 0.02) and e-health literacy scores (72.6% intervention vs. 64.0% control, p = 0.02). In conclusion, a consumer app integrated with primary health care EHRs was not effective in increasing medication adherence. Borderline improvements in risk factors and modest behavior changes were observed

A digital health intervention for cardiovascular disease management in primary care (CONNECT) randomized controlled trial

Digital health applications (apps) have the potential to improve health behaviors and outcomes. We aimed to examine the effectiveness of a consumer web-based app linked to primary care electronic health records (EHRs). CONNECT was a multicenter randomized controlled trial involving patients with or at risk of cardiovascular disease (CVD) recruited from primary care (Clinical Trial registration ACTRN12613000715774). Intervention participants received an interactive app which was pre-populated and refreshed with EHR risk factor data, diagnoses and, medications. Interactive risk calculators, motivational messages and lifestyle goal tracking were also included. Control group received usual health care. Primary outcome was adherence to guideline-recommended medications (≥80% of days covered for blood pressure (BP) and statin medications). Secondary outcomes included attainment of risk factor targets and eHealth literacy. In total, 934 patients were recruited; mean age 67.6 (±8.1) years. At 12 months, the proportion with >80% days covered with recommended medicines was low overall and there was no difference between the groups (32.8% vs. 29.9%; relative risk [RR] 1.07 [95% CI, 0.88–1.20] p = 0.49). There was borderline improvement in the proportion meeting BP and LDL targets in intervention vs. control (17.1% vs. 12.1% RR 1.40 [95% CI, 0.97–2.03] p = 0.07). The intervention was associated with increased attainment of physical activity targets (87.0% intervention vs. 79.7% control, p = 0.02) and e-health literacy scores (72.6% intervention vs. 64.0% control, p = 0.02). In conclusion, a consumer app integrated with primary health care EHRs was not effective in increasing medication adherence. Borderline improvements in risk factors and modest behavior changes were observed