Non-Markovian Levy diffusion in nonhomogeneous media

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the L\'evy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure

Measuring subdiffusion parameters

We propose a method to extract from experimental data the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_\alpha$ which are defined by means of the relation $=2D_\alpha/\Gamma(1+\alpha) t^\alpha$ where $$ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. Using such a system, we experimentally study a diffusion of glucose and sucrose in a gel solvent. We find a fully analytic solution of the fractional subdiffusion equation with the initial and boundary conditions representing the system under study. Confronting the experimental data with the derived formulas, we show a subdiffusive character of the sugar transport in gel solvent. We precisely determine the parameter $\alpha$, which is smaller than 1, and the subdiffusion coefficient $D_\alpha$.Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.

Elastically and Plastically Foldable Electrothermal Micro‐Origami for Controllable and Rapid Shape Morphing

Integrating origami principles within traditional microfabrication methods can produce shape morphing microscale metamaterials and 3D systems with complex geometries and programmable mechanical properties. However, available micro‐origami systems usually have slow folding speeds, provide few active degrees of freedom, rely on environmental stimuli for actuation, and allow for either elastic or plastic folding but not both. This work introduces an integrated fabrication–design–actuation methodology of an electrothermal micro‐origami system that addresses the above‐mentioned challenges. Controllable and localized Joule heating from electrothermal actuator arrays enables rapid, large‐angle, and reversible elastic folding, while overheating can achieve plastic folding to reprogram the static 3D geometry. Because the proposed micro‐origami do not rely on an environmental stimulus for actuation, they can function in different atmospheric environments and perform controllable multi‐degrees‐of‐freedom shape morphing, allowing them to achieve complex motions and advanced functions. Combining the elastic and plastic folding enables these micro‐origami to first fold plastically into a desired geometry and then fold elastically to perform a function or for enhanced shape morphing. The proposed origami systems are suitable for creating medical devices, metamaterials, and microrobots, where rapid folding and enhanced control are desired.An elastically and plastically foldable micro‐origami is developed and tested to create controllable and functional 3D shape morphing systems with multiple active degrees of freedom. The work demonstrates a versatile design–fabrication–actuation method to achieve rapid folding, enhanced control, and function in different atmospheric environments, enabling applications in microrobots, medical devices, and metamaterials.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163442/2/adfm202003741.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163442/1/adfm202003741-sup-0001-SuppMat.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163442/3/adfm202003741_am.pd

Stationarity-conservation laws for certain linear fractional differential equations

The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.Comment: 28 page

The W51 Giant Molecular Cloud

We present 45"-47" angular resolution maps at 50" sampling of the 12CO and 13CO J=1-0 emission toward a 1.39 deg x 1.33 deg region in the W51 HII region complex. These data permit the spatial and kinematic separation of several spectral features observed along the line of sight to W51, and establish the presence of a massive (1.2 x 10^6 Mo), large (83 pc x 114 pc) giant molecular cloud (GMC), defined as the W51 GMC, centered at (l,b,V) = (49.5 deg, -0.2 deg, 61 km/s). A second massive (1.9 x 10^5 Mo), elongated (136 pc x 22 pc) molecular cloud is found at velocities of about 68 km/s along the southern edge of the W51 GMC. Of the five radio continuum sources that classically define the W51 region, the brightest source at lambda 6cm (G49.5-0.4) is spatially and kinematically coincident with the W51 GMC and three (G48.9-0.3, G49.1-0.4, and G49.2-0.4) are associated with the 68 km/s cloud. Published absorption line spectra indicate that the fifth prominent continuum source (G49.4-0.3) is located behind the W51 molecular cloud. The W51 GMC is among the upper 1% of clouds in the Galactic disk by size and the upper 5-10% by mass. While the W51 GMC is larger and more massive than any nearby molecular cloud, the average H2 column density is not unusual given its size and the mean H2 volume density is comparable to that in nearby clouds. The W51 GMC is also similar to other clouds in that most of the molecular mass is contained in a diffuse envelope that is not currently forming massive stars. We speculate that much of the massive star formation activity in this region has resulted from a collision between the 68 km/s cloud and the W51 GMC.Comment: Accepted for publication by the Astronomical Journal. 21 pages, plus 7 figures and 1 tabl

Levi-Civita cylinders with fractional angular deficit

The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index {\alpha}. When the fractional index is continued into the negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder and in an Israel shell.Comment: 5 figure

Hyperbolic subdiffusive impedance

We use the hyperbolic subdiffusion equation with fractional time derivatives (the generalized Cattaneo equation) to study the transport process of electrolytes in media where subdiffusion occurs. In this model the flux is delayed in a non-zero time with respect to the concentration gradient. In particular, we obtain the formula of electrochemical subdiffusive impedance of a spatially limited sample in the limit of large and of small pulsation of the electric field. The boundary condition at the external wall of the sample are taken in the general form as a linear combination of subdiffusive flux and concentration of the transported particles. We also discuss the influence of the equation parameters (the subdiffusion parameter and the delay time) on the Nyquist impedance plots.Comment: 10 pages, 5 figure

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

Operationalizing NIMH Research Domain Criteria (RDoC) in naturalistic clinical settings

Recently, the National Institute of Mental Health (NIMH) introduced the Research Domain Criteria (RDoC) initiative to address two major challenges facing the field of psychiatry: (1) the lack of new effective personalized treatments for psychiatric disorders, and (2) the limitations associated with categorically-defined psychiatric disorders. While the potential of RDoC to revolutionize personalized psychiatric medicine and psychiatric nosology has been acknowledged, it is unclear how to implement RDoC in naturalistic clinical settings as part of routine outcomes research. In this paper we present the major RDoC principles and then show how these principles are operationalized in the Menninger Clinic’s McNair Initiative for Neuroscience Discovery-Menninger & Baylor College of Medicine (MIND-MB) study. We discuss how RDoC-informed outcomes-based assessment in clinical settings can transform personalized clinical care through multimodal treatments

Impact of Spacecraft Shielding on Direct Ionization Soft Error Rates

No abstract availabl