Thermodynamic curvature measures interactions

Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln\Omega$ to express the number of states in terms of entropy: $\Omega= \exp(S/k_B)$. The theory's Gaussian approximation is discussed in most statistical mechanics texts. I review work showing how to go beyond the Gaussian approximation by adding covariance, conservation, and consistency. This generalization leads to a fundamentally new object: the thermodynamic Riemannian curvature scalar $R$, a thermodynamic invariant. I argue that $|R|$ is related to the correlation length and suggest that the sign of $R$ corresponds to whether the interparticle interactions are effectively attractive or repulsive.Comment: 29 pages, 7 figures (added reference 27

Embedding initial data for black hole collisions

We discuss isometric embedding diagrams for the visualization of initial data for the problem of the head-on collision of two black holes. The problem of constructing the embedding diagrams is explicitly presented for the best studied initial data, the Misner geometry. We present a partial solution of the embedding diagrams and discuss issues related to completing the solution.Comment: (27pp text, 11 figures

Implement Smart Sensors With Wireless Communication Protocols With Embedded Microcontrollers in a Capstone Project Design

Wireless communication has become popular and widely used in our daily lives. Their applications are: Cellular Wireless for telephone systems, data collection, voice communication, and other mobile or extremely remote devices, Bluetooth for low-power applications in short range and moderate date bandwidth, Proprietary ISM (industrial, scientific, medical) protocols used in open frequency bands from 260 to 470 MHz, 902 to 928 MHz, and 2.4GHz, 802.11/WiFi in wireless data communications, 802.15/ZigBee for mesh networks of sensors and controllers, and Z-Wave for low speed wireless protocol of home electronics devices to intercommunicate using reliable protocol that easily travels through walls, floors, and cabinets1. Sensors with embedded intelligence and integrated with cost effective wireless protocols have been recognized as smart sensors in many applications, such as smart home appliances, home automation, green technology in energy conservation and harvesting, and remote data logging etc2. This application project is implemented in the classification between Proprietary ISM, ZigBee, and Z-Wave wireless applications. It is built based on the MRF24J40MA (2.4GHz RF modules) that follows the IEEE 802.15.4TM-2003 rules7, standards, and software protocols designs with SPI (Serial Peripheral Interface)9 interfacing to a PIC16F877A microcontroller. The project uses three 2.4 GHz RF modules (MRF24J40MA), and three PIC16F877A units hosted in three previously developed low cost PIC microcontroller training systems3. The sensor stations are designed as Slave units and responsible for conditioning and reporting temperature, humidity, and atmospheric pressure. The control unit is categorized as a Master station and responsible for interacting with user/host to decide when, where, and how to report the data to the inquiries. In addition to sensors on the Slaves station, there are assistances from real time clock and external serial EEPROM devices to provide time stamped real time data for future inquiry from the Master. All the communications between the Master and multiple Slaves are through wireless RF signals with customized software protocol designs4

Determination of electromagnetic medium from the Fresnel surface

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is described by an antisymmetric $2\choose 2$-tensor $\kappa$. In this setting, the Tamm-Rubilar tensor density determines a polynomial surface of fourth order in each cotangent space. This surface is called the Fresnel surface and acts as a generalisation of the light-cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speed as a function of direction. Favaro and Bergamin have recently proven that if $\kappa$ has only a principal part and if the Fresnel surface of $\kappa$ coincides with the light cone for a Lorentz metric $g$, then $\kappa$ is proportional to the Hodge star operator of $g$. That is, under additional assumptions, the Fresnel surface of $\kappa$ determines the conformal class of $\kappa$. The purpose of this paper is twofold. First, we provide a new proof of this result using Gr\"obner bases. Second, we describe a number of cases where the Fresnel surface does not determine the conformal class of the original $2\choose 2$-tensor $\kappa$. For example, if $\kappa$ is invertible we show that $\kappa$ and $\kappa^{-1}$ have the same Fresnel surfaces.Comment: 23 pages, 1 figur

Location-dependent threat and associated neural abnormalities in clinical anxiety

Anxiety disorders are characterized by maladaptive defensive responses to distal or uncertain threats. Elucidating neural mechanisms of anxiety is essential to understand the development and maintenance of anxiety disorders. In fMRI, patients with pathological anxiety (ANX, n = 23) and healthy controls (HC, n = 28) completed a contextual threat learning paradigm in which they picked flowers in a virtual environment comprising a danger zone in which flowers were paired with shock and a safe zone (no shock). ANX compared with HC showed 1) decreased ventromedial prefrontal cortex and anterior hippocampus activation during the task, particularly in the safe zone, 2) increased insula and dorsomedial prefrontal cortex activation during the task, particularly in the danger zone, and 3) increased amygdala and midbrain/periaqueductal gray activation in the danger zone prior to potential shock delivery. Findings suggest that ANX engage brain areas differently to modulate context-appropriate emotional responses when learning to discriminate cues within an environment

Speed and sensitivity of phototransduction in Drosophila depend on degree of saturation of membrane phospholipids.

Drosophila phototransduction is mediated via a G-protein-coupled PLC cascade. Recent evidence, including the demonstration that light evokes rapid contractions of the photoreceptors, suggested that the light-sensitive channels (TRP and TRPL) may be mechanically gated, together with protons released by PLC-mediated PIP2 hydrolysis. If mechanical gating is involved we predicted that the response to light should be influenced by altering the physical properties of the membrane. To achieve this, we used diet to manipulate the degree of saturation of membrane phospholipids. In flies reared on a yeast diet, lacking polyunsaturated fatty acids (PUFAs), mass spectrometry showed that the proportion of polyunsaturated phospholipids was sevenfold reduced (from 38 to ∼5%) but rescued by adding a single species of PUFA (linolenic or linoleic acid) to the diet. Photoreceptors from yeast-reared flies showed a 2- to 3-fold increase in latency and time to peak of the light response, without affecting quantum bump waveform. In the absence of Ca(2+) influx or in trp mutants expressing only TRPL channels, sensitivity to light was reduced up to ∼10-fold by the yeast diet, and essentially abolished in hypomorphic G-protein mutants (Gαq). PLC activity appeared little affected by the yeast diet; however, light-induced contractions measured by atomic force microscopy or the activation of ectopic mechanosensitive gramicidin channels were also slowed ∼2-fold. The results are consistent with mechanosensitive gating and provide a striking example of how dietary fatty acids can profoundly influence sensory performance in a classical G-protein-coupled signaling cascade.This research was supported by the Biotechnology and Biological Sciences Research Council (BBSRC; to M.J.O.W. and Q.Z., BBSRC Grant BB/G006865/1 to R.C.H., BB/H013849/1 to M.J., and BBSRC doctoral awards to A.S.R. and S.A.D.), the State Key Laboratory of Cognitive Neuroscience and Learning Open Research Fund (to M.J.), Jane and Aatos Erkko Foundation Fellowship (to M.J.), the Leverhulme Trust Grant (RPG-2012-567 to M.J.), and the UK Medical Research Council (Career Development Award to K.F.).This is the final published version of the article, originally published in the Journal of Neuroscience, February 11, 2015, 35(6): 2731–2746, DOI: 10.1523/JNEUROSCI.1150-14.201

Clock-Comparison Tests of Lorentz and CPT Symmetry in Space

Clock-comparison experiments conducted in space can provide access to many unmeasured coefficients for Lorentz and CPT violation. The orbital configuration of a satellite platform and the relatively large velocities attainable in a deep-space mission would permit a broad range of tests with Planck-scale sensitivity.Comment: 4 page