There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Thank you for reading principles of optics electromagnetic theory of propagation interference and diffraction of light. As you may know, people have search hundreds times for their favorite novels like this principles of optics electromagnetic theory of propagation interference and diffraction of light, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they are facing with some infectious bugs inside their computer.

Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

Dynamic atomic force microscopy methods

Mechanical interactions are fundamental to biology. Mechanical forces of chemical origin determine motility and adhesion on the cellular scale, and govern transport and affinity on the molecular scale. Biological sensing in the mechanical domain provides unique opportunities to measure forces, displacements and mass changes from cellular and subcellular processes. Nanomechanical systems are particularly well matched in size with molecular interactions, and provide a basis for biological probes with single-molecule sensitivity. Here we review micro- and nanoscale biosensors, with a particular focus on fast mechanical biosensing in fluid by mass- and force-based methods, and the challenges presented by non-specific interactions. We explain the general issues that will be critical to the success of any type of next-generation mechanical biosensor, such as the need to improve intrinsic device performance, fabrication reproducibility and system integration. We also discuss the need for a greater understanding of analyte–sensor interactions on the nanoscale and of stochastic processes in the sensing environment.

Comparative advantages of mechanical biosensors

The advances in micro- and nanofabrication technologies enable the preparation of increasingly smaller mechanical transducers capable of detecting the forces, motion, mechanical properties and masses that emerge in biomolecular interactions and fundamental biological processes. Thus, biosensors based on nanomechanical systems have gained considerable relevance in the last decade. This review provides insight into the mechanical phenomena that occur in suspended mechanical structures when either biological adsorption or interactions take place on their surface. This review guides the reader through the parameters that change as a consequence of biomolecular adsorption: mass, surface stress, effective Young's modulus and viscoelasticity. The mathematical background needed to correctly interpret the output signals from nanomechanical biosensors is also outlined here. Other practical issues reviewed are the immobilization of biomolecular receptors on the surface of nanomechanical systems and methods to attain that in large arrays of sensors. We then describe some relevant realizations of biosensor devices based on nanomechanical systems that harness some of the mechanical effects cited above. We finally discuss the intrinsic detection limits of the devices and the limitation that arises from non-specific adsorption.

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Biosensors based on nanomechanical systems

Force curves taken during a load–unload cycle show the presence of a hysteresis loop. The area enclosed by the loop is used to measure the energy dissipated by the tip-sample interaction in tapping-mode scanning force microscopy. The values of the energy loss obtained from force curves are compared with the results derived from a model based on phase shift measurements. The agreement obtained between both methods demonstrates that for the same operating conditions, the higher the phase shift the larger the amount of energy dissipated by the tip-sample interaction. It also confirms the prediction that phase-contrast images can only arise if there are tip-sample inelastic interactions.

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Relationship between phase shift and energy dissipation in tapping-mode scanning force microscopy

The dependence of phase contrast in tapping-mode scanning force microscopy on elastic and inelastic interactions is studied. The cantilever–tip ensemble is simulated as a driven, damped harmonic oscillator. It is found that for tip–sample elastic interactions, phase contrast is independent of the sample’s elastic properties. However, phase contrast associated with elastic modulus variations are observed if viscous damping or adhesion energy hysteresis is considered during tip–sample contact. The phase shift versus tip–sample equilibrium separation was measured for a compliant material (polypropylene) and for a stiff sample (mica). The agreement obtained between theory and experiment supports the conclusions derived from the model. These results emphasize the relevance of energy dissipating processes at the nanometer scale to explain phase contrast imaging in tapping-mode force microscopy.

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Effects of elastic and inelastic interactions on phase contrast images in tapping-mode scanning force microscopy

A silicon nanowire vibrating in two dimensions can be used to measure the mass and stiffness of atoms and molecules deposited on it.

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Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires

Blood contains a range of protein biomarkers that could be used in the early detection of disease. To achieve this, however, requires sensors capable of detecting (with high reproducibility) biomarkers at concentrations one million times lower than the concentration of the other blood proteins. Here, we show that a sandwich assay that combines mechanical and optoplasmonic transduction can detect cancer biomarkers in serum at ultralow concentrations. A biomarker is first recognized by a surface-anchored antibody and then by an antibody in solution that identifies a free region of the captured biomarker. This second antibody is tethered to a gold nanoparticle that acts as a mass and plasmonic label; the two signatures are detected by means of a silicon cantilever that serves as a mechanical resonator for ‘weighing’ the mass of the captured nanoparticles and as an optical cavity that boosts the plasmonic signal from the nanoparticles. The capabilities of the approach are illustrated with two cancer biomarkers: the carcinoembryonic antigen and the prostate specific antigen, which are currently in clinical use for the diagnosis, monitoring and prognosis of colon and prostate cancer, respectively. A detection limit of 1 × 10−16 g ml−1 in serum is achieved with both biomarkers, which is at least seven orders of magnitude lower than that achieved in routine clinical practice. Moreover, the rate of false positives and false negatives at this concentration is extremely low, ∼10−4. A sandwich assay labelled with gold nanoparticles can be mechanically and optically detected with the help of a silicon cantilever, allowing cancer biomarkers to be identified in serum at very low concentrations.

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Javier Tamayo

Papers

Biosensors based on nanomechanical systems

Relationship between phase shift and energy dissipation in tapping-mode scanning force microscopy

Effects of elastic and inelastic interactions on phase contrast images in tapping-mode scanning force microscopy

Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires

Detection of cancer biomarkers in serum using a hybrid mechanical and optoplasmonic nanosensor