Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption

We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground state.Comment: 40 page

A network model to investigate structural and electrical properties of proteins

One of the main trend in to date research and development is the miniaturization of electronic devices. In this perspective, integrated nanodevices based on proteins or biomolecules are attracting a major interest. In fact, it has been shown that proteins like bacteriorhodopsin and azurin, manifest electrical properties which are promising for the development of active components in the field of molecular electronics. Here we focus on two relevant kinds of proteins: The bovine rhodopsin, prototype of GPCR protein, and the enzyme acetylcholinesterase (AChE), whose inhibition is one of the most qualified treatments of Alzheimer disease. Both these proteins exert their functioning starting with a conformational change of their native structure. Our guess is that such a change should be accompanied with a detectable variation of their electrical properties. To investigate this conjecture, we present an impedance network model of proteins, able to estimate the different electrical response associated with the different configurations. The model resolution of the electrical response is found able to monitor the structure and the conformational change of the given protein. In this respect, rhodopsin exhibits a better differential response than AChE. This result gives room to different interpretations of the degree of conformational change and in particular supports a recent hypothesis on the existence of a mixed state already in the native configuration of the protein.Comment: 25 pages, 12 figure

A Centre-Stable Manifold for the Focussing Cubic NLS in R1+3R^{1+3}

Consider the focussing cubic nonlinear Schr\"odinger equation in $R^3$: $$i\psi_t+\Delta\psi = -|\psi|^2 \psi.$$ It admits special solutions of the form $e^{it\alpha}\phi$, where $\phi$ is a Schwartz function and a positive ($\phi>0$) solution of $$-\Delta \phi + \alpha\phi = \phi^3.$$ The space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the eight-dimensional manifold that consists of functions of the form $e^{i(v \cdot + \Gamma)} \phi(\cdot - y, \alpha)$. We prove that any solution starting sufficiently close to a standing wave in the $\Sigma = W^{1, 2}(R^3) \cap |x|^{-1}L^2(R^3)$ norm and situated on a certain codimension-one local Lipschitz manifold exists globally in time and converges to a point on the manifold of standing waves. Furthermore, we show that \mc N is invariant under the Hamiltonian flow, locally in time, and is a centre-stable manifold in the sense of Bates, Jones. The proof is based on the modulation method introduced by Soffer and Weinstein for the $L^2$-subcritical case and adapted by Schlag to the $L^2$-supercritical case. An important part of the proof is the Keel-Tao endpoint Strichartz estimate in $R^3$ for the nonselfadjoint Schr\"odinger operator obtained by linearizing around a standing wave solution.Comment: 56 page

Evolution of the complex refractive index in the UV spectral region in ageing secondary organic aerosol

The chemical and physical properties of secondary organic aerosol (SOA) formed by the photochemical degradation of biogenic and anthropogenic volatile organic compounds (VOC) are as yet still poorly constrained. The evolution of the complex refractive index (RI) of SOA, formed from purely biogenic VOC and mixtures of biogenic and anthropogenic VOC, was studied over a diurnal cycle in the SAPHIR photochemical outdoor chamber in Jülich, Germany. The correlation of RI with SOA chemical and physical properties such as oxidation level and volatility was examined. The RI was retrieved by a newly developed broadband cavity-enhanced spectrometer for aerosol optical extinction measurements in the UV spectral region (360 to 420 nm). Chemical composition and volatility of the particles were monitored by a high-resolution time-of-flight aerosol mass spectrometer, and a volatility tandem differential mobility analyzer. SOA was formed by ozonolysis of either (i) a mixture of biogenic VOC (α-pinene and limonene), (ii) biogenic VOC mixture with subsequent addition of an anthropogenic VOC (<i>p</i>-xylene-d₁₀), or (iii) a mixture of biogenic and anthropogenic VOC. The SOA aged by ozone/OH reactions up to 29.5 h was found to be non-absorbing in all cases. The SOA with <i>p</i>-xylene-d₁₀ showed an increase of the scattering component of the RI correlated with an increase of the O / C ratio and with an increase in the SOA density. There was a greater increase in the scattering component of the RI when the SOA was produced from the mixture of biogenic VOCs and anthropogenic VOC than from the sequential addition of the VOCs after approximately the same ageing time. The increase of the scattering component was inversely correlated with the SOA volatility. Two RI retrievals determined for the pure biogenic SOA showed a constant RI for up to 5 h of ageing. Mass spectral characterization shows the three types of the SOA formed in this study have a significant amount of semivolatile components. The influence of anthropogenic VOCs on the oxygenated organic aerosol as well as the atmospheric implications are discussed

Biases in the perceived timing of perisaccadic perceptual and motor events

Subjects typically experience the temporal interval immediately following a saccade as longer than a comparable control interval. One explanation of this effect is that the brain antedates the perceptual onset of a saccade target to around the time of saccade initiation. This could explain the apparent continuity of visual perception across eye movements. Thisantedating account was tested in three experiments in which subjects made saccades of differing extents and then judged either the duration or the temporal order of key events. Postsaccadic stimuli underwent subjective temporal lengthening and had early perceived onsets. A temporally advanced awareness of saccade completion was also found, independently of antedating effects. These results provide convergent evidence supporting antedating and differentiating it from other temporal biases

Cloud condensation nuclei activity, droplet growth kinetics, and hygroscopicity of biogenic and anthropogenic secondary organic aerosol (SOA)

© 2016 Author(s).Interaction of biogenic volatile organic compounds (VOCs) with Anthropogenic VOC (AVOC) affects the physicochemical properties of secondary organic aerosol (SOA). We investigated cloud droplet activation (CCN activity), droplet growth kinetics, and hygroscopicity of mixed anthropogenic and biogenic SOA (ABSOA) compared to pure biogenic SOA (BSOA) and pure anthropogenic SOA (ASOA). Selected monoterpenes and aromatics were used as representative precursors of BSOA and ASOA, respectively. We found that BSOA, ASOA, and ABSOA had similar CCN activity despite the higher oxygen to carbon ratio (O/C) of ASOA compared to BSOA and ABSOA. For individual reaction systems, CCN activity increased with the degree of oxidation. Yet, when considering all different types of SOA together, the hygroscopicity parameter, κ$_CCN$, did not correlate with O/C. Droplet growth kinetics of BSOA, ASOA, and ABSOA were comparable to that of (NH$_4$)$_2$SO$_4$, which indicates that there was no delay in the water uptake for these SOA in supersaturated conditions. In contrast to CCN activity, the hygroscopicity parameter from a hygroscopic tandem differential mobility analyzer (HTDMA) measurement, κ$_HTDMA$, of ASOA was distinctively higher (0.09-0.10) than that of BSOA (0.03-0.06), which was attributed to the higher degree of oxidation of ASOA. The ASOA components in mixed ABSOA enhanced aerosol hygroscopicity. Changing the ASOA fraction by adding biogenic VOC (BVOC) to ASOA or vice versa (AVOC to BSOA) changed the hygroscopicity of aerosol, in line with the change in the degree of oxidation of aerosol. However, the hygroscopicity of ABSOA cannot be described by a simple linear combination of pure BSOA and ASOA systems. This indicates that additional processes, possibly oligomerization, affected the hygroscopicity. Closure analysis of CCN and HTDMA data showed κ$_HTDMA$ was lower than κ$_CCN$ by 30-70 %. Better closure was achieved for ASOA compared to BSOA. This discrepancy can be attributed to several reasons. ASOA seemed to have higher solubility in subsaturated conditions and/or higher surface tension at the activation point than that of BSOA.EUROCHAMP2 European Commission 7th framework, NordForsk, VILLUM Foundatio

A system of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify a system of ODEs similar to those from Comech and Pelinovsky (2003), which model the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, which is in accord with the conclusions of Pelinovsky, Afanasjev, and Kivshar (1996). For initial data which supports a soliton structure, a generic initial perturbation oscillates around the stable family of solitons. For initial data which is expected to disperse, the finite dimensional dynamics follow the unstable portion of the soliton curve.Comment: Minor edit

Resection of the liver for colorectal carcinoma metastases - A multi-institutional study of long-term survivors

In this review of a collected series of patients undergoing hepatic resection for colorectal metastases, 100 patients were found to have survived greater than five years from the time of resection. Of these 100 long-term survivors, 71 remain disease-free through the last follow-up, 19 recurred prior to five years, and ten recurred after five years. Patient characteristics that may have contributed to survival were examined. Procedures performed included five trisegmentectomies, 32 lobectomies, 16 left lateral segmentectomies, and 45 wedge resections. The margin of resection was recorded in 27 patients, one of whom had a positive margin, nine of whom had a less than or equal to 1-cm margin, and 17 of whom had a greater than 1-cm margin. Eighty-one patients had a solitary metastasis to the liver, 11 patients had two metastases, one patient had three metastases, and four patients had four metastases. Thirty patients had Stage C primary carcinoma, 40 had Stage B primary carcinoma, and one had Stage A primarycarcinoma. The disease-free interval from the time of colon resection to the time of liver resection was less than one year in 65 patients, and greater than one year in 34 patients. Three patients had bilobar metastases. Four of the patients had extrahepatic disease resected simultaneously with the liver resection. Though several contraindications to hepatic resection have been proposed in the past, five-year survival has been found in patients with extrahepatic disease resected simultaneously, patients with bilobar metastases, patients with multiple metastases, and patients with positive margins. Five-year disease-free survivors are also present in each of these subsets. It is concluded that five-year survival is possible in the presence of reported contraindications to resection, and therefore that the decision to resect the liver must be individualized. © 1988 American Society of Colon and Rectal Surgeons