Microcanonical Origin of the Maximum Entropy Principle for Open Systems

The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the closed universe consisting of the open system and the heat bath, by taking the limit where the heat bath is much larger than the system of interest. Alternatively, the Boltzmann distribution can be derived from the Maximum Entropy Principle, where the Gibbs-Shannon entropy is maximized under the constraint that the mean energy of the open system is fixed. To make the connection between these two apparently distinct methods for deriving the Boltzmann distribution, it is first shown that the uniform distribution for a microcanonical distribution is obtained from the Maximum Entropy Principle applied to a closed system. Then I show that the target function in the Maximum Entropy Principle for the open system, is obtained by partial maximization of Gibbs-Shannon entropy of the closed universe over the microstate probability distributions of the heat bath. Thus, microcanonical origin of the Entropy Maximization procedure for an open system, is established in a rigorous manner, showing the equivalence between apparently two distinct approaches for deriving the Boltzmann distribution. By extending the mathematical formalism to dynamical paths, the result may also provide an alternative justification for the principle of path entropy maximization as well.Comment: 12 pages, no figur

Tests of a Semi-Analytical Case 1 and Gelbstoff Case 2 SeaWiFS Algorithm with a Global Data Set

A semi-analytical algorithm was tested with a total of 733 points of either unpackaged or packaged-pigment data, with corresponding algorithm parameters for each data type. The 'unpackaged' type consisted of data sets that were generally consistent with the Case 1 CZCS algorithm and other well calibrated data sets. The 'packaged' type consisted of data sets apparently containing somewhat more packaged pigments, requiring modification of the absorption parameters of the model consistent with the CalCOFI study area. This resulted in two equally divided data sets. A more thorough scrutiny of these and other data sets using a semianalytical model requires improved knowledge of the phytoplankton and gelbstoff of the specific environment studied. Since the semi-analytical algorithm is dependent upon 4 spectral channels including the 412 nm channel, while most other algorithms are not, a means of testing data sets for consistency was sought. A numerical filter was developed to classify data sets into the above classes. The filter uses reflectance ratios, which can be determined from space. The sensitivity of such numerical filters to measurement resulting from atmospheric correction and sensor noise errors requires further study. The semi-analytical algorithm performed superbly on each of the data sets after classification, resulting in RMS1 errors of 0.107 and 0.121, respectively, for the unpackaged and packaged data-set classes, with little bias and slopes near 1.0. In combination, the RMS1 performance was 0.114. While these numbers appear rather sterling, one must bear in mind what mis-classification does to the results. Using an average or compromise parameterization on the modified global data set yielded an RMS1 error of 0.171, while using the unpackaged parameterization on the global evaluation data set yielded an RMS1 error of 0.284. So, without classification, the algorithm performs better globally using the average parameters than it does using the unpackaged parameters. Finally, the effects of even more extreme pigment packaging must be examined in order to improve algorithm performance at high latitudes. Note, however, that the North Sea and Mississippi River plume studies contributed data to the packaged and unpackaged classess, respectively, with little effect on algorithm performance. This suggests that gelbstoff-rich Case 2 waters do not seriously degrade performance of the semi-analytical algorithm

Optical trapping using ultrashort 12.9fs pulses

We demonstrate stable three-dimensional optical trapping of 780nm silica particles using a dispersion-compensated 12.9fs infrared pulsed laser and a trapping microscope system with 1.40NA objective. To achieve these pulse durations we use the Multiphoto

Resolving inter-particle position and optical forces along the axial direction using optical coherence gating

We demonstrate the use of coherence gating to resolve particle positions and forces in the axial direction. High depth resolvability (axial) and weak optical force (10-15 N) measurements in an optical trapping system is achieved

Tailoring the surface charge of dextran-based polymer coated SPIONs for modulated stem cell uptake and MRI contrast

Tracking stem cells in vivo using non-invasive techniques is critical to evaluate the efficacy and safety of stem cell therapies. Superparamagnetic iron oxide nanoparticles (SPIONs) enable cells to be tracked using magnetic resonance imaging (MRI), but to obtain detectable signal cells need to be labelled with a sufficient amount of iron oxide. For the majority of SPIONs, this can only be obtained with the use of transfection agents, which can adversely affect cell health. Here, we have synthesised a library of dextran-based polymer coated SPIONs with varying surface charge from −1.5 mV to +18.2 mV via a co-precipitation approach and investigated their ability to be directly internalised by stem cells without the need for transfection agents. The SPIONs were colloidally stable in physiological solutions. The crystalline phase of the particles was confirmed with powder X-ray diffraction and their magnetic properties were characterised using SQUID magnetometry and magnetic resonance. Increased surface charge led to six-fold increase in uptake of particles into stem cells and higher MRI contrast, with negligible change in cell viability. Cell tracking velocimetry was shown to be a more accurate method for predicting MRI contrast of stem cells compared to measuring iron oxide uptake through conventional bulk iron quantification