By using and extending earlier results (Liu & Ricca,J. Phys. A, vol. 45, 2012, 205501), we derive the skein relations of the HOMFLYPT polynomial for ideal fluid knots from helicity, thus providing a rigorous proof that the HOMFLYPT polynomial is a new, powerful invariant of topological fluid mechanics. Since this invariant is a two-variable polynomial, the skein relations are derived from two independent equations expressed in terms of writhe and twist contributions. Writhe is given by addition/subtraction of imaginary local paths, and twist by Dehn’s surgery. HOMFLYPT then becomes a function of knot topology and field strength. For illustration we derive explicit expressions for some elementary cases and apply these results to homogeneous vortex tangles. By examining some particular examples we show how numerical implementation of the HOMFLYPT polynomial can provide new insight into fluid-mechanical behaviour of real fluid flows.

We report the thermal tuning of the mechanical nonlinearity in GaAs double-clamped MEMS beam resonators for sensitive thermal sensing applications. We have estimated the mechanical nonlinearity in GaAs MEMS beam resonator by measuring its resonance frequency as a function of oscillation amplitude. The MEMS resonator shows a hardening nonlinearity with a small linear oscillation range of ∼30 nm. When electrical heat is applied to the MEMS beam, we have observed a significant reduction in the mechanical nonlinearity of MEMS resonators near the buckling point of the MEMS beam. The decrease in the mechanical nonlinearity originates from the bending of the MEMS beam, which gives a softening nonlinearity term and, hence, compensates the total nonlinearity. With the thermal tuning effect, MEMS resonator can maintain a very large quasi linear oscillation amplitude of ∼300 nm, which is ∼10 times larger than the linear oscillation range without the control of nonlinearity.

We report on a giant enhancement in the thermal responsivity of doubly clamped $\mathrm{Ga}\mathrm{As}$ microelectromechanical-system- (MEMS) beam resonators by using the internal-mode-coupling effect. This is achieved by coupling the fundamental bending mode with the fundamental torsional mode of the MEMS-beam resonators through the cubic Duffing nonlinearity. In the mode-coupling regime, we find that when the input heat to the MEMS resonators is modulated at a particular frequency, the resonance-frequency shift caused by heating can be enhanced by almost 2 orders of magnitude. The observed effect is promising for realization of high-sensitivity thermal sensing by use of MEMS resonators, such as ultrasensitive terahertz detection at room temperature.

Window profiles of amino acids in protein sequences are used to describe the amino acid environment. The relative entropy or Kullback-Leibler distance derived from these profiles is used as a measure of dissimilarity for comparison of amino acids and secondary structure conformations. Distance matrices of amino acid pairs at different conformations are obtained, which display a non-negligible dependence of amino acid similarity on conformations. Based on the conformation specific distances, a clustering analysis for amino acids is conducted.

Physical knots observed in various contexts – from DNA biology to vortex dynamics and condensed matter physics – are found to undergo topological simplification through iterated recombination of knot strands following a common, qualitative pattern that bears remarkable similarities across fields. Here, by interpreting evolutionary processes as geodesic flows in a suitably defined knot polynomial space, we show that a new measure of topological complexity allows accurate quantification of the probability of decay pathways by selecting the optimal unlinking pathways. We also show that these optimal pathways are captured by a logarithmic best-fit curve related to the distribution of minimum energy states of tight knots. This preliminary approach shows great potential for establishing new relations between topological simplification pathways and energy cascade processes in nature.

Bandwidth extension is an effective technique for enhancing the quality of audio signals by reconstructing their high-frequency components. In this paper, a novel blind bandwidth extension method is proposed based on phase space reconstruction. Phase space reconstruction is introduced to convert the low-frequency modified discrete cosine transform coefficients of wideband audio to a multi-dimensional space, and the high-frequency modified discrete cosine transform coefficients of the audio signal are reconstructed by a non-linear prediction model. The performance of the proposed method was evaluated through objective and subjective tests. It is found that the proposed method achieves a better performance than the typical linear extrapolation method, and its performance is comparable to the conventional efficient high-frequency bandwidth extension method.