Nodal variations and long-term changes in the main tides on the coasts of China

The long-term changes in the main tidal constituents (O1, K1, M2, N2, and S2) along the coasts of China and in adjacent seas are investigated based on 17 tide-gauge records covering the period 1954–2012. The observed 18.61 year nodal modulations of the diurnal constituents O1 and K1 are in agreement with the equilibrium tidal theory, except in the South China Sea. The observed modulations of the M2 and N2 amplitudes are smaller than theoretically predicted at the northern stations and larger at the southern stations. The discrepancies between the theoretically predicted nodal variations and the observations are discussed. The 8.85 year perigean cycle is identifiable in the N2 parameters at most stations, except those in the South China Sea. The radiational component of S2 contributes on average 16% of the observed S2 except in the Gulf of Tonkin, on the south coast, where it accounts for up to 65%. We confirmed the existence of nodal modulation in S2, which is stronger on the north coast. The semidiurnal tidal parameters show significant secular trends in the Bohai and Yellow Seas, on the north coast, and in the Taiwan Strait. The largest increase is found for M2 for which the amplitude increases by 4–7 mm/yr in the Yellow Sea. The potential causes for the linear trends in tidal constants are discussed.

Calcium turns sinister in left-right asymmetry

A major challenge in deciphering the development of left-right asymmetry in vertebrates is uncovering how subtle early differences between the left and right sides are translated into robust differences in gene expression. Recently, Raya and colleagues suggested that asymmetric localization of extracellular calcium ions at the node could differentially modulate Notch signalling, resulting in asymmetric expression of the signalling molecule Nodal on the left side of the node. In this article, I examine the implications of this finding and explore their relevance to the evolution of asymmetry in vertebrates and invertebrates.

Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

Simplified parameter adaptive control

A simple parameter adaptive controller design methodology is introduced in which steady-state servo tracking properties provide the major control objective. This is achieved without cancellation of process zeros and hence the underlying design can be applied to non-minimum phase systems. As with other self-tuning algorithms, the design (user specified) polynomials of the proposed algorithm define the performance capabilities of the resulting controller. However, with the appropriate definition of these polynomials, the synthesis technique can be shown to admit different adaptive control strategies, e.g. self-tuning PID and self-tuning pole-placement controllers. The algorithm can therefore be thought of as an embodiment of other self-tuning design techniques. The performances of some of the resulting controllers are illustrated using simulation examples and the on-line application to an experimental apparatus.

In vitro micro-tuber initiation and dormancy in yam

Dormancy is a mechanism that regulates the timing of sprouting (germination) of affected plant parts as well as ensures that the food quality of edible parts is maintained in storage until the following growing season. In yam, however, little is known about the control of tuber initiation or tuber dormancy. The objective of this study was to determine the effects of selected plant growth regulators (PGRs) on tuber initiation and dormancy, using an in vitro system. In two replicated experiments, 2-chloroethylphosphonic acid (ethephon, an ethylene source), abscisic acid (ABA) and gibberellin (GA3) – and their inhibitors silver nitrate, fluridone and 2-chloroethyl-trimethylammonium chloride, respectively – were added at two concentrations to the culture medium prior to explant culture. Dates of micro-tuber initiation and sprouting (end of dormancy) and tuber number were recorded. In the control (no PGR) in Experiment 1, micro-tubers were initiated at the base of the stem after 176 days and sprouted 235 days later, that is 411 days after culturing. Most PGR treatments had only small effects (±30 days) on the duration of dormancy and the time of micro-tuber initiation. However, in GA3 micro-tuber initiation occurred after 76 days, about 100 days earlier than in the control, whereas fluridone affected the position of micro-tubers and duration of dormancy. With fluridone treatments, tubers were found at the base of the stem (normal position) and on lower and upper nodes. Lower node tubers sprouted within 225 days of culturing compared with about 420 days after culturing at other nodal positions and in other PGR treatments. These data suggest an important role for ABA and gibberellic acid in yam micro-tuber initiation and the induction of dormancy.

A simplified mathematical model for urban microclimate simulation

Techniques for modelling urban microclimates and urban block surfaces temperatures are desired by urban planners and architects for strategic urban designs at the early design stages. This paper introduces a simplified mathematical model for urban simulations (UMsim) including urban surfaces temperatures and microclimates. The nodal network model has been developed by integrating coupled thermal and airflow model. Direct solar radiation, diffuse radiation, reflected radiation, long-wave radiation, heat convection in air and heat transfer in the exterior walls and ground within the complex have been taken into account. The relevant equations have been solved using the finite difference method under the Matlab platform. Comparisons have been conducted between the data produced from the simulation and that from an urban experimental study carried out in a real architectural complex on the campus of Chongqing University, China in July 2005 and January 2006. The results show a satisfactory agreement between the two sets of data. The UMsim can be used to simulate the microclimates, in particular the surface temperatures of urban blocks, therefore it can be used to assess the impact of urban surfaces properties on urban microclimates. The UMsim will be able to produce robust data and images of urban environments for sustainable urban design.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Sea level extremes at the coasts of China

Hourly sea level records from 1954 to 2012 at 20 tide gauges at and adjacent to the Chinese coasts are used to analyze extremes in sea level and in tidal residual. Tides and tropical cyclones determine the spatial distribution of sea level maxima. Tidal residual maxima are predominantly determined by tropical cyclones. The 50 year return level is found to be sensitive to the number of extreme events used in the estimation. This is caused by the small number of tropical cyclone events happening each year which lead to other local storm events included thus significantly affecting the estimates. Significant increase in sea level extremes is found with trends in the range between 2.0 and 14.1 mm yr−1. The trends are primarily driven by changes in median sea level but also linked with increases in tidal amplitudes at three stations. Tropical cyclones cause significant interannual variations in the extremes. The interannual variability in the sea level extremes is also influenced by the changes in median sea level at the north and by the 18.6 year nodal cycle at the South China Sea. Neither of PDO and ENSO is found to be an indicator of changes in the size of extremes, but ENSO appears to regulate the number of tropical cyclones that reach the Chinese coasts. Global mean atmospheric temperature appears to be a good descriptor of the interannual variability of tidal residual extremes induced by tropical cyclones but the trend in global temperature is inconsistent with the lack of trend in the residuals.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Susceptibility of faba bean (Vicia faba L.) to heat stress during floral development and anthesis

Experiments were conducted over two years to quantify the response of faba bean (Vicia faba L.) to heat stress. Potted winter faba bean plants (cv. Wizard) were exposed to temperature treatments (18/10; 22/14; 26/18; 30/22; 34/26°C day/night) for five days during floral development and anthesis. Developmental stages of all flowers were scored prior to stress, plants were grown in exclusion from insect pollinators to prevent pollen movement between flowers, and yield was harvested at an individual pod scale, enabling effects of heat stress to be investigated at a high resolution. Susceptibility to stress differed between floral stages, flowers were most affected during initial green-bud stages. Yield and pollen germination of flowers present before stress showed threshold relationships to stress, with lethal temperatures (t50) ~28°C and ~32°C, while whole plant yield showed a linear negative relationship to stress with high plasticity in yield allocation, such that yield lost at lower nodes was partially compensated at higher nodal positions. Faba bean has many beneficial attributes for sustainable modern cropping systems but these results suggest that yield will be limited by projected climate change, necessitating the development of heat tolerant cultivars, or improved resilience by other mechanisms such as earlier flowering times.