Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Optical loading sensor based on single polarization fiber laser incorporating an intra-cavity 45°-TFG

We have experimentally demonstrated an active loading sensor system based on a fiber ring laser with single-polarization output using an intra-cavity 45°-tilted fiber grating (45°-TFG). When the laser cavity fiber subjected to loading, the laser output is encoded with the load and can be measured and monitored by a power metre. A loading sensitivity as high as 0.033/ (kg·m-1) has been achieved using this laser. The experiment results clearly show that single polarization fiber laser may be developed to a low-cost high-sensitivity loading sensor system. © 2014 SPIE.

All-fiber loading sensor based on 45° and 81° tilted fiber gratings

Cardiovascular health of the human population is a major concern for medical clinicians, with cardiovascular diseases responsible for 48% of all deaths worldwide, according to the World Health Organisation. Therefore the development of new practicable and economical diagnostic tools to scrutinise the cardiovascular health of humans is a major driver for clinicians. We offer a new technique to obtain seismocardiographic signals covering both ballistocardiography (below 20Hz) and audible heart sounds (20Hz upwards). The detection scheme is based upon an array of curvature/displacement sensors using fibre optic long period gratings interrogated using a variation of the derivative spectroscopy interrogation technique. © 2014 SPIE.

Polarisation mode coupling of excessively tilted fibre Bragg gratings with directional transverse loading

We report a distinctive polarisation mode coupling behaviour of tilted fibre Bragg gratings (TFBGs) with tilted angle exceeding 45°. The ex-45° TFBGs exhibit pronounced polarisation mode splitting resulted from grating structure asymmetry induced birefringence. We have studied and analysed the property of ex-45° TFBGs under transverse load applied to their equivalent fast- and slow-axis. The results show that the coupling between the orthogonally polarised modes takes place only when the load is applied to its fast-axis, giving a prominent directional loading response. This transverse load related polarisation property may be exploitable for implementation of optical fibre vector sensors capable of measuring the magnitude and orientation of the applied transverse load.

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.

Mechanistic modeling of fracture in asphalt mixtures under compressive loading

When an asphalt mixture is subjected to a destructive compressive load, it experiences a sequence of three deformation stages, as follows: the (1) primary, (2) secondary, and (3) tertiary stages. Most literature research focuses on plastic deformation in the primary and secondary stages, such as prediction of the flow number, which is in fact the initiation of the tertiary stage. However, little research effort has been reported on the mechanistic modeling of the damage that occurs in the tertiary stage. The main objective of this paper is to provide a mechanistic characterizing method for the damage modeling of asphalt mixtures in the tertiary stage. The preliminary study conducted by the writers illustrates that deformation during the tertiary flow of the asphalt mixtures is principally caused by the formation and propagation of cracks, which was signaled by the increase of the phase angle in the tertiary phase. The strain caused by the growth of cracks is the viscofracture strain, which can be obtained by conducting the strain decomposition of the measured total strain in the destructive compressive test. The viscofracture strain is employed in the research reported in this paper to mechanistically characterize the time-dependent fracture (viscofracture) of asphalt mixtures in compression. By using the dissipated pseudostrain energy-balance principle, the damage density and true stress are determined and both are demonstrated to increase with load cycles in the tertiary stage. The increased true stress yields extra viscoplastic strain, which is the reason why the permanent deformation is accelerated by the occurrence of cracks. To characterize the evolution of the viscofracture in the asphalt mixtures in compression, a pseudo J-integral Paris' law in terms of damage density is proposed and the material constants in the Paris' law are determined, which can be employed to predict the fracture of asphalt mixtures in compression. © 2013 American Society of Civil Engineers.

Hydrothermal saline promoted grafting:a route to sulfonic acid SBA-15 silica with ultra-high acid site loading for biodiesel synthesis

A simple grafting protocol is reported which affords a ten-fold enhancement in acid site density of mesoporous sulfonic acid silicas compared to conventional syntheses, offering improved process efficiency and new opportunities for tailored supported solid acids in sustainable chemistry. This journal is

Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

Properties of Lp (K)-Solutions of Linear Nonhomogeneous Impulsive Differential Equations with Unbounded Linear Operator

Sufficient conditions for the existence of Lp(k)-solutions of linear nonhomogeneous impulsive differential equations with unbounded linear operator are found. An example of the theory of the linear nonhomogeneous partial impulsive differential equations of parabolic type is given.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

A review of the effects of distributed energy resources and power-electronic controlled loading on distribution network stability

This paper looks at potential distribution network stability problems under the Smart Grid scenario. This is to consider distributed energy resources (DERs) e.g. renewable power generations and intelligent loads with power-electronic controlled converters. The background of this topic is introduced and potential problems are defined from conventional power system stability and power electronic system stability theories. Challenges are identified with possible solutions from steady-state limits, small-signal, and large-signal stability indexes and criteria. Parallel computation techniques might be included for simulation or simplification approaches are required for a largescale distribution network analysis.

Method of Averaging for Impulsive Differential Inclusions

AMS subject classification: Primary 49N25, Secondary 49J24, 49J25.

Optical loading sensor based on ring-cavity fiber laser incorporating a 45°-tilted fiber polarizing grating

We have experimentally demonstrated an active loading sensor system based on a fiber ring laser with singlepolarization output using an intra-cavity 45°-tilted fiber grating. When the laser cavity fiber is subjected to loading, the laser output is encoded with the loading information that can be measured and monitored by a standard power meter. The achieved loading sensitivity is 0.033/kg • m-1 and 0.042/kg • m-1 for two different interaction lengths. The experimental results clearly show that such a single-polarization fiber laser may be commercially developed into a low-cost, high-sensitivity loading sensor system.

All-fiber loading sensor based on a hybrid 45° and 81° tilted fiber grating structure

We experimentally demonstrate an all-fiber loading sensor system based on a 45° and an 81° tilted fiber grating (TFG). We have fabricated two TFGs adjacent to each other in a single fiber to form a hybrid structure. When the transverse load applied to the 81° TFG, the light coupling to the two orthogonally polarized modes will interchange the power according to the load applied to the fiber, which provides a solution to measure the load. For real applications, we further investigated the interrogation of this all-fiber loading sensor system using a low-cost and compact-size single wavelength source and a power meter. The experimental results have clearly shown that a low-cost high-sensitivity loading sensor system can be developed based on the proposed TFG configuration.