Partition Function Expansion on Region-Graphs and Message-Passing Equations

Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional `real' systems persist to be very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of partition function expansion and the concept of region-graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region-graph, such as belief-propagation and survey-propagation, are also derived rigorously.Comment: 10 pages including two figures. New theoretical and numerical results added. Will be published by JSTAT as a lette

What kinds of coordinate can keep the Hawking temperature invariant for the static spherically symmetric black hole?

By studying the Hawking radiation of the most general static spherically symmetric black hole arising from scalar and Dirac particles tunnelling, we find the Hawking temperature is invariant in the general coordinate representation (\ref{arbitrary1}), which satisfies two conditions: a) its radial coordinate transformation is regular at the event horizon; and b) there is a time-like Killing vector.Comment: 10 page

Cyber-risks in the Industrial Internet of Things (IIoT): towards a method for continuous assessment.

Continuous risk monitoring is considered in the context of cybersecurity management for the Industrial Internet-of-Thing. Cyber risk management best practice is for security controls to be deployed and configured in order to bring down risk exposure to an acceptable level. However, threats and known vulnerabilities are subject to change, and estimates of risk are subject to many uncertainties, so it is important to review risk assessments and update controls when required. Risks are typically reviewed periodically (e.g. once per month), but the accelerating pace of change means that this approach is not sustainable, and there is a requirement for continuous monitoring of cybersecurity risks. The method described in this paper aims to alert security staff of significant changes or trends in estimated risk exposure to facilitate rational and timely decisions. Additionally, it helps predict the success and impact of a nascent security breach allowing better prioritisation of threats and selection of appropriate responses. The method is illustrated using a scenario based on environmental control in a data centre

Recurrence and Polya number of general one-dimensional random walks

The recurrence properties of random walks can be characterized by P\'{o}lya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities $l$ and $r$, or remain at the same position with probability $o$ ($l+r+o=1$). We calculate P\'{o}lya number $P$ of this model and find a simple expression for $P$ as, $P=1-\Delta$, where $\Delta$ is the absolute difference of $l$ and $r$ ($\Delta=|l-r|$). We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability $l$ equals to the right-moving probability $r$.Comment: 3 page short pape

Demonstrating Additional Law of Relativistic Velocities based on Squeezed Light

Special relativity is foundation of many branches of modern physics, of which theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use of convenient substitute, i.e. squeezed light in present paper. Squeezed light is very important in the field of quantum optics and the corresponding transformation can be regarded as the coherent state of SU(1; 1). In this paper, the connection between the squeezed operator and Lorentz boost is built under certain conditions. Furthermore, the additional law of relativistic velocities and the angle of Wigner rotation are deduced as well

Non-Markovian Quantum Trajectories of Many-Body Quantum Open Systems

A long-standing open problem in non-Markovian quantum state diffusion (QSD) approach to open quantum systems is to establish the non-Markovian QSD equations for multiple qubit systems. In this paper, we settle this important question by explicitly constructing a set of exact time-local QSD equations for $N$-qubit systems. Our exact time-local (convolutionless) QSD equations have paved the way towards simulating quantum dynamics of many-body open systems interacting with a common bosonic environment. The applicability of this multiple-qubit stochastic equation is exemplified by numerically solving several quantum open many-body systems concerning quantum coherence dynamics and dynamical control.Comment: 8 pages, 2 figures. manuscript revised and reference update

Object Picture of Quasinormal Modes for Stringy Black Holes

We study the quasinormal modes (QNMs) for stringy black holes. By using numerical calculation, the relations between the QNMs and the parameters of black holes are minutely shown. For (1+1)-dimensional stringy black hole, the real part of the quasinormal frequency increases and the imaginary part of the quasinormal frequency decreases as the mass of the black hole increases. Furthermore, the dependence of the QNMs on the charge of the black hole and the flatness parameter is also illustrated. For (1+3)-dimensional stringy black hole, increasing either the event horizon or the multipole index, the real part of the quasinormal frequency decreases. The imaginary part of the quasinormal frequency increases no matter whether the event horizon is increased or the multipole index is decreased.Comment: 4 pages, 5 figure

Freestanding Functional Structures by Aerosol-Jet Printing for Stretchable Electronics and Sensing Applications

The requirements for modern electronic devices, particularly those intended for wearable or human health monitoring applications, have rapidly evolved to being both flexible and stretchable. Hence devices, as well as interconnects, need to be capable of retaining functionality even when being mechanically deformed. Most approaches towards achieving this rely on printing or transferring structures onto elastomeric substrates that can withstand stretching. However, the processing involved can often be cumbersome, and the structures themselves tend to suffer from poor fatigue and/or are limited by the mechanical properties of the underlying substrate. Here, we introduce an aerosol-jet printing technique by which fully freestanding functional structures can be built up layer by layer, which are stable and robust upon repeated stretching. The process involves printing a combination of layers of different materials with the desired functionality, onto a substrate coated with a sacrifical film that is subsequently dissolved to release the printed structure. Using this method, we demonstrate freestanding conductive wires can be used as stretchable interconnects/electrodes, and that also function as strain-sensors. We also show that a freestanding capacitive structure functions as a robust, stretchable humidity sensor, paving the way for the development of other multi-layer, multifunctional stretchable devices and sensors

Aerosol-Jet Printed Fine-Featured Triboelectric Sensors for Motion Sensing

Triboelectric motion sensors, based on the generation of a voltage across two dissimilar materials sliding across each other as a result of the triboelectric effect, have generated interest due to the relative simplicity of the typical grated device structures and materials required. However, these sensors are often limited by poor spatial and/or temporal resolution of motion due to limitations in achieving the required device feature sizes through conventional lithography or printing techniques. Furthermore, the reliance on metallic components that are relatively straightforward to pattern into fine features limits the possibility to develop transparent sensors. Polymers would allow for transparent devices, but these materials are significantly more difficult to pattern into fine features when compared to metals. Here, we use an aerosol-jet printing (AJP) technique to develop triboelectric sensors using a wide variety of materials, including polymers, which can be directly printed into finely featured grated structures for enhanced sensitivity to displacement and speed of motion. We present a detailed investigation highlighting the role of material selection and feature size in determining the overall resolution of the resulting motion sensor. A 3-channel rotary sensor is also presented, demonstrating the versatility of the AJP technique in developing more complex triboelectric motion sensors.European Research Council (ERC-2014-STG-639526, NANOGEN) Marie Sklodowska Curie Fellowship (H2020-MSCA-IF-2015-702868