Demonstration of an optomechanical system that works as a quantum interface between light and micro-mechanical motion. The possibility of controlling the quantum states of micro- and nanomechanical oscillators has been of great interest in recent years. Although various mechanical resonators have been cooled to their quantum ground state, there are few reports of experiments in which this quantum regime is further explored and used, for example, to exchange quantum information. Previously, quantum coupling between mechanical degrees of freedom and microwave radiation has been shown. Now, Verhagen et al. demonstrate an optomechanical system, cooled by radiation pressure, that works as a quantum interface between a mechanical oscillator and optical photons, offering the advantage that standard optical fibres can be used to extract the quantum information. Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions1,2, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities3,4,5,6. If the optomechanical coupling is ‘quantum coherent’—that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate—quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures7,8. Optical experiments have not attained this regime owing to the large mechanical decoherence rates9 and the difficulty of overcoming optical dissipation10. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links11,12,13,14,15.

Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode

A model for pore pressure-dependent cleat permeability is presented for gas-desorbing, linear elastic coalbeds under uniaxial strain conditions experienced in producing reservoirs. In the model, changes in the cleat permeability of coalbeds, which are idealised to have a bundled matchstick geometry, is controlled by the prevailing effective horizontal stresses normal to the cleats. Variations in the effective horizontal stresses under uniaxial strain conditions are expressed as a function of pore pressure reduction during drawdown, which includes a cleat compression term and a matrix shrinkage term that have competing effects on cleat permeability. A comprehensive analysis has revealed that the shape of the stress – pore pressure curve is predominantly determined by the magnitude of recovery pressure and rebound pressure relative to the initial reservoir pressure. A total of five possible scenarios have been identified with regard to response of the horizontal stress function to reservoir drawdown. When applied to four coalbed wells at two separate sites in the fairway of the San Juan basin, the model predictions at one site, where the three wells have shown increased absolute permeability during gas production, are in excellent agreement with the published pore pressure dependent permeability changes that were obtained independently from history matching the field production data. At a separate site the model correctly predicts, at least qualitatively, a strong permeability rebound at lower drawdown pressures that has been inferred through history matching the production data. An analysis of the effects of initial reservoir pressure on the response of effective horizontal stress to drawdown was carried out, with reference to the range of pressure likely to be encountered in the San Juan basin. The implications of this in terms of pore pressure dependent permeability are discussed.

Drawdown Induced Changes in Permeability of Coalbeds: A New Interpretation of the Reservoir Response to Primary Recovery

A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed. Because the heat conduction equation in the case 1≤α≤2 interpolates the parabolic equation (α = 1) and the wave equation (α = 2), the proposed theory interpolates a classical thermoelasticity and a thermoelasticity without energy dissipation introduced by Green and Naghdi. The Caputo fractional derivative is used. The stresses corresponding to the fundamental solutions of a Cauchy problem for the fractional heat conduction equation are found in one-dimensional and two-dimensional cases.

Fractional heat conduction equation and associated thermal stress

A three-phase-lag model of the linearized theory of coupled thermoelasticity is formulated by considering the heat condition law that includes temperature gradient and the thermal displacement gradient among the constitutive variables. The Fourier law is replaced by an approximation to a modification of the Fourier law with three different translations for the heat flux vector, the temperature gradient and also for the thermal displacement gradient. The model formulated is an extension of the thermoelastic models proposed by Lord–Shulman, Green–Naghdi and Tzou.

On A Thermoelastic Three-Phase-Lag Model

In this paper, we consider molecular communication, with information conveyed in the time of release of molecules. These molecules propagate to the transmitter through a fluid medium, propelled by a positive drift velocity and Brownian motion. The main contribution of this paper is the development of a theoretical foundation for such a communication system; specifically, the additive inverse Gaussian noise (AIGN) channel model. In such a channel, the information is corrupted by noise that follows an IG distribution. We show that such a channel model is appropriate for molecular communication in fluid media. Taking advantage of the available literature on the IG distribution, upper and lower bounds on channel capacity are developed, and a maximum likelihood receiver is derived. Results are presented which suggest that this channel does not have a single quality measure analogous to signal-to-noise ratio in the additive white Gaussian noise channel. It is also shown that the use of multiple molecules leads to reduced error rate in a manner akin to diversity order in wireless communications. Finally, some open problems are discussed that arise from the IG channel model.

Molecular Communication in Fluid Media: The Additive Inverse Gaussian Noise Channel

Dynamic problems of thermoelasticity

1 Basic Laws of Thermoelasticity 1 Introduction 2 Stresses and Tractions 3 Equations of Motion 4 Coordinate Transformation. Principal Axes 5 Principal Stresses and Stress Invariants 6 Displacement and Strain Tensor 7 Compatibility Equations. Simply Connected Region 8 Compatibility Conditions. Multiply Connected Regions 9 Constitutive Laws of Linear Thermoelasticity 10 Displacement Formulation of Thermoelasticity 11 Stress Formulation of Thermoelasticity 12 Two-Dimensional Thermoelasticity 13 Michell conditions 2 Thermodynamics of Elastic Continuum 1 Introduction 2 Thermodynamics Definitions 3 First Law of Thermodynamics 4 Second Law of Thermodynamics 5 Variational Formulation of Thermodynamics 6 Thermodynamics of Elastic Continuum 7 General Theory of Thermoelasticity 8 Free Energy Function of Hookean Materials 9 Fourier's Law and Heat Conduction Equation 10 Generalized Thermoelasticity. Second Sound 11 Thermoelasticity without Energy Dissipation 12 Uniqueness Theorem 13 Variational Principle of Thermoelasticity 14 Reciprocity Theorem 15 Initial and Boundary Conditions 3 Basic Problems of Thermoelasticity 1 Introduction 2 Temperature Distribution for Zero Thermal Stress 3 Analogy of Thermal Gradient with Body Forces 4 General Solution of Thermoelastic Problems 5 General Solution in Cylindrical Coordinates 6 Solution of Two-Dimensional Navier Equations 7 Solution of Problems in Spherical Coordinates 4 Heat Conduction Problems 1 Introduction 2 Problems in Rectangular Cartesian Coordinates 2.1 Steady State One-Dimensional Problems 2.2 Steady Two-Dimensional Problems. Separation of Variables 2.3 Fourier Series 2.4 Double Fourier Series 2.5 Bessel Functions and Fourier-Bessel series 2.6 Nonhomogeneous Differential Equations and Boundary Condition 2.7 Lumped Formulation 2.8 Steady State Three-Dimensional Problems 2.9.Transient Problems 3 Problems in Cylindrical coordinates 3.1 Steady-State One-Dimensional Problems (Radial Flow) 3.2. Steady -State Two-Dimensional Problems 3.3 Steady-State Three-Dimensional Problems 3.4 Transient Problems 4 Problems in Spherical Coordinates 4.1 Steady-State One-Dimensional Problems 4.2 Steady-State Two- and Three-Dimensional Problems 4.3 Transient Problems 5 Thermal Stresses in Beams 1 Introduction 2 Elementary Theory of Thermal Stresses in Beams 3 Deflection Equation of Beams 4 Boundary Conditions 5 Shear Stress in a Beam 6 Beams of Rectangular Cross Section 7 Transient Thermal Stresses in Rectangular Beams 8 . Beam with Internal Heat Generation 9 Bimetallic Beam 10 Functionally Graded Beams 11 Transient Thermal Stresses in Functionally Graded Beams 12 Thermal Stresses in Thin Curved Beams and Rings 13 Deflection of Thin Curved Beams and Rings 6 Disks, Cylinders, and Spheres 1 Introduction 2 . Cylinders with Radial Temperature Variation 3 Thermal Stresses in Disks 4 Thick Spheres 5 Thermal Stresses in a Rotating Disk 6 Non-Axisymmetrically Heated cylinders 7 Method of Complex Variables 8 Functionally Graded Thick Cylinders 9 Axisymmetric Thermal Stresses in FGM Cylinders 10.Transient Thermal Stresses in Thick Spheres 11 Functionality Graded Spheres 7 Thermal Expansion in Piping Systems 1 Introduction 2 Definition of the Elastic Center 3 . Piping Systems in Two Dimensions 4 Piping Systems in Three-dimensions 5 Pipelines with Large Radius Elbows 8 Coupled and Generalized Thermoelasticity 1 Introduction 2 Governing Equations of Coupled Thermoelasticity 3 Coupled Thermoelasticity for Infinite Space 4 Variable Heat Source 5 One-Dimensional Coupled Problem 6 Propagation of Discontinuities 7 Half-Space Subjected to a Harmonic Temperature 8 Coupled Thermoelasticity of Thick Cylinders 9 Green-Naghdi Model of a Layer 10 Generalized Thermoelasticity of Layers 11 Generalized Thermoelasticity of Spheres and Cylinders

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Thermal Stresses -- Advanced Theory and Applications

A study of the one-dimensional thermoelastic waves produced by an instantaneous plane source of heat in homogeneous isotropic infinite and semi-infinite bodies of the Green-Lindsay (G-L) type is presented. Closed-form Green's functions corresponding to the plane heat source are obtained using the decomposition theorem for a potential-temperature wave of the G-L theory. Qualitative analysis of the results is included.

Generalized thermoelasticity: closed-form solutions

The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, is applied to the nondimensional equations of coupled thermoelasticity. The disadvantages of using the thermoelastic potential are thus avoided. The results obtained can be used to generate solutions in the Laplace-transform domain to a broad class of problems in thermoelasticity. Applications to problems pertaining to a half-space and a layer are presented.

Richard B. Hetnarski

Papers

Dynamic problems of thermoelasticity

Thermal Stresses -- Advanced Theory and Applications

Generalized thermoelasticity: closed-form solutions

State space afproach to thermoelasticity

Nonclassical dynamical thermoelasticity