Microfluidic Acoustic Metamaterial SAW Based Sensor

Introduction. Microacoustic sensors based on surface acoustic wave (SAW) devices allow the sensor integration into a wafer based microfluidic analytical platforms such as lab-on-a-chip. Currently exist various approaches of application of SAW devices for liquid properties analysis. But this sensors probe only a thin interfacial liquid layer. The motivation to develop the new SAW-based sensor is to overcome this limitation. The new sensor introduced here uses acoustic measurements, including surface acoustic waves (SAW) and acoustic methamaterial sensor approaches. The new sensor can become the starting point of a new class of microsensor. It measures volumetric properties of liquid analytes in a cavity, not interfacial properties to some artificial sensor surface as the majority of classical chemical and biochemical sensors.Objective. The purpose of the work is to find solutions to overcome SAW-based liquid sensors limitations and the developing of a new sensor that uses acoustic measurements and includes a SAW device and acoustic metamaterial.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. Lithium niobate (LiNbO3) 127.86° Y-cut with wave propagation in the X direction was chosen as a substrate material. Microfluidic structure was designed as a set of rectangular shape channels. A method for measuring volumetric properties of liquids, based on SAW based fluid sensor concept, comprising the steps of: (a) providing sensor structure with the key elements: a SAW resonator, a high-Q set of liquid-filled cavities and intermediate layer with artificial elastic properties between them; (b) measuring of resonance frequency shift, associated with the resonance in liquid-filled cavity, in the response of weakly coupled resonators of SAW resonator loaded by periodic microfluidic structure; (c) determination of volumetric properties of the fluid on the basis of a certain relationship between the speed of sound in liquid, the resonant frequency of the set of liquid-filled cavities, and the geometry design of the cavity.Results. The new sensor approach is introduced. The eigenmodes of the sensor structure with a liquid analyte are carried out. The characteristic of sensor structure is determined. The key elements of introduced microfluidic sensor are a SAW structure, an acoustic metamaterial with a periodic set of microfluidic channels. The SAW device acts as electromechanical transducer. It excites surface waves propagating in the X direction lengthwise the periodic structure and detects the acoustic load generated by the microfluidic structure resonator. The origin of the sensor signal is a small frequency change caused by small variations of acoustic properties of the analyte within the set of microfluidic channels.Conclusion. The principle of the new microacoustic sensor, which can become the basis for creating a new class of microfluidic sensors, is shown.Introduction. Microacoustic sensors based on surface acoustic wave (SAW) devices allow the sensor integration into a wafer based microfluidic analytical platforms such as lab-on-a-chip. Currently exist various approaches of application of SAW devices for liquid properties analysis. But this sensors probe only a thin interfacial liquid layer. The motivation to develop the new SAW-based sensor is to overcome this limitation. The new sensor introduced here uses acoustic measurements, including surface acoustic waves (SAW) and acoustic methamaterial sensor approaches. The new sensor can become the starting point of a new class of microsensor. It measures volumetric properties of liquid analytes in a cavity, not interfacial properties to some artificial sensor surface as the majority of classical chemical and biochemical sensors.Objective. The purpose of the work is to find solutions to overcome SAW-based liquid sensors limitations and the developing of a new sensor that uses acoustic measurements and includes a SAW device and acoustic metamaterial.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. Lithium niobate (LiNbO3) 127.86° Y-cut with wave propagation in the X direction was chosen as a substrate material. Microfluidic structure was designed as a set of rectangular shape channels. A method for measuring volumetric properties of liquids, based on SAW based fluid sensor concept, comprising the steps of: (a) providing sensor structure with the key elements: a SAW resonator, a high-Q set of liquid-filled cavities and intermediate layer with artificial elastic properties between them; (b) measuring of resonance frequency shift, associated with the resonance in liquid-filled cavity, in the response of weakly coupled resonators of SAW resonator loaded by periodic microfluidic structure; (c) determination of volumetric properties of the fluid on the basis of a certain relationship between the speed of sound in liquid, the resonant frequency of the set of liquid-filled cavities, and the geometry design of the cavity.Results. The new sensor approach is introduced. The eigenmodes of the sensor structure with a liquid analyte are carried out. The characteristic of sensor structure is determined. The key elements of introduced microfluidic sensor are a SAW structure, an acoustic metamaterial with a periodic set of microfluidic channels. The SAW device acts as electromechanical transducer. It excites surface waves propagating in the X direction lengthwise the periodic structure and detects the acoustic load generated by the microfluidic structure resonator. The origin of the sensor signal is a small frequency change caused by small variations of acoustic properties of the analyte within the set of microfluidic channels.Conclusion. The principle of the new microacoustic sensor, which can become the basis for creating a new class of microfluidic sensors, is shown

Reality property of discrete Wronski map with imaginary step

For a set of quasi-exponentials with real exponents, we consider the discrete Wronskian (also known as Casorati determinant) with pure imaginary step 2h. We prove that if the coefficients of the discrete Wronskian are real and for every its roots the imaginary part is at most |h|, then the complex span of this set of quasi-exponentials has a basis consisting of quasi-exponentials with real coefficients. This result is a generalization of the statement of the B. and M. Shapiro conjecture on spaces of polynomials. The proof is based on the Bethe ansatz for the XXX model.Comment: Latex, 9 page

On reality property of Wronski maps

We prove that if all roots of the discrete Wronskian with step 1 of a set of quasi-exponentials with real bases are real, simple and differ by at least 1, then the complex span of this set of quasi-exponentials has a basis consisting of quasi-exponentials with real coefficients. This result generalizes the B. and M.Shapiro conjecture about spaces of polynomials. The proof is based on the Bethe ansatz method for the XXX model.Comment: Latex, 20 page

First order dipolar phase transition in the Dicke model with infinitely coordinated frustrating interaction

We found analytically a first order quantum phase transition in the Cooper pair box array of $N$ low-capacitance Josephson junctions capacitively coupled to a resonant photon in a microwave cavity. The Hamiltonian of the system maps on the extended Dicke Hamiltonian of $N$ spins one-half with infinitely coordinated antiferromagnetic (frustrating) interaction. This interaction arises from the gauge-invariant coupling of the Josephson junctions phases to the vector potential of the resonant photon field. In $N \gg 1$ semiclassical limit, we found a critical coupling at which ground state of the system switches to the one with a net collective electric dipole moment of the Cooper pair boxes coupled to superradiant equilibrium photonic condensate. This phase transition changes from the first to second order if the frustrating interaction is switched off. A self-consistently `rotating' Holstein-Primakoff representation for the Cartesian components of the total superspin is proposed, that enables to trace both the first and the second order quantum phase transitions in the extended and standard Dicke models respectively.Comment: 12 pages, 10 figure