Tunneling between helical Majorana modes and helical Luttinger liquids

We propose and study the charge transport through single and double quantum point contacts setup between helical Majorana modes and an interacting helical Luttinger liquid. We show that the differential conductance decreases for stronger repulsive interactions and that the point contacts become insulating above a critical interaction strength. For a single point contact, the differential conductance as a function of bias voltage shows a series of peaks due to Andreev reflection of electrons in the Majorana modes. In the case of two point contacts, interference phenomena make the structure of the individual resonance peaks less universal and show modulations with different separation distance between the contacts. For small separation distance the overall features remain similar to the case of a single point contact.Comment: v.2: 14 pages, 11 figures; adding one figure, an appendix, and some minor change

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation

A microfluidic oligonucleotide synthesizer

De novo gene and genome synthesis enables the design of any sequence without the requirement of a pre-existing template as in traditional genetic engineering methods. The ability to mass produce synthetic genes holds great potential for biological research, but widespread availability of de novo DNA constructs is currently hampered by their high cost. In this work, we describe a microfluidic platform for parallel solid phase synthesis of oligonucleotides that can greatly reduce the cost of gene synthesis by reducing reagent consumption (by 100-fold) while maintaining a 100 pmol synthesis scale so there is no need for amplification before assembly. Sixteen oligonucleotides were synthesized in parallel on this platform and then successfully used in a ligation-mediated assembly method to generate DNA constructs 200 bp in length

Exact solution of a quantum forced time-dependent harmonic oscillator

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator

Oxygen Measurement During Cell Culture: From Multiwell Plates to Microfluidic Devices

Oxygen is an important regulator of normal cell behavior. Proper supply of oxygen is required to maintain ATP production, while perturbation of oxygen supply alters cell behavior and leads to tissue damage and cell death. In vivo, cells are exposed to a mean partial pressure of oxygen between 0.03 to 0.09 atm that is tissue specific. In contrast, conventional cell cultures are routinely performed at an atmospheric oxygen level of 0.21 atm. The disparity between in vivo and in vitro oxygen levels have been shown to affect cell viability, growth and differentiation. Continuous measurements and control of oxygen levels are thus critical to maintaining proper cell behavior. Current methods of oxygen measurement are invasive, difficult to integrate with microscopy and lack imaging capabilities. To improve the current state of measurements, we have developed a new non-invasive oxygen sensor for in vitro cell culture. The sensor was prepared by incorporating a porphyrin dye, Pt(II) meso-Tetra(pentafluoro-phenyl)porphine (PtTFPP), into gas permeable poly(dimethylsiloxane) (PDMS) thin films. The response of the sensor to oxygen followed the linear Stern-Volmer equation and demonstrated an order of magnitude higher sensitivity compared to other sensors (KSV = 548 ± 71 atm-1). A multilayer design created by sandwiching the PtTFPP-PDMS with a thin film of Teflon AF followed by a second layer of PDMS effectively mitigated against cytotoxicity effects and provided a suitable substrate for cell attachment. To demonstrate the utility of the sensor, oxygen measurements were made continuously with NIH 3T3 mouse fibroblast cells. The oxygen levels were found to decrease as a result of oxygen consumption by the cells. Using Fick's law, the data was analyzed and a per-cell oxygen consumption rate for the 3T3 fibroblasts was calculated. In addition, cells were clearly visualized on the sensor demonstrating the ability to integrate with phase-contrast and fluorescence microscopy. Next, human hepatocellular carcinoma HepG2 were cultured on the oxygen sensor and continuous oxygen measurements showed a drastic decrease in oxygen level such that the cells were exposed to hypoxic conditions within 24 h. The per-cell oxygen consumption rate for HepG2 was determined to be 30 times higher than the 3T3 fibroblasts, confirming the high metabolic nature of these cells. At high densities, oxygen flux measurements showed an asymptotic behavior reaching the theoretical maximum of the culture condition. When the oxygen diffusion barrier was reduced, the oxygen flux increased, demonstrating insufficient oxygenation for HepG2 at these densities. In routine culture, HepG2 adhere to their neighboring cells which results in formation of cell clusters. Oxygen measurement confirmed the presence of oxygen gradient across the cell clusters with the lowest oxygen levels observed in the middle. Finally, we successfully integrated the oxygen sensor into microfluidic systems. The sensor provided real-time non-invasive measurements of oxygen levels on-chip. To regulate the oxygen levels in the device, water with different dissolved oxygen concentrations was used instead of gas. This method successfully mitigated the problems of pervaporation associated with previous devices. Physiologically relevant oxygen levels and oxygen gradients were easily generated on the device and the results showed excellent agreement with numerical simulations