Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble

We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our findings are compared with known exact results for $\beta=1$ finding good agreement. We also consider the case of almost square matrices finding new universal rate functions describing large fluctuations.Comment: 4 pages, 2 figure

An electrically operated kola nut pods breaking machine

Kola nut pod breaking is a very tedious task manually; therefore its mechanization is essential for effective processing.  The objectives of this study are to design and fabricate a kola nut pod breaking machine and performance evaluation of kola nut pods breaking machine.  Some physical and mechanical properties required for machine design were determined using standard methods.  The machine was powered by an electric motor, with the hammer attached to the shaft using a drum with a rope tension of 171.68N, cross–sectional area of 5.027 x 10-5m2 and 3414.90 kN/m2 tensile stress.  The speed of the machine used by the pulley was 308.57 r/min to operate. The machine was evaluated by using one to four pods at a time, and was replicated four times.The average moisture content was 68.87% wet basis. The average length, breadth, width and thickness were 108.54±7.79, 60.60±13.31, 46.97±10.23 and 10.37±1.54 mm for large whole kola nut pods respectively.  The average mass, volume and density of whole kola nut pods were 0.154±0.071 kg, 1.475±6.071x10-4m3, and 471.374±98.756 kg/m3, respectively.The force required to break kola nut pods along its lateral axis was 2691.27±1030.74 N and 421.66±363.97 N for longitudinal axis. The energy needed to break a pod along its lateral axis was 19.78±10.27 J; and 7.617±2.798 J for longitudinal axis.  The lateral force and energy were more in both cases; hence it will be better to break the pod along its longitudinal axis.A pod breaking machine with optimum machine capacity of 501.081 kg/h, maximum machine efficiency of 80.94 % and total cost of N40, 200 k was developed.

The Unavoidable Ecclesiastical Collision in Virginia

Section 5 7-9(A) of the Code of Virginia is a statute that purports to resolve church property disputes. There is, however, a significant amount of controversy as to whether the statute encroaches on the free exercise rights of hierarchical churches located in Virginia and enmeshes Virginia courts in the ecclesiastical thicket. Given the debate surrounding Section 57-9(A) and the controversial shift of several mainstream denominations in matters of substantive church doctrine, Virginia is a fertile breeding ground for church property disputes. Accordingly, the Commonwealth is in the midst of an ecclesiastical crisis. The impact of the crisis is evidenced by the recent division within the Episcopal Church\u27s Diocese of Virginia and the subsequent church property litigation that ensued following the division. This Comment examines the constitutional standards surrounding various courses of action states may pursue to resolve church property disputes and provides a specific analysis of Virginia\u27s statutory scheme for doing so. Current Supreme Court of the United States precedent establishes that courts have three constitutional options they can rely on in resolving church property disputes. Courts may defer to the decision of the religious organization\u27s adjudicatory body, a method of resolution known as the deference approach. Courts may also decide the case on the basis of a neutral principle of law such as property law or contact law. Finally, states may enact special statutes to direct courts on how to resolve church property disputes. This article argues that Section 57-9(A) does not operate as a constitutional method of resolving church property disputes within the Supreme Court\u27s established framework for doing so. Accordingly, due to the constitutional issues with Section 57- 9(A), the law in Virginia regulating church property disputes is on a path leading to an unavoidable ecclesiastical collision

The Unavoidable Ecclesiastical Collision in Virginia

Section 5 7-9(A) of the Code of Virginia is a statute that purports to resolve church property disputes. There is, however, a significant amount of controversy as to whether the statute encroaches on the free exercise rights of hierarchical churches located in Virginia and enmeshes Virginia courts in the ecclesiastical thicket. Given the debate surrounding Section 57-9(A) and the controversial shift of several mainstream denominations in matters of substantive church doctrine, Virginia is a fertile breeding ground for church property disputes. Accordingly, the Commonwealth is in the midst of an ecclesiastical crisis. The impact of the crisis is evidenced by the recent division within the Episcopal Church\u27s Diocese of Virginia and the subsequent church property litigation that ensued following the division. This Comment examines the constitutional standards surrounding various courses of action states may pursue to resolve church property disputes and provides a specific analysis of Virginia\u27s statutory scheme for doing so. Current Supreme Court of the United States precedent establishes that courts have three constitutional options they can rely on in resolving church property disputes. Courts may defer to the decision of the religious organization\u27s adjudicatory body, a method of resolution known as the deference approach. Courts may also decide the case on the basis of a neutral principle of law such as property law or contact law. Finally, states may enact special statutes to direct courts on how to resolve church property disputes. This article argues that Section 57-9(A) does not operate as a constitutional method of resolving church property disputes within the Supreme Court\u27s established framework for doing so. Accordingly, due to the constitutional issues with Section 57- 9(A), the law in Virginia regulating church property disputes is on a path leading to an unavoidable ecclesiastical collision

The Unaviodable Ecclesiastical Collision in Virginia

Section 57-9(A) of the Code of Virginia is a statute that purports to resolve church property disputes. There is, however, a significant amount of controversy as to whether the statute encroaches on the free exercise rights of hierarchical churches located in Virginia and enmeshes Virginia courts in the ecclesiastical thicket. Given the debate surrounding Section 57-9(A) and the controversial shift of several mainstream denominations in matters of substantive church doctrine, Virginia is a fertile breeding ground for church property disputes. Accordingly, the Commonwealth is in the midst of an ecclesiastical crisis. The impact of the crisis is evidenced by the recent division within the Episcopal Church’s Diocese of Virginia and the subsequent church property litigation that ensued following the division. This Comment examines the constitutional standards surrounding various courses of action states may pursue to resolve church property disputes and provides a specific analysis of Virginia’s statutory scheme for doing so. Current Supreme Court of the United States precedent establishes that courts have three constitutional options they can rely on in resolving church property disputes. Courts may defer to the decision of the religious organization’s adjudicatory body, a method of resolution known as the deference approach. Courts may also decide the case on the basis of a neutral principle of law such as property law or contact law. Finally, states may enact special statutes to direct courts on how to resolve church property disputes. This article argues that Section 57-9(A) does not operate as a constitutional method of resolving church property disputes within the Supreme Court’s established framework for doing so. Accordingly, due to the constitutional issues with Section 57- 9(A), the law in Virginia regulating church property disputes is on a path leading to an unavoidable ecclesiastical collision

Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons

Metamaterials and plasmonics are powerful tools for unconventional manipulation and harnessing of light. Metamaterials can be engineered to possess intriguing properties lacking in natural materials, such as negative refractive index. Plasmonics offers capabilities to confine light in subwavelength dimensions and to enhance light-matter interactions. Recently,graphene-based plasmonics has revealed emerging technological potential as it features large tunability, higher field-confinement and lower loss compared to metal-based plasmonics. Here,we introduce hybrid structures comprising graphene plasmonic resonators efficiently coupled to conventional split-ring resonators, thus demonstrating a type of highly tunable metamaterial, where the interaction between the two resonances reaches the strong-coupling regime. Such hybrid metamaterials are employed as high-speed THz modulators, exhibiting over 60% transmission modulation and operating speed in excess of 40 MHz. This device concept also provides a platform for exploring cavity-enhanced light-matter interactions and optical processes in graphene plasmonic structures for applications including sensing, photo-detection and nonlinear frequency generation

Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm to find the low-lying spectrum of a Hamiltonian. While the number of elementary quantum gates does scale polynomially with the size of the system, it increases inversely to the desired error bound $\epsilon$. Making such simulations robust to decoherence using fault-tolerance constructs requires an additional factor of $1/ \epsilon$ gates. These constraints are illustrated by using a three qubit nuclear magnetic resonance system to simulate a pairing Hamiltonian, following the algorithm proposed by Wu, Byrd, and Lidar.Comment: 6 pages, 2 eps figure