Effective memory reduction of the novel look-up table with one-dimensional sub-principle fringe patterns in computer-generated holograms

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

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Synthesis of New Chalcogenide Materials. The Novel One-Dimensional Semiconductor K4 Ti3 S14

MRS Proceedings ◽

10.1557/proc-97-391 ◽

1987 ◽

Vol 97 ◽

Cited By ~ 8

Author(s):

Steven A. Sunshine ◽

Doris Kang ◽

James A. Ibers

Keyword(s):

Electrical Conductivity ◽

Solid State ◽

Alkali Metal ◽

The Novel ◽

Conductivity Measurements ◽

One Dimensional ◽

General Utility ◽

Solid State Materials ◽

Chalcogenide Materials

ABSTRACTThe use of A2 Q/Q melts (A - alkali metal, Q - S or Se) for the synthesis of new one-dimensional solid-state materials is found to be of general utility and is illustrated here for the synthesis of K4 Ti3 SI4. Reaction of Ti metal with a K2 S/S melt at 375°C for 50 h affords K4 Ti3 SI4. The structure possesses one-dimensional chains of seven and eightcoordinate Ti atoms with each chain isolated from all others by surrounding K atoms. There are six S-S pairs (dave - 2.069(3) Å) so that the compound is one of TiIV and may be described as K4 [Ti3 (S)2 (S2)6]. Electrical conductivity measurements indicate that this material is a semiconductor.

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Self-Consistent Solution of the Multi Band Boltzmann, Poisson and Hole-Continuity Equations

VLSI Design ◽

10.1155/1998/14582 ◽

1998 ◽

Vol 6 (1-4) ◽

pp. 257-260

Author(s):

Surinder P. Singh ◽

Neil Goldsman ◽

Isaak D. Mayergoyz

Keyword(s):

Boltzmann Transport Equation ◽

The Novel ◽

Boltzmann Transport ◽

One Dimensional ◽

Bipolar Junction Transistor ◽

Continuity Equations ◽

The Poisson Equation ◽

Curvilinear Grid ◽

Consistent Solution ◽

Junction Transistor

The Boltzmann transport equation (BTE) for multiple bands is solved by the spherical harmonic approach. The distribution function is obtained for energies greater than 3 eV. The BTE is solved self consistently with the Poisson equation for a one dimensional npn bipolar junction transistor (BJT). The novel features are: the use of boundary fitted curvilinear grid, and Scharfetter Gummel type discretization of the BTE.

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Synthesis and Structural Systematics of Nitrogen Base Adducts of Group 2 Salts. VII. Some Complexes of Group 2 Metal Halides With Aromatic N,N'-Bidentate Ligands

Australian Journal of Chemistry ◽

10.1071/ch9960099 ◽

1996 ◽

Vol 49 (1) ◽

pp. 99 ◽

Cited By ~ 21

Author(s):

BW Skelton ◽

AF Waters ◽

AH White

Keyword(s):

Room Temperature ◽

The Novel ◽

Bidentate Ligands ◽

Nitrogen Base ◽

One Dimensional ◽

X Ray ◽

L System ◽

L Systems ◽

Group 2 ◽

Structural Characterizations

Syntheses and room-temperature single-crystal X-ray structural characterizations are recorded for a number of adducts of Group 2 halides with the aromatic N,N′- bidentate ligands L = 2,2'-bipyridine ( bpy ) and 1,10-phenanthroline ( phen ). One adduct of 1 : 1 MX2/L stoichiometry is recorded: [( bpy )Ca(μ-Br)(4/2)](∞ ׀ ∞) (1) is monoclinic, C 2/c, a l7.102(5), b 9.845(1), c 7.600(2) Ǻ, β 107.65(2)°, Z = 4 f.u .; conventional R on #1472; F ׀ at convergence was 0.057 for No 817 independent 'observed' ( I > 3σ(I)) reflections, the compound being a one-dimensional polymer… CaL (μ-Br)2CaL(μ-Br)2…, with six-coordinate calcium, cis-CaN2(μ-Br)4, on a twofold axis. 1 : 2 MX2/L systems have been described for two types of array: [( bpy )2CaI2] (2), orthorhombic, Pnca, a 16.914(4), b 13.80(1), c 9.290(4) Ǻ, Z = 4 f.u .; R 0.039 for No 1738, is discrete mononuclear, containing cis-CaN4I2 six-coordinate calcium, whereas the barium analogue is an infinite one-dimensional polymer, [( bpy )2Ba(μ-I)(4/2)](∞׀ ∞) (3), triclinic, Pī, a 11.318(2), b 11.078(2), c 9.206(4) Ǻ, α 80.87(2), β 77.52(2), γ 87.53(1)°, Z = 2 f.u .; R 0.032 for No 4154, with eight-coordinate (N2)2Ba(μ-I)4. The perchlorate analogue, [( bpy )2Ba(μ-OClO2O)(4/2)](∞ ׀ ∞) (4), although of similar stoichiometry, has a trans-rather than a cis-linked chain; it is monoclinic, P 21/c, a 6.606(2), b 18.661(7), c 19.440(8) Ǻ, β 109.45(4)°, Z = 4 f.u .; R 0.044 for No 4060, with μ-I replaced by O,O'-ClO4 bridging units and eight-coordinate barium, (N2)2BaO4. The 1 : 3 MX2/L system is represented (as its hemi( bipyridine ) 'solvate') by mononuclear [( bpy )3SrI2].0.5bpy (5), monoclinic, P 21/c, a 20.834(8), b 9.735(4), c 18.460(7) Ǻ, β 114.87(3)°, Z = 4 f.u .; R 0.039 for No 3711, containing eight-coordinate strontium, [(N2)3SrI2]; there is also an isomorphous calcium/ perchlorate analogue [( bpy )3Ca(OClO3)2].0.5bpy (6), a 21.413(6), b 9.813(4), c 18.659(2) Ǻ, β 115.67(2)°, R 0.057 for No 3090, in which unidentate O-ClO4 ligands replace the iodine about the metal atom. A 1 : 4 adduct is obtained with CaI2/phen; ionic [Ca( phen )4] I2 (7), triclinic, Pī , a 14.703(3), b 13.292(3), c 11.38(1) Ǻ, α 92.78(4), β 96.15(4), γ 105.22(2)°, Z = 2 f.u ., R 0.053 for No 3658, contains eight-coordinate Ca(N2)4 arrays, while the novel 1 : 5 adduct [ Ba ( phen )4] I2.MeCN (8) is triclinic, Pī , a 12.170(6), b 13.760(7), c 18 254(8) Ǻ, α 77.05(9), ,β 71.96(4), γ 70.83(9)°, Z = 2 f.u ., R 0.040 for No 4447, containing 10-coordinate barium, [ Ba (N2)5]. A 1 : 4 adduct formed with BaBr2 is [ BrBa( phen )4] Br.MeOH (9), triclinic, Pī , a 17.748(4), b 17.418(2), c 15.535(7) Ǻ, α 91.63(2), β 100.53(3), γ 115.39(1)°, Z = 4 f.u ., R 0.062 for No 4092, containing nine-coordinate barium, [ BrBa (N2)4].

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Fast calculation method for curved computer-generated holograms using look-up-table

10.1364/dh.2021.dtu7b.4 ◽

2021 ◽

Author(s):

Dapu Pi ◽

Juan Liu

Keyword(s):

Calculation Method ◽

Fast Calculation ◽

Look Up Table ◽

Computer Generated Holograms

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A Comparison of Different Counting Methods for a Holographic Particle Counter: Designs, Validations and Results

Sensors ◽

10.3390/s20103006 ◽

2020 ◽

Vol 20 (10) ◽

pp. 3006

Author(s):

Georg Brunnhofer ◽

Isabella Hinterleitner ◽

Alexander Bergmann ◽

Martin Kraft

Keyword(s):

Three Dimensional ◽

Nano Particles ◽

The Novel ◽

Computational Speed ◽

Hologram Plane ◽

Detection And Counting ◽

Sampling Volume ◽

Fringe Patterns ◽

Selection Of

Digital Inline Holography (DIH) is used in many fields of Three-Dimensional (3D) imaging to locate micro or nano-particles in a volume and determine their size, shape or trajectories. A variety of different wavefront reconstruction approaches have been developed for 3D profiling and tracking to study particles’ morphology or visualize flow fields. The novel application of Holographic Particle Counters (HPCs) requires observing particle densities in a given sampling volume which does not strictly necessitate the reconstruction of particles. Such typically spherical objects yield circular intereference patterns—also referred to as fringe patterns—at the hologram plane which can be detected by simpler Two-Dimensional (2D) image processing means. The determination of particle number concentrations (number of particles/unit volume [#/cm 3 ]) may therefore be based on the counting of fringe patterns at the hologram plane. In this work, we explain the nature of fringe patterns and extract the most relevant features provided at the hologram plane. The features aid the identification and selection of suitable pattern recognition techniques and its parameterization. We then present three different techniques which are customized for the detection and counting of fringe patterns and compare them in terms of detection performance and computational speed.

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