In fact, Eq. Thus, |J1| |J2|=|∂u/∂z|2|∂z/∂u|2=1⁠, and α and β have the same values in Eqs. Editor: Yuwen Zhang. (5) represents a superposition such temperature distributions along the boundary. In Fig. Redken Hot Sets 22 Thermal Setting Mist | For All Hair Types | Protects Against Heat Damage. Read honest and unbiased product reviews from our users. 00 ($4.00/Fl Oz) Save more with Subscribe & Save. Maurizia Hair Stylist di Reggio Emilia ci consiglia come utilizzare al meglio la pasta modellante Shape Factor 22 di Redken. The integral is a superposition of such sources of strength h(ζ) around the boundary σ. Stay healthy, stay safe. 00. ASME. Köp Redken SHAPE FACTOR 22 - Stylingprodukter - - för 189,00 kr (2020-11-10) på Zalando. Isotherms are in red and adiabats in gray. Compare all Redken Styling Cream. Popular searches in Hair Products. Free shipping. where K(m) and K′(m) are the real and imaginary quarter periods and m is calculated from this equation [12]. For other rotations of the disk prior to mapping to the square, the shape factor would be unchanged, but the boundary conditions on the square would rotate around the perimeter. This leave-in texturizing sculpting cream paste is excellent for controlling short hair and creating updos with high control and a matte finish. We begin with heat conduction in the disk. Maximum control matte  cream-paste that feels like a paste but spreads like a cream for ultimate flexibility with a touchable feel. Redken Redken Shape Factor 22 Sculpting Cream Paste 1.7 Oz. Out of stock. The mapped disk is shown in Fig. This distribution is precisely the function ha,1(ϕ) proposed in Eq. The computational domain had 100 times the area of the inner square and had a square external boundary at the average perimeter temperature of the interior square (θ = 1/2). Assoc. By Renata K. sedrowoolley. The disk has two 90 deg isothermal edges and two opposing 90 deg adiabatic edges (boundary conditions rotated −45 deg from Fig. To demonstrate the ideas developed thus far, we will map reference cases for which the shape factor is known to cases for which it is not easily calculated. For simple configurations, such as a rectangle or an annular sector with opposing isothermal edges, S is easily found; but for more complicated shapes, finding S rapidly becomes analytically difficult. Kober writes this expression in terms of the elliptic function parameter, k: m = k2. Always read labels and instructions before using a product. The resulting Lua functions were supplied to PGFPLOTS [17] to generate the charts. Because θe is bounded at infinity, the heat flux goes to zero as 1/r2 so that no heat is transferred to infinity.2. These issues are discussed in the examples that follow. For the circular disk, Eq. Redken Shape Factor 22 50ml Met de Flex stylingslijn van redken geef je het haar optimale vorm met ultieme flexibiliteit. $54.00. Configuration and coordinates for Green's functions: (a) interior region and (b) exterior region, Coordinates for the Green's function on the unit disk. Build shape, separation, texturize, and lock hair into place with Shape Factor 22 Sculpting Cream. Mappings of a rectangle of aspect ratio a : b = 1:1 to the interior and exterior of a unit disk. ... Do not have a Redken Salon Professional account? However, we have made the empirical observation that, for some specific cases including this one, the exterior shape factor is the same as the interior shape factor. 1, showing that S = 1, so we will not compute this mapping. Shape factors for steady heat conduction enable quick and highly simplified calculations of heat transfer rates within bodies having a combination of isothermal and adiabatic boundary conditions. 10(b)). [9], this plot was first obtained by Schwarz in 1869. Write a review. That S = 1 may be confirmed from Fig. The interior solution on the disk can be mapped to the exterior solution using the reciprocal map, which takes points (u, v) inside the disk in the w-plane to the outside of the disk in the t-plane: t = 1/w, with t=(u′,v′)⁠. Solutions for heat conduction interior to the square obtained using the reverse mapping by Eq. 00 $18.00 $ 18. The conformal mapping from the square to the disk, Eq. For example, a disk with 357 deg of its boundary at θ = 1, two adiabatic segments of 1 deg arc, and a 1 deg segment at θ = 0 would require a far field temperature only slightly below 1, roughly θ ≈ 358/360. 13 reviews. The mapping is unique to within an arbitrary rotation of the disk, and the significance of such rotations is discussed in the section Reverse Map From the Disk to the Square. [13].) $19.45 ( Redken Shape Factor 22 Modellier 50 ml. ... Redken Iron Shape 11 Finishing Spray 8.5 oz. Provides serious sculpting with a flexible finish. 5, where again there are ten heat flow channels and ten temperature increments. The Riemann mapping theorem shows that for a plane simply connected region R with boundary σ containing an interior point ζ, there exists a function w = f(z, ζ), analytic on R, that conformally maps R one-to-one onto the unit disk in the w-plane, taking σ to the disk's circumference and ζ to w = 0 [4,8]. The inverse map, from w to z, is discussed below (see Eq. Further, isotherms and adiabats remain orthogonal under conformal maps. $20.00 $ 20. The mapping from the interior of the disk to the exterior of the square is, We now generalize the analysis done for the unit disk to any arbitrary two-dimensional region. Redken Shape Factor 22 50mL. 30). We will assume that the only heat source and sink are the isothermal edges of the region, and we assume that the interior and exterior conductivities are uniform but not equal. Isotherms are in color and adiabats are in gray, S = 1. Redken Flex Shape Factor 22 create styles with serious sculpting and a flexible finish. The asymptotic expansion for |z|→∞ is θe(z)∼θ∞e+a1/z+a2/z2+⋯ where θ∞e is given by Eq. Specifically, for any circle in E that encompasses σ, the integral of temperature around the circle gives the limiting value of temperature as |z|→∞⁠. Comparing Eqs. The interior and exterior thermal conductivities must be uniform, but need not be equal. Apply to damp hair and sculpt. In other words, the temperature at infinity is the average temperature around the perimeter of the unit disk. (Numerical details in Appendix  A). Provides serious sculpting  with a flexible finish. The shape factor is obviously unchanged by any rotation of the disk as well. Out of stock. (38) also maps the region exterior to the unit disk into the unit disk, so this result is expected from Eq. 1 was based in part on a code provided by Andrew J. Lienhard. Redken Shape Factor 22 Sculpting Cream Paste is a matte hair cream-paste provides serious sculpting but with a flexible finish. Then, conformal mapping is used to relate known configurations for squares and rectangles to the solutions for the disk. Redken-inspired hair styles & products such as shampoos and conditioners. Stock info: in stock. The thermal conductivities of the exterior and interior regions can be entirely different. Redken Shape Factor $ 22.00. The region R is simply connected. In contrast, Figs. Matte hair cream-paste provides serious sculpting but with a flexible finish. In this paper, we show that known shape factors for the interior of two-dimensional objects are identical to the corresponding shape factors for the exterior of those objects. Find hairspray, styling products shampoo, and conditioner designed for specific needs with simple solutions. $13.50. 10(a). When ζ = 0, we will simply write w = f(z). Shop Redken Professional hair care products at ULTA. Met de Shape Factor 22 breng je vorm aan en definieer je het haar. Provides serious sculpting with a flexible finish.High ControlIdeal for short hair and upstyles.Lea (13) and (17), that shape factors interior and exterior to a disk are equal, (ii) the preservation of S under conformal mapping, (iii) the importance of rotations of the disk, and, (iv) the equality of the interior and exterior shape factors for the square. BENEFITS Create styles with serious sculpting and a flexible finish. Pickup not available. We also require ge(z, ζ) to produce a bounded solution for θe as |z|→∞ [8]. (10) provides the necessary temperature at large radius. FREE Shipping on your first order shipped by Amazon. Stuff4Beauty offers your favorite name brand salon hair products and beauty products and supplies at everyday low prices! In order for solutions to these two-dimensional problems to exist, the temperature at infinity must be bounded9 and take on a specific value that ensures no net heat transfer to locations distant from the boundary, σ. $18.00 $ 18. We have considered conduction shape factors for two-dimensional, simply connected objects that have two isothermal boundaries, each at different temperature and separated by two adiabatic boundaries. 4 may be remapped to the z-plane using this inverse mapping, and the entirely unsurprising result is shown in Fig. The solution for the disk shown in Fig. Free shipping. Search for other works by this author on: Shape factors for steady heat conduction have been tabulated in a number of publications [. No heat flows to C2 or C4, which are assumed adiabatic. This is currently the cheapest offer among 6 retailers. This result is like Eq. Mappings of a rectangle of aspect ratio a : b = 1.5:1 to the interior and exterior of a unit disk, S = b/a = 2/3⁠. We therefore provide the following simple (and perhaps original) explanation. We do not know the equations for these distributions; but, for the present purpose, it is sufficient that we know that they exist and correspond to the condition in which C2 and C4 are adiabatic. 5 Fl Oz. Note that ge(z|ζ)→0 as |z|→∞⁠. The canonical case of the interior and exterior of a disk is examined first. Gratis levering på bestillinger over 189 kr. (In fact, the situations in Fig. Shape Factor 22 Sculpting Cream Paste by Redken for Unisex, 1.7 oz: Provides serious sculpting with a flexible finish In some cases, we will consider the exterior Dirichlet problem for conduction in the region exterior to σ, in which case we consider the exterior region, E, to be the extended complex plane, including the point at infinity. It will work to create definition and detail, and will allow you to shape, sculpt and reshape your hair. (39) is also ge(z|ζ)⁠.8 The normal direction, however, is reversed for the exterior problem. - L.M. Variations on this mapping are discussed by Fong [11]. In addition, the “Yin-Yang” phenomenon for conduction shape factors is explained as a rotation of the unit disk prior to conformal mapping. where in the second step, we revert to the interior normal direction, with signs canceling; and in the third step, we substitute from Eqs. However, for asymmetric conditions, the far-field temperature may take some other value between 0 and 1. For example, the solution for heat conduction from one side of the interior of a square of height a to the other side is trivial to find analytically: Q˙=kaΔT/a⁠, so S = 1. 7(a), to the square because this mapping provides a solution for the square with isothermal half-boundaries at opposing corners (Fig. (35), we see that the exterior solution is just Eq. However, the analytical determination of shape factors for any but the simplest configurations can quickly come to involve complicated mathematics, and, for that reason, it is desirable to extend the available results as far as possible. Bought this for my boyfriend and it seems to work great on … Shape Factor 22 Sculpting Cream-Paste. Select locations now offer curbside pickup & home delivery The shape factor for the square is S = 1 as previously discussed and as also evident because Fig. If the sections C2 and C4 were adiabatic, each would have some smoothly varying temperature distribution. (44) to Eq. Can be blended with other products for the ultimate cream-paste texture. Redken. Redken Shape Factor 22 Sculpting Cream Paste allows you to build controlled, extremely shaped hairstyles. Redken Shape Factor 22 Sculpting Cream-Paste | SalonCentric (10). By signing up, I agree to receive emails from Redken and other L'Oréal brands and programs. Since there are no temperature sources other than the boundary. - Sculpts and defines - Matte finish - Maximum control - Ideal for short hair or updos Bought this for my boyfriend and it seems to work great on fine hair that just need a bit of UMF! For added texture and sculpting, apply to dry hair. Only the inner 30% of the computational domain is shown in the figure; however, temperature variation in the excluded region is less than 10% of the overall temperature difference. The reciprocal map reflects the boundary conditions about the x-axis, but this has no effect on S. Finally, using the mapping function, we may plot the temperature distribution along either adiabatic edge (Fig. 4.67 This mapping produces a disk with opposing 90 deg isothermal edges and with the same number of temperature increments and heat flow channels as the original square: S = 1. where K(m) is the complete Legendre elliptic integral of the first kind with modulus m and F(φ | m) is the incomplete Legendre elliptic integral of the first kind with complex amplitude φ. Do not have a Redken Salon Professional account? Disclaimer: Content on this site is for reference purposes only and is not a substitute for advice from a licensed health-care professional. The hot and cold boundaries act as a source and sink, respectively. If z and ζ lie outside the unit disk, the Green's function is unaffected; and so Eq. Are you a salon professional? [10]. dimensionless length of sides of square or rectangle, simply connected region exterior to curve, temperature distribution on adiabatic edge, Eq. The elliptic functions were computed in Lua using an algorithm from Press et al. Disk with two 90 deg isothermal edges and two opposing 90 deg adiabatic edges. De producten zijn geschikt voor elk haartype en stijl! Redken Shape Factor 22 Sculpting Cream Paste Item#: redken_shape_factor. The solution for conduction exterior to the square is discussed later in this section. (9). Categories: Hair, Redken Product ID: 4158. Sixteen isotherms are in color and eleven adiabats are in gray: (a) map of a rectangle of 1.5:1 aspect ratio to interior of the unit disk and (b) map of a rectangle of 1.5:1 aspect ratio to exterior of the unit disk. Heat Transfer. Both have made a number of helpful comments on the manuscript. Call the scalar multiplier J. Lowest price for Redken Shape Factor 22 Sculpting Cream-Paste 50ml 2-pack is £21. Note that the interior and exterior thermal conductivities need not be the same. 4, the axis of symmetry is either the u- or the v-axis. The Yin-Yang bodies are those having a geometrical axis of symmetry on either side of which the adiabatic and isothermal boundary conditions are interchanged. Redken Move Ability 05 Lightweight Defining Cream Paste, 1.7 Ounce . Isotherms are in color and adiabats are in gray, S=b/a =1/2⁠: (a) map of a rectangle of 2:1 aspect ratio to interior of the unit disk and (b) map of a rectangle of 2:1 aspect ratio to exterior of the unit disk. We will show this result in several ways: for the fundamental case of a unit disk; as a property of conformal maps between arbitrary shapes and the unit disk (including a few examples of such maps); and for a more general region, by using Green's functions. Lienhard, J. H., V (April 16, 2019). Qty: Get in-stock alert. Shape factor 22 is a high hold hairspray polymer & polyol system with the shaping power of a hairspray in cream-wax form. The mapping takes the corner at z = (w1, 0) to w = (1, 0), that at z = (0, w1) to w = (0, 1), and so on. The influence function is the temperature at z that would be produced by a boundary temperature that is a delta function at ζ (e.g., like a unit-strength point source). Delivery not available. shape factor 22 is a high hold hairspray polymer & polyol system with the shaping power of a hairspray in cream-wax form. Let us assume that these two distributions are none other than ha,1(ϕ) and ha,2(ϕ). The gsl C code was compiled using XCode under Mac OS X. 10(b), the axis of symmetry is a line through the origin at either 45 deg or –45 deg; and in Fig. This Product Has Been Discontinued Click Here To Continue Shopping Skincare By Alana. Pack available: 1.7 oz. Try this edgy, cool girl pony with side swept bangs for a on trend, effortless downtown vibe. In particular, these cases illustrate: (i) the result of Eqs. Fri frakt på beställningar över 229 kr. Register with our professional site to receive exclusive content, event invites and contest geared toward our salon professionals!. Some amount of heat flows from the source to the interior and some amount flows, in the opposite direction, to the exterior. We have already presented a finite element solution for the exterior in Fig. Rough Paste 12 Working Material Medium control hair paste Stay High 18 High-Hold Gel To Mousse Both are Yin-Yang configurations [13]: (a) the reverse mapping from the disk to the square, S =1⁠, and (b) rotated boundary conditions based on the rectangle with a/b =1⁠, S = 1. Dostawa do 24 godzin. PURCHASE 2 OF EACH REDKEN … In particular, the Riemann mapping theorem guarantees that any simply connected region in the plane can be mapped to the unit disk. $16.15 (My Beauty Buy) Redken - 22 Shape Factor Sculpting Cream 1.7 oz. 1 may also have a far field temperature of θ = 1/2. $12.00 Used. PureOlogy, Aquage, Redken, Paul Mitchell, Nioxin, Graham Webb, Biosilk, Matrix, Kenra, Artec, GHD, OSIS and Wella are just a few of our name brands! Several of the figures use the perceptually uniform colormaps, Viridis and Plasma, by van der Walt and Smith [21]. While this principle is known in other contexts (e.g., for electrical resistance), the present original arguments may be useful for instructional purposes. With this information, a lengthy but straightforward calculation shows that the influence function, As for the unit disk, we can imagine the boundary of, For the exterior problem, the normal direction is reversed, We can more formally demonstrate that the integral defining the shape factor is unchanged by a conformal map. Product code: 2970 . Both geometrical and mathematical proofs are given to show that conduction shape factors are invariant when an object is conformally mapped onto another object. (B4) and (B7). According to Ref. Sold & shipped by Maison Rouge. Producing a matte finish, it's great for short styles. The mapped boundary section has length. Twenty equally spaced isotherms are shown in red and twenty identically spaced adiabats in black, giving ni=19 temperature increments and na=19 heat flow channels. Redken Shape Factor 22 Sculpting Cream-Paste 50 ml pro definici a tvar vlasů pro ženy. (39) consists of sources at ζ and at its image point ζ*, plus a constant term that makes g = 0 for z on σ. Redken professional salons offering hair styles, cuts and hair color for men & women. June 2019; 141(6): 061301. Redken Styling - Shape Factor 22 Sculpting Cream-Paste (50ml) boasts a polymer and polyol system to give your hair the same high levels of hold as hairspray, whilst creating detail and definition that can be sculpted, shaped and reshaped. (13) and (17), Si = Se. (Translation of the coordinates is also possible, but not important here.). where ki is the thermal conductivity inside the disk. Matte hair cream-paste provides serious sculpting but with a flexible finish. Heat conduction outside a square. Viewed as a flux plot [3], this figure shows that S=na/ni=1⁠. $16.88 New. Professional Beauty. This product was designed to give the power of a hairspray in a cream-wax form. 3 has an equal number of heat flow channels and temperature increments: na = ni = 10 so that S = na/ni = 1. The result is shown in Fig. 10 are examples 2a and 2b from Ref. 10(b), since the number of temperature increments equals the number of heat flow channels. Redken Shape Factor 22 Sculpting Cream Paste is the perfect styling product for short hair. In fact, a conformal mapping may be shown to consist of a rotation and a scalar multiplication of the original coordinates, where the angle of rotation and the scalar are different at different points. Note that the reciprocal map reflects the disk about the horizontal axis, S = 1. The heat fluxes at any point are generally not the same. 10(a), this axis of symmetry is either the x- or the y-axis; in Fig. This sign up is for U.S. consumers. An important consequence of the Riemann mapping theorem is that if E is the portion of the extended complex plane3 outside a simple closed curve σ, then E can be mapped conformally to the inside of the unit disk. where |w|≤1 [4]. where z = (x, y) is the (possibly complex) coordinate in the plane and h(z) is the distribution of temperature on the curve. (11), simply connected region interior to curve, real, imaginary coordinates in the w-plane, real, imaginary coordinates in the t-plane, real, imaginary coordinates in the z-plane. Consider an integral in the mapped, Similarly, the transformation of the skew gradient is, Multiplication of the Jacobian matrices produces a considerable simplification, Putting these pieces together, denoting the, Formfactor and Formwiderstand Der Stationären Mehrdimensionalen Wärmeleitung, Conduction and Thermal Contact Resistances (Conductances), A First Course in Partial Differential Equations, Boundary Value Problems of Mathematical Physics, Heat Conduction Through ‘Yin-Yang’ Bodies, Manual for Package PGFPLOTS, Version 1.15, Tutorial: Using External C Libraries With the LuaLaTeX FFI, Copyright © 2019 by ASME; reuse license CC-BY 4.0, Copyright © 2020 The American Society of Mechanical Engineers, This site uses cookies. décembre 8 2018, 1:49 pm. (30) from the disk for two sets of boundary conditions. Solutions on the unit disk and the effect of mapping on shape factors are therefore of central importance to what follows. A matlab solution based on high-resolution finite element calculations (Fig. A much more interesting result is obtained by mapping the rotated disk, Fig. In words, line integrals of the normal derivative are unchanged by conformal maps. We may consider the edges at ±a to be isothermal and those at ±b to be adiabatic. Customers also viewed. Eleven isotherms and eleven adiabats for the square are shown in Fig. Since the mappings are one-to-one, we can alternatively choose boundary conditions on R, map R to inside of the disk, and then map the disk to E, with the same S in all three cases. (10) and see discussion in the final section. (An example of ha,1(ϕ) is shown in Fig. 4.7 out of 5 stars (34) Total Ratings 34, 92% agree - Would recommend. The boundary influence function I(z|ζ) is defined as shown. Temperature distribution along one adiabatic edge of the disk. Finally, the general case is demonstrated using Green's functions. 1) illustrates the nature of this complexity. An elementary property of conformal maps is that isothermal boundaries map to isothermal boundaries and adiabatic boundaries map to adiabatic boundaries. Redken Shape Factor 22 Maximum control matte cream-paste that feels like a paste but spreads like a cream for ultimate flexibility with a touchable feel. By constructing such a circle for a given object, the necessary condition at infinity may be estimated or calculated. None of these rotations affect S. In fact, these rotated cases are examples of a larger class of so-called Yin-Yang bodies described by Lienhard [13] for which S = 1. Parametric equations for the isotherms and adiabats as functions of, The temperature along both adiabatic edges varies linearly from 0 to 1, and is given by, The result of this mapping is shown for three values of. We may find the solution of the Dirichlet problem, Eqs. "Exterior Shape Factors From Interior Shape Factors." Shop Redken Shape Factor 22 Sculpting Cream Paste - compare prices, see product info & reviews, add to shopping list, or find in store. Provides serious sculpting with a flexible finish. Redken; Redken Shape Factor 22 Sculpting Cream Paste, 1.7 Ounce; Hover over main image to zoom. The solution interior (or exterior) to such a square is very difficult to calculate analytically; however, the conformal invariance of the shape factor dictates that S = 1 here as well. Maximum control matte cream paste that feels like a paste but spreads like a cream for ultimate flexibility with a touchable feel. Promocje Redken Shape Factor 22 bezkonkurencyjne ceny w internetowej perfumerii ELNINO PARFUM! Two reference cases of interest are the interior of a square or a rectangle, for which the conduction problem is trivially solved. [10]. **Includes: Move Ability 05, Mess Around 10, Shape Factor 22, Pillow Proof Blow Dry Express Primer and Two Day Extender, Outshine 01, Satinwear 02, Rewind 06, Duo Shield 07, Full Frame 07, Iron Shape 11, Quick Dry 18, Control Addict 28. The conformal invariance of electrical resistance is well known [9] and entirely analogous; but we have not seen the result in the heat transfer literature. A conformal map preserves angles—which is why such mappings are useful in cartography—but the linear scale varies with position under mapping. davines oi. The matlab code used to produce Fig. Redken Flex Shape Factor 22 50ml; Return to Previous Page. The Poisson kernel represents the temperature at (r, ϕ) produced by a boundary temperature distribution that is a delta function at (1, ϕ0); and Eq. 7(a), under differing rotations of the disk about the origin. This observation is unexpected because the heat transfer rates inside and outside need not be the same. Redken Shades EQ Color Gloss Hair Color for Unisex, 000 Crystal Clear, 33.79 Ounce Redken Intra Force System 2 Scalp Treatment 5.1 oz. REDKEN Concrete 22 Cement Paste 5oz. Manuscript received September 3, 2018; final manuscript received January 12, 2019; published online April 16, 2019. Consistent with the previous analysis, the shape factor for conduction on the exterior of the 90 deg disk is also S = 1. 6). AQUA / WATER / EAU, ISOPROPYL MYRISTATE, VA/CROTONATES/VINYL NEODECANOATE COPOLYMER, CERA MICROCRISTALLINA / MICROCRYSTALLINE WAX / CIRE MICROCRISTALLINE, SORBITOL, STEARYL ALCOHOL, ISOCETETH-20, CANDELILLA CERA / CANDELILLA WAX / CIRE DE CANDELILLA,PROPYLENE GLYCOL, STEARIC ACID, LAMIDE/ACRYLATES/BUTYLAMINOETHYL METHACRYLATE COPOLYMER, PALMITIC ACIDTRIETHANOLAMINE, OLETH-30, BIS-DIGLYCERYL POLYACYLADIPATE-2, BUTYLENE GLYCOL, ALCOHOL DENAT., PARFUM / FRAGRANCE, AMINOMETHYL PROPANOL, PHENOXYETHANOL, CERA ALBA /BEESWAX / CIRE DABEILLE, GLYCERYL STEARATE, CAPRYLYL GLYCOL, CARBOMER, MYRISTIC ACID, HEXYL CINNAMAL, BENZYL SALICYLATE, LIMONENE, LINALOOL, BENZYL ALCOHOL, BUTYLPHENYL METHYLPROPIONAL, CITRONELLOL, GERANIOL, COUMARIN, CITRAL, CI 19140 / YELLOW 5, BHT, CI 42090 / BLUE 1 (D185542/1). (47), we see again that Se = Si. Get it as soon as Tue, Oct 20. Isotherms are in color and adiabats are in gray, S = 1. olaplex 3. kérastase chronologiste. Figure 1 was generated using matlab's finite element method algorithms with 181,700 nodes to compute both harmonic conjugates, which were then interpolated to a 501 × 501 grid and overlaid.